The population (in millions) of Calcedonia as a function of time t (years) is P(1) = 55 . 20^005t. Determine the number of years it takes the population to double. (Give an exact answer. Use symbolic notation and fractions where needed.) years: Let g(t) = a2^kt. Determine the expression for g(t + 1/ķ) (for any positive constants a and k). (Express numbers in exact form. Use symbolic notation and fractions where needed. Give the expression in terms of a, k, and t.
g(t+1/k)
Interpret the obtained results. - The population does not change significantly over time. - The population increases by 1/k after one year. - The population doubles after 1/k years - The population halves after 1/k years

Answers

Answer 1

Give the expression in terms of a, k, and t is g(t+1/k) = a2^(k(t+1/k)) = a2^kt * 2^(1/k)

The population doubles when P(t) = 2 * P(0), so we can set up the equation:

2 * 55 = 20^(5t)

Solving for t:

t = log(2)/(5 * log(20)) = log(2)/log(400)

The population doubles after approximately 0.173 years or 63.1 days.

g(t+1/k) = a2^(k(t+1/k)) = a2^kt * 2^(1/k)

Interpretation: g(t+1/k) is the population at time t+1/k, where a and k are positive constants. The population at t+1/k is equal to the population at time t multiplied by 2^(1/k). This means that if k is a large number, the population will change very little over time, if k is a small number, the population will change more quickly.

To learn more about equations visit: brainly.com/question/11897796

#SPJ4


Related Questions

Please help i need it quickly too please

Answers

The final answer would be x= 4 and y = 0.

3 c 9 8. following is a statement of a theorem about certain cubic equations. for this theorem, b represents a real number. theorem a. if f is a cubic function of the form f .x/ d x 3 x c b and b > 1, then the function f has exactly one x-intercept. following is another theorem about x-intercepts of functions: theorem b. if f and g are functions with g.x/ d k f .x/, where k is a nonzero real number, then f and g have exactly the same x-intercepts. using only these two theorems and some simple algebraic manipulations, what can be concluded about the functions given by the following

Answers

Both f(x) and g(x) have one x-intercept at x = -1/3.

Theorem A states that for a cubic function of the form f(x) = x^3 + x + b, with b > 1, the function f has exactly one x-intercept. Using Theorem B, we can conclude that for any nonzero real number k, the function g(x) = kf(x) = kx^3 + kx + bk also has exactly one x-intercept.

For example, if f(x) = x^3 + x + 5 and k = 2, then g(x) = 2x^3 + 2x + 10. Both f(x) and g(x) have exactly one x-intercept. This can be shown by solving the quadratic equation formed by setting f(x) = 0 or g(x) = 0. Doing this yields x = -1/3. Therefore, both f(x) and g(x) have one x-intercept at x = -1/3.4

Learn more about x-intercept here:

https://brainly.com/question/14180189

#SPJ4

need the answer please

Answers

Answer:

Step-by-step explanation:

Answer:

1.91 lb

Step-by-step explanation:

1 3/4 cups of pecans per pie = 1.75 cups.

For 5 pies, 5 × 1.75 cups = 8.75 cups are needed.

1 cup = 99 g

8.75 cup × (99 g) / (1 cup) = 866.25 g

Exact conversion: 453.59237 g = 1 lb

866.25 g × (1 lb)/(453.59237 g) = 1.91 lb

Answer: 1.91 lb

1. The normal temperature for the human body is 37 °C (degrees Celsius). A patient suffering from malaria has a temperature of 40,2 °C. How many °C must his temperature decrease to reach a normal temperature? ​

Answers

Answer:

3,2 °C

Step-by-step explanation:

40,2 °C - 37 °C = 3,2 °C

A local art group wishes to raise $8,000. Currently, they have raised $4,200. what percent has the art group raised

Answers

Answer:

raised 53%

Step-by-step explanation:

goal = $8,000

raised = $4,200

$4,200/$8,000 = 0.525 = about 53%

The quadratic functions f(x) and g(x) are described in the table.


x f(x) g(x)
−6 36 4
−5 25 1
−4 16 0
−3 9 1
−2 4 4
−1 1 9
0 0 16
1 1 25
2 4 36

In which direction and by how many units should f(x) be shifted to match g(x)?
Left by 4 units
Right by 4 units
Left by 8 units
Right by 8 units

Answers

In the horizontal direction and by 4 units to the left, f(x) should be shifted to match g(x).

The correct option is A.

What is transformation on the graphs?

The function provided by the basic function f(x) and the constant

g(x) = f(x - k),

may be drawn by horizontally moving the f(x) k unit coordinates.

The shift's direction depends on the value of k. Specifically,

The base graph moves k units to the right if k > 0, and

The base graph moves k units to the left if k < 0.

Given:

The quadratic functions f(x) and g(x) are described in the table.

From the table, the functions,

f(x) = x².

