Please help Solving linear and quadratic equations​

Answer:

None

Step-by-step explanation:

The answers are:

1. g(10) -31

2. x= -17/3

3. f(3)= 2

4.x= √30

5. h(-2)= 1

6. x= 0

7. h(a)= 1

In mathematics, a function is represented as a rule that produces a distinct result for each input x. In mathematics, a function is indicated by a mapping or transformation. Typically, these functions are identified by letters like f, g, and h. The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range. The set of values that could be a function's outputs is known as the co-domain.

Given:

f(x) = x² – 7

g(x) = -3x - 1

j(x)= 2x-9

h(x) = 1

1. g(10)= -3(10) -1 = -30 - 1= -31

2. g(x) = 16

-3x- 1= 16

-3x = 17

x= -17/3

3. f(3)= (3)² – 7 = 9- 7= 2

4. f(x)= 23

x² – 7=  23

x² = 30

x= √30

5. h(-2)= 1

6. x= 0

7. h(a)= 1

8. S(-1) = 3

The value of function s(a) at a=-1 is 3.

10. g(4) = -1

The value of function g(a) at a=4 is -1.

11. h(2) = 8

The value of function h(a) at a=2 is 8.

12. k(2) = 9​

The value of function k