And g(x) = (x + 4)².

In the attached image,

the blue curve is the function of f(x).

And red line is the function of g(x).

From the graph,

Left by 4 units, f(x) should be shifted  to match g(x).

Therefore, left by 4 units, f(x) should be shifted to match g(x).

To learn more about the transformation on the graphs;

https://brainly.com/question/19040905

#SPJ1

Answer: A

Step-by-step explanation: took the test

Write an algebraic expression that Marshall can use to determine the total cost of buying a watermelon that weigh w pounds and some tomatoes that weigh t pounds. How much will it cost to buy a watermelon that weighs 18.5 pounds and 5 pounds of tomatoes? Tomatoes are $3.25 / lb and Watermelon is $0.68 / lb

Answers

The algebraic expression which represents the total cost of buying watermelons and tomatoes as described is; C = 0.68w + 3.25t.

The cost of buying a watermelon that weighs 18.5 pounds and 5 pounds of tomatoes is; $28.83.

What is the cost of buying watermelons and tomatoes?

It follows from the task content that the cost of buying Tomatoes are $3.25 / lb and Watermelon is $0.68 / lb.

Hence, the algebraic expression which represents the cost of buying a watermelon that weighs, w pounds and tomatoes that weigh t pounds is;

C = 0.68w + 3.25t.

Hence, if the watermelon bought weighs 18.5 pounds and tomatoes weigh 5 pounds,

C = 0.68 (18.5) + 3.25 (5)

C = 12.58 + 16.25

C = $28.83.

Read more on algebraic expressions;

https://brainly.com/question/17532559

#SPJ1

FILL IN THE BLANK When aligning tow shafts, the reason to rotate the coupling hubs before making each measurement is so each measurement is ____________

Answers

When we are aligning two shafts, the reason behind rotating the coupling hubs before taking each measurement is so that each of the measurements is taken from the same place on the hub every time.

Shafts are basically a component of circular cross section which rotates and transmits the power from a driving device like an engine or a motor through a particular machine. Coupling hubs are basically the attachment of the coupling to shaft in a device.

During the alignment of two shafts, the angular as well as parallel misalignment is thoroughly checked. The coupling hubs are rotated before taking each measurement is so that each of the measurements is taken from the same place on the hub every time.

To know more about shafts here

https://brainly.com/question/12976718

#SPJ4

exercise 1.2.3 the augmented matrix of a system of linear equations has been carried to the following by row operations. in each case solve the system.1 2 1 3 1 | 10 1 -1 0 1 | 1c = 0 0 0 1 -1 | 00 0 0 0 0 | 0

Answers

The presented system of linear equations has no solution.

The final form of the augmented matrix suggests that the system of linear equations has no solution, as the last row represents an equation with 0 = 0, which is always true but doesn't provide any information about the variables.

To see this more clearly, let's use the augmented matrix to write out the system of linear equations:

1x - 1y + 2z = 4

2y + 1z = -1

z = 1

The first two equations are consistent and have a unique solution, but the last equation is trivial and provides no information about x and y. In other words, infinitely many pairs of x and y satisfy the first two equations, but none satisfy the third equation. Therefore, the given system of linear equations has no solution.

To know more about augmented matrix, here

https://brainly.com/question/12994814

#SPJ4

You mix 1 half cup of salt with 3 cups of sugar. Which below is the ratio of salt to sugar.

Answers

In a case whereby you mix 1 half cup of salt with 3 cups of sugar the ratio of salt to sugar.

What is ratio?

The concept that will be used is ratio. An ordered pair of numbers a and b, represented as a / b, is a ratio if b is not equal to 0. A proportion is an equation that sets two ratios at the same value. For instance, you could express the ratio as follows: 1: 3 if there is 1 boy and 3 girls (for every one boy there are 3 girls)

we were told that there were 1 half cup of salt with 3 cups of sugar

Then the ratio can be written as

salt/sugar

= (1 1/2)/3

Since the amount of the salt is in mixed fraction, we can reduce to improper fraction for easy calculation.

=( 3/2)/ 3

= 3/6

=1/2

Hence, the ratio is 1:2

Learn more about  ratio at:

https://brainly.com/question/2328454

#SPJ1

missing options:

A. 2:3

B.1:2

C.2:1

D. 5:6

HELP PLEASE someone ?????

Answers

Question 4 would be c hope this helps

Freshman and sophomores were surveyed during lunch about their favorite professional football team.

A bar graph with the first bar labeled Jaguars, divided into freshmen from 0 to 40 percent and sophomores from 40 to 100 percent. The second bar is labeled Dolphins, with freshman from 0 to 45 percent and sophomores from 45 to 100 percent, and the third bar is labeled Buccaneers, with freshmen from 0 to 45 percent and sophomores from 45 to 100 percent.

If 140 students selected Jaguars, how many of those students are freshman?

56 students
63 students
77 students
84 students

Answers

There are 56 students as freshmen. The correct answer would be an option (A).

What is the percentage?

The percentage is defined as a ratio expressed as a fraction of 100.

A bar graph with the first bar labeled Jaguars, divided into freshmen from 0 to 40 percent and sophomores from 40 to 100 percent.

This can be determined by multiplying the percentage of freshmen who selected Jaguars (40%) by the total number of students surveyed (140).

⇒ 40% × 140 = 56

So there are 56 students as freshmen.

Hence, the correct answer would be option (A).

Learn more about the percentages here:

brainly.com/question/24159063

#SPJ1

Please help ASAP or a huge cockroach will crawl into in your ear

In this figure, GH=12, GP=16, and FP=2.

What is EF?

Enter your answer in the box.

EF

Answers

Answer:

This is nonsense, if GP = 16 and GH = 12 then HP = 4 (16 - 12 = 4). FP is looking basically the same size as HP, so FP = 4, not 2.

Step-by-step explanation:

These are all lies, your teacher is a liar and EF must be around 12 too.

Answer:

30

Step-by-step explanation:

in problems 21 through 30, first verify that the given vectors are solutions of the given system. then use the wronskian to show that they are linearly independent. finally, write the general solution of the system. 25

Answers

It is verified that the given vectors x₁ and x₂ are solutions of the given system. Using Wronskian it is shown that they are linearly independent. Then, [tex]W(t)=7e^{-3t}[/tex]. The general solution of the given system is written as [tex]x(t)=\left[\begin{array}{c}3c_1e^{2t}+c_2e^{-5t}\\2c_1e^{2t}+3c_2e^{-5t}\end{array}\right][/tex].

Wronskian analysis helps to determine whether a solution is linearly dependent or independent.

Given the system is [tex]x'=\left[\begin{array}{ccc}4&-3\\6&-7\end{array}\right]x[/tex].

Let's differentiate x₁ concerning t, and we get,

[tex]\begin{aligned}x_1'&=\left[\begin{array}{c}\frac{d}{dt}(3e^{2t})&\\\frac{d}{dt}(2e^{2t})&\end{array}\right] \\&=\left[\begin{array}{c}6e^{2t}&\\4e^{2t}&\end{array}\right] \end{aligned}[/tex]

Now,

[tex]\begin{aligned}\left[\begin{array}{ccc}4&-3\\6&-7\end{array}\right]x_1&=\left[\begin{array}{ccc}4&-3\\6&-7\end{array}\right]\left[\begin{array}{c}3e^{2t}\\2e^{2t}\end{array}\right]\\&=\left[\begin{array}{c}12e^{2t}-6e^{2t}\\18e^{2t}-14e^{2t}\end{array}\right]\\&=\left[\begin{array}{c}6e^{2t}\\4e^{2t}\end{array}\right]\\&=x_1'\end{aligned}[/tex]

From this, we can write,

[tex]x_1'=\left[\begin{array}{cc}4&-3\\6&-7\end{array}\right]x_1[/tex]

Therefore, we conclude that x₁ is a solution to the given system.

Let's differentiate x₂ concerning t, and we get,

[tex]\begin{aligned}x_2'&=\left[\begin{array}{c}\frac{d}{dt}(e^{-5t})&\\\frac{d}{dt}(3e^{-5t})&\end{array}\right] \\&=\left[\begin{array}{c}-5e^{-5t}&\\-15e^{-5t}&\end{array}\right] \end{aligned}[/tex]

Now,

[tex]\begin{aligned}\left[\begin{array}{ccc}4&-3\\6&-7\end{array}\right]x_2&=\left[\begin{array}{ccc}4&-3\\6&-7\end{array}\right]\left[\begin{array}{c}e^{-5t}\\3e^{-5t}\end{array}\right]\\&=\left[\begin{array}{c}4e^{-5t}-9e^{-5t}\\6e^{-5t}-21e^{-5t}\end{array}\right]\\&=\left[\begin{array}{c}-5e^{-5t}\\-15e^{-5t}\end{array}\right]\\&=x_2'\end{aligned}[/tex]

From this, we can write,

[tex]x_2'=\left[\begin{array}{cc}4&-3\\6&-7\end{array}\right]x_2[/tex]

Therefore, we conclude that x₂ is also a solution to the given system.

Now, find the Wronskian of x₁ and x₂, we get,

[tex]\begin{aligned}W(t)&=\text{det}[x_1\;x_2]\\&=\text{det}\left[\begin{array}{cc}3e^{2t}&e^{-5t}\\2e^{2t}&3e^{-5t}\end{array}\right] \\&=(3e^{2t}\times3e^{-5t})-(e^{-5t}\times2e^{2t})\\&=9e^{2t-5t}-2e^{2t-5t}\\&=9e^{-3t}-2e^{-3t}\\&=7e^{-3t}\\&\neq0\end{aligned}[/tex]

From this, we can conclude that x₁ and x₂ are independent.

Finally, we write the general solution of the system as follows,

[tex]\begin{aligned}x(t)&=c_1x_1+c_2x_2\\&=c_1 \left[\begin{array}{c}3e^{2t}\\2e^{2t}\end{array}\right] +c_2\left[\begin{array}{c}e^{-5t}\\3e^{-5t}\end{array}\right] \\&=\left[\begin{array}{c}3c_1e^{2t}\\2c_1e^{2t}\end{array}\right] +\left[\begin{array}{c}c_2e^{-5t}\\3c_2e^{-5t}\end{array}\right]\\&=\left[\begin{array}{c}3c_1e^{2t}+c_2e^{-5t}\\2c_1e^{2t}+3c_2e^{-5t}\end{array}\right] \end{aligned}[/tex]

The complete question is -

First, verify that the given vectors are solutions of the given system. Then use the Wronskian to show that they are linearly independent. Finally, write the general solution of the system.

[tex]x'=\left[\begin{array}{ccc}4&-3\\6&-7\end{array}\right]x;\; x_1=\left[\begin{array}{ccc}3e^{2t}\\2e^{2t}\end{array}\right], \;x_2=\left[\begin{array}{cc}e^{-5t}\\3e^{-5t}\end{array}\right][/tex]

To know more about Wronskian:

https://brainly.com/question/14309076

#SPJ4

Use the motion map to answer the question. A motion map. The position line is a long black arrow pointing right with x as the reference point at left. Above the line are 3 dots with short vector arrows moving toward x, then a dot, then 2 dots with longer vector arrows moving away from x. Describe the position and velocity of the object based on the motion map.

Answers

The direction and position of the fourth and fifth arrows indicate that the object then moves towards the origin, with a smaller velocity.

What are Motion maps?

Motion maps are used to illustrate the direction and position of an object. Using the motion map, the description of the object position and velocity is as follows:

The object starts its movement from the origin with a large velocity, before moving back to the origin with a smaller velocity. It stops for 1 second in the origin, then moves away with a larger velocity, Finally, it moves back towards the origin with a smaller velocity.

See attachment for the motion map, where the number on each arrow in the map, represents the position of the object.

Note that; the long arrow means large velocity while the short arrow means small velocity.

We analyze the direction and position using the arrows

The first arrow shows that the object starts from the origin with a large velocity.The direction and length of the second arrow show that, the object then returned to the origin with a smaller velocity.There is a dot in front of the second arrow. This dot indicates that the object stops for one second.The third arrow means that, the object moved from the origin with a larger velocityThe direction and position of the fourth and fifth arrows indicate that the object then moves towards the origin, with a smaller velocity.

Therefore, the direction and position of the fourth and fifth arrows indicate that the object then moves towards the origin, with a smaller velocity.

Learn more about motion map here:

brainly.com/question/13987788.

#SPJ1

Answer:

Based on the motion map, the object starts at the reference point "x" on the left side of the position line. The three dots with short vector arrows moving toward "x" indicate that the object is moving in the direction of the reference point and gaining speed. This suggests that the object is accelerating. Then, there is a single dot, which might indicate a momentary pause or a constant velocity. Afterward, the two dots with longer vector arrows moving away from "x" suggest that the object is decelerating or slowing down. In summary, the motion map shows an object that starts from rest, accelerates towards the reference point, maintains a constant velocity for a brief moment, and then decelerates away from the reference point.

Step-by-step explanation:

Use chat gpt to give you unique answer.

help asap! Giving brainliest
The table below shows the ratio of a bird's brain to body weight.


Brain (part) 0.6 B 1.8 E
Body (part) A 14.3 19.8 33
Total (whole) 7.2 C D 36


Which table shows the correct missing values?

Brain (part) 0.6 1.3 1.8 3
Body (part) 6.6 14.3 19.8 33
Total (whole) 12.6 27.3 37.8 36

Brain (part) 0.6 1.2 1.8 3
Body (part) 1.2 14.3 19.8 33
Total (whole) 7.2 15.6 21.6 36

Brain (part) 0.6 1.2 1.8 3
Body (part) 6.0 14.3 19.8 33
Total (whole) 6.6 15.5 37.8 36

Brain (part) 0.6 1.3 1.8 3
Body (part) 6.6 14.3 19.8 33
Total (whole) 7.2 15.6 21.6 36

Answers

The complete table is given as follows -

Brain (part)    0.6    1.3    1.8     3

Body (part)    6.6   14.3  19.8   33

Total (whole) 7.2   15.6  21.6   36

What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.

Given is that an interior designer recently spent £1359.55 buying 25 kettles and 20 toasters for a smaller group of new houses. For her current assignment she needs 80 kettles and 56 toasters.

The given table is -

Brain (part)   0.6   B   1.8      E

Body (part)   A    14.3   19.8  33

Total (whole) 7.2  C      D     36

We can write the expressions as -

0.6 + A = 7.2                                           .... Eq( 1 )

A = 6.6

1.8 + 19.8 = D                                            .... Eq( 2 )

21.6 = D

E + 33 = 36

E = 3                                                              .... Eq( 3 )

Therefore, the complete table is given as follows -

Brain (part)    0.6    1.3    1.8     3

Body (part)    6.6   14.3  19.8   33

Total (whole) 7.2   15.6  21.6   36

To solve more questions on algebraic expressions, visit the link below -

brainly.com/question/1041084

#SPJ1

event a occurs with probability 0.. teh conditional probability that event b occurs, given that a occurs is 0.5. the probability that both a and b occurs is

Answers

The probability of event a occurring is 0 and the conditional probability of event b occurring given that event a has occurred is 0.5.

The probability that both event A and event B occur is calculated using the formula P(A and B) = P(A) x P(B|A).

In this case, P(A) = 0 and P(B|A) = 0.5. When we plug these values into the equation, P(A and B) = 0 x 0.5 = 0. Therefore, the probability of both event A and event B occurring is 0. The probability that both events a and b occur is determined by multiplying the probability of event a occurring with the conditional probability of event b occurring given that event a has already occurred. This can be expressed mathematically as P(A∩B)=P(A)*P(B|A). In this case, the probability of both events a and b occurring is 0.5*0.5=0.25, since the probability of event a occurring is 0 and the conditional probability of event b occurring given that event a has occurred is 0.5.

This makes sense, since event A has a probability of 0 and cannot occur in the first place, so the probability of both events occurring together is 0.

Learn more about probability here:

https://brainly.com/question/30034780

#SPJ4

A town has a population of 1600 people at time t=0. In each of the following cases, write a formula for the population P, of the town as a function of year t.(a) The population increases by 70 people per year.(b) The population increases by 9 percent a year.

Answers

The population of the town at any given time t can be determined using the formulas provided. For example, if the town's population at time t=5 years is desired, the population can be calculated as follows:(a) P(5) = 1600 + 70(5) = 2100 people (b) P(5) = 1600(1.09)^5 = 2266.05 people

(a) P(t) = 1600 + 70t

(b) P(t) = 1600(1.09)^t

(a) In this case, the population increases by 70 people per year, so the formula for the population as a function of time is P(t) = 1600 + 70t. This means that the population is 1600 people at time t=0 and increases by 70 people for each additional year.

(b) In this case, the population increases by 9 percent each year, so the formula for the population as a function of time is P(t) = 1600(1.09)^t. This means that the population is 1600 people at time t=0 and increases by a factor of 1.09 (9 percent) for each additional year.

The population of the town at any given time t can be determined using the formulas provided. For example, if the town's population at time t=5 years is desired, the population can be calculated as follows:

(a) P(5) = 1600 + 70(5) = 2100 people

(b) P(5) = 1600(1.09)^5 = 2266.05 people

Learn more about population here

https://brainly.com/question/19538277

#SPJ4

Three friends each ordered a large cheese pizza. Shauntee ate $\frac{2}{3}$ of her pizza, Carlos ate $\frac{8}{9}$ of his pizza and Rocco ate $\frac{26}
{27}$ of his pizza. If the remaining portions from the three pizzas are put together, what fraction of a large pizza do they make? Express your answer as a common fraction.

Answers

The remaining portions from the three pizzas together make up 13/27 of a large pizza.

What is the fraction?

A fraction is defined as a numerical representation of a part of a whole that represents a rational number.

Shauntee ate 2/3 of her pizza, so she has 1/3 left.

Carlos ate 8/9 of his pizza, so he has 1/9 left.

Rocco ate 26/27 of his pizza, so he has 1/27 left.

To determine the combined fraction of the remaining portions of the three pizzas, we add the fractions that are left:

1/3 + 1/9 + 1/27 = (1/3) + (1/9) + (1/27)

Simplifying this fraction by finding the least common denominator, which is 27:

(1/3) + (1/9) + (1/27) = (9/27) + (3/27) + (1/27) = 13/27

So they together make up 13/27 of a large pizza.

Learn more about the fraction here:

brainly.com/question/10354322

#SPJ1

what is a system of linear equations whose solution is (6,19)

Answers

Answer:

A system of linear equations is a set of two or more equations containing two or more variables. The solution to a system of linear equations is the set of values for the variables that makes all the equations in the system true.

For example, a system of linear equations whose solution is (6,19) could be represented by the following equations:

x + 2y = 25

3x - 4y = 6

Solving this system would yield x = 6 and y = 19 as the solution.

The life span of fruit fly have a bell shaped distribution, with a mean of 32 days and a standard deviation of 5 days. What is the Z score of the fruit flys at 37 ,30 and 47 days

Answers

Answer:

The Z-score (also known as a standard score) represents the number of standard deviations a value is away from the mean of a distribution. The formula for the Z-score is:

Z = (X - μ) / σ

Where X is the value of interest, μ is the mean of the distribution, and σ is the standard deviation of the distribution.

Given the information in the problem, we know that the mean of the fruit fly's lifespan is 32 days and the standard deviation is 5 days.

To find the Z-score of a fruit fly whose lifespan is 37 days:

Z = (37 - 32) / 5 = 1

To find the Z-score of a fruit fly whose lifespan is 30 days:

Z = (30 - 32) / 5 = -0.4

To find the Z-score of a fruit fly whose lifespan is 47 days:

Z = (47 - 32) / 5 = 2.4

Therefore, a fruit fly whose lifespan is 37 days has a Z-score of 1, a fruit fly whose lifespan is 30 days has a Z-score of -0.4, and a fruit fly whose lifespan is 47 days has a Z-score of 2.4.

what are the factors and zeros of the function f(x)=x2-5x+6

Answers

The factors and zeros of the function f(x)=x2-5x+6 are x-3, x-2 and 3 and 2 respectively

How to determine the zeros of the function

Given the quadratic function as;

f(x) = x² - 5x + 6

Using the factorization method of solving quadratic function, we have to multiply the coefficient of x² by the constant of the function

Then find the pair factors of the function that sums up to -5

The pair factors area -2 and -3

Substitute the values, we get;

x²- 2x - 3x + 6

Pair the expression

(x² -2x) - (3x + 6)

Factorize the value

x(x -2) -3(x - 2)

The zeros are;

x-3 = 0

x = 3

Then,

x -2 = 0

x =2

Hence, the values are 2 and 3

Learn about quadratic equations here:

https://brainly.com/question/1214333

#SPJ1

42.735 rounded to the nearest ones places

Answers

Answer: 43 because 7 is greater than 5 so you round up. Have a nice day ;)

The correct answer is 43.  0.735 is greater than 0.5, so you round it up to 43

8.498 ? 8.478 use >,<,=

Answers

The inequality equation is 8.498 > 8.478

What is an Inequality Equation?

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.

Given data ,

Let the inequality equation be represented as A

Now , the value of A is

Let the first number be represented as = p

Let the second number be represented as = q

Now , the value of p = 8.498

The value of q = 8.478

And , the hundredths value in the number 8.498 is greater than the hundredths value in the number 8.478

So , the value of p is greater than q

Therefore , 8.498 > 8.478

Hence , the inequality is 8.498 > 8.478

To learn more about inequality equations click :

https://brainly.com/question/11897796

#SPJ1

Provide explanation for how to solve this problem.

Answers

The numeric value of the function is given as follows:

2x + h + 9.

How to find the numeric value of a function or of an expression?

To find the numeric value of a function or of an expression, we replace each instance of the variable in the function or in the expression by the value at which we want to find the numeric value.

The function in this problem is given as follows:

f(x) = x² + 9x.

At x = x + h, the function is defined as follows:

f(x + h) = (x + h)² + 9(x + h)

f(x + h) = x² + 2xh + h² + 9x + 9h

f(x + h) = x² + 2xh + h² + 9x + 9h.

Subtracting by f(x), we have that:

f(x + h) - f(x) = h² + 2xh + 9h.

f(x + h) - f(x) = h(h + 2x + 9).

Dividing by h, the numeric value is given as follows:

2x + h + 9.

Meaning that the first option is the correct option.

Learn more about the numeric values of a function at brainly.com/question/28367050

#SPJ1

Which graph represents the solution set of the compound inequality below?
x+3<= (4x-12) < 20
OH
4 5 6 7 8 9 10 11 12
4 5 6 7 8 9 10 11 12
6 7 8 9 10 11 12 13 14
6 7 8 9 10 11 12 13 14

Answers

A graph that represents the solution set of the compound inequality is: graph D.

What is an inequality?

In Mathematics, an inequality simply refers to a mathematical relation that is typically used for comparing two (2) or more numerical data and variables in an algebraic equation based on any of the following inequality symbols:

Less than (<).Greater than (>).Greater than or equal to (≥).Less than or equal to (≤).

Next, we would solve the given compound inequality by making x the subject of formula as follows;

x + 3 < 1/2(4x - 12) < 20

Multiplying all through by 2, we have the following:

2x + 6 < 4x - 12 < 40

Next, we would solve the compound inequality in parts:

2x + 6 < 4x - 12

4x - 2x < 12 + 6

2x < 18

x < 18/2

x < 9.

4x - 12 < 40

4x < 40 + 12

4x < 52

x < 52/4

x < 13.

In conclusion, the line on a number line (graph) should be open when the inequality symbol is greater than (>) or less than (<).

Read more on inequality here: brainly.com/question/27976143

#SPJ1

Which statements regarding Triangle E F G are true? Select three options. EF + FG > EG EG + FG > EF EG - FG < EF EF- FG > EG EG + EF < FG

Answers

we can conclude that option (A) , (B) and (C) are true.

We know that in a triangle,

• Sum of any to sides is greater than the third side.

• Difference between any two sides is smaller than the third side.

So, in ∆EFG, we have,

• EF + FG > EG

• FG + EG> EF

• EF + EG > FG

and,

• EF - FG <EG or FG - EF <EG

• FG - EG < EF or EG - FG < EF

• EF - EG <FG or EG - EF < FG

From options now we get,

A) EF + FG > EG is true

B)EG + FG > EF is true

C) EG - FG < EF is true

D) EF - FG > EG is false

E) EG + EF < FG is false

Therefore, we can conclude that option () , () and () are true.

To learn more about triangle:

https://brainly.com/question/41379168

#SPJ4

We can conclude that option (A) , (B) and (C) are true.

We know that in a triangle,

Sum of any to sides is greater than the third side.

Difference between any two sides is smaller than the third side.

So, in ∆EFG, we have,

• EF + FG > EG

• FG + EG> EF

• EF + EG > FG

and,

• EF - FG <EG or FG - EF <EG

• FG - EG < EF or EG - FG < EF

• EF - EG <FG or EG - EF < FG

From options now we get,

A) EF + FG > EG is true

B)EG + FG > EF is true

C) EG - FG < EF is true

D) EF - FG > EG is false

E) EG + EF < FG is false

Therefore, we can conclude option (A) , (B) and (C) are true.

To learn more about triangle:

brainly.com/question/2773823

#SPJ4

c x 3 c 9 7. followingis a statement of a theorem which can be proven using the quadratic formula. for this theorem, a, b, and c are real numbers. theorem if f is a quadratic function of the form f .x/ d ax2 c bx c c and ac < 0, then the function f has two x-intercepts. using only this theorem, what can be concluded about the functions given by the follo

Answers

The conclusion about given functions are given below.

Quadratic equations are the polynomial equations of degree 2 in one variable of type f(x) = ax2 + bx + c = 0 where a, b, c, ∈ R and a ≠ 0. It is the general form of a quadratic equation where 'a' is called the leading coefficient and 'c' is called the absolute term of f (x).

We have the following theorem:

If f is a quadratic function of the form f(x) = ax²+bx+c and ac < 0 , then the function f has two x-intercepts.

(a) g(x) = -8x²+5x-2

For this function a = -8 and c = -2, then -8 × -2 = 16 is greater than zero. Therefore, we cannot conclude anything.

(b) h(x) = [tex]-\frac{1}{3}x^{2} + 3x[/tex]

For this function a = -8 and we don't know the value of c. Therefore, we cannot conclude anything.

(c) k(x) = 8x²-5x-7

For this function a = 8 and c = -7, then 8 × -7 = -56 is less than zero. Therefore, we can conclude that the function k has two x-intercepts.

(d) j(x) = [tex]-\frac{71}{99}x^{2} + 210[/tex]

For this function a = [tex]-\frac{71}{99}[/tex] and c = 210, then [tex]-\frac{71}{99}[/tex] × 210 = [tex]-\frac{4970}{33}[/tex] is less than zero. Therefore, we can conclude that the function k has two x-intercepts.

(e) f(x) = 4x²-3x+7

For this function a = 4 and c = 7, then 4×7 = 28 is greater than zero. Therefore, we cannot conclude anything.

(f) F(x) = [tex]-x^{4} + x^{3} + 9[/tex]

We cannot conclude anything because this is not a quadratic function.

The conclusion about given functions are given above in explanation.

To learn more about quadratic equation visit : brainly.com/question/29011747

#SPJ4

complete question : Following is a statement of a theorem which can be proven using the quadratic formula. For this theorem, a, b, and c are real numbers. Theorem If f is a quadratic function of the form f .x/ D ax2 C bx Cc and ac < 0, then the function f has two x-intercepts. Using only this theorem, what can be concluded about the functions given by the following formulas(a) g (x) = -8x^2 + 5x - 2 (b) h (x) = -(1/3)x^2 + 3x (c) k (x) = 8x^2 - 5x - 7 (d) j (x) = -(71/99)x^2 + 210 (e) f (x) = 4x^2 - 3x + 7 (f) F (x) = -x^4 + x^3 + 9

B. In square EFGH, find the length of EG.

Answers

Answer:

  6√2

Step-by-step explanation:

You want one side of a square whose half-diagonal has length 6.

Right triangle

If X is the center point of the square where the diagonals cross at right angles, triangle EXG is an isosceles right triangle with leg length 6. The hypotenuse of an isosceles right triangle is √2 times the leg length, so ...

  EG = 6√2

__

Additional comment

If you like, you can use the Pythagorean theorem to prove that.

  EG² + EX² +GX² = 6² +6² = 72

  EG = √72 = √(36·2) = 6√2

A square is a rhombus, so the diagonals cross at right angles. A square is a rectangle, so the diagonals are the same length. A square is a parallelogram, so the diagonals bisect each other.

suppose phone calls arrive at an office according a poisson process at a mean rate of 5 calls per hour. the expected waiting time in hours until the first call arrived is

Answers

The expected waiting time in hours until the first call arrived is 0.00045.

The formula for poisson distribution is expressed as

P(x = r) = (e^- µ × µ^r)/r!

Where ,

µ=  represents the mean of the theoretical distribution.

r = represents the number of successes of the event.

According to the question,

µ = 5            

For the probability that there are one in one hour, it is expressed as

P(x = 1) ,

Therefore,

P(x = 1)

= (e^- 10 × 10^1)/1! = 0.00045

Therefore,

P(x = 1)

= 0.00045

Poisson distribution

A Poisson distribution is a discrete probability distribution. It gives the probability of an event happening a certain number of times (k) within a given interval of time or space.

Learn more about probability here :-

https://brainly.com/question/30034780

#SPJ4

Other Questions
a 22-year-old woman pregnant with a single fetus has a preconception body mass index (bmi) of 24. when she was seen in the clinic at 14 weeks of gestation, she had gained 1.8 kg (4 lb) since conception. how would the nurse interpret this? What is the purpose of this section of the US Constitution?to limit the powers of the representativesto establish rules for electing representatives to Congressto explain how the representatives of government will make lawsto show how the three branches of representatives will work togetherAnswer=B A mountain has a snow line at an elevation of 9000 feet which runs parallel to its base. The mountain is a triangle, the length of the snow line is 2. 4 times the height of the snow covered part of the mountain. If the snow covers 1,200,000 square feet of part of the mountain, how high is the mountain? This image is by Milton Glaser, and was a poster for tenth anniversary of holocaust museum. It was created using a stone press on which areas are made receptive to ink. This form of printing is known as at westville high school there are 315 seniors and 389 juniors. 65% of the seniors have parkign passes and 42% of teh juior have parking passes. the statistics teacher selects a srs of 30 seniors and a seperate srs of 30 juniors. imagine that a recent study found that people who eat large amounts of bananas get bitten by mosquitoes on average more often than people who eat smaller amounts of bananas. what causal relationship can we conclude from this study alone? is the lower legislative house in the united states congress. A 3.0-cm object is placed 8.0 cm in front of a mirror. The virtual image is 4.0 cm further from the mirror when the mirror is concave than when it is planar. . Determine the focal length of the concave mirror. (a) 6.0 cm (c) 24 cm (e) 96 cm (b) 12 cm (d) 48 cm . Determine the image height in the concave mirror. (a) 0.5 (c) 2.0 (e) 4.5 (b) 1.5 (d) 3.0 whats the mean median mode and range of 75 55 68 44 82 28 19 31 75 36 59 93 48 I need the answer as soon as possible!3x + 4y^2 ; x = -3 and y = 5Thank You! Please help. No rush and thank you for who helps. 40 points rewarded. The definition of software engineering that points to a multiperson construction of multiversion software is from:a. Ian Sommerville.b. the U.S. Department of Defense.c. Shari Pfleeger.d. the NATO conference.e. David Parnas. What is a nosocomial infection?A)a negative response to medical treatmentB)a condition with symptoms not attributable to any diseaseC)a disease acquired in a clinical settingD) a disease without a known cause in the healthy relationship lecture, the constructs of communication, consent, and boundaries were discussed as being critical in both sexual or romantic relationships and in non-sexual or non-romantic relationships.T/F one of the ways an author develops a character is by describing how the character interacts with the setting. the narrator provides many details about the setting in the early part of the story. how does lizabeth feel about her town? use textual evidence to explain the effect the setting has on lizabeth, and how she interacts with the setting. 13y+7-11-4y as a sum camila writes down five positive integers. the unique mode of these integers is 2 greater than their median, and the median is 2 greater than their arithmetic mean. what is the least possible value for the mode? Complete the table to combine like terms when adding Expression One and Expression Two. Expression One Expression Two 143a 7a9 Read the sentence from the mother's dialogue in Paragraph 19.So you must hold your tongue, you naughty girl; for, though you are so ready to leaveus, you know very well we cannot part with you.Which statement most accurately describes the sentiments and tone of thissentence?A. A harsh rebuke to prevent Agnes from exerting her independence.B. A stern reprimand to scold Agnes from speaking and behavinginappropriately.C. A gentle reminder to make sure Agnes understands she has aresponsibility to her family.D. A playful expression to tell Agnes that the family loves her andwants her to stay at home. in brazil, supporters of the former president ________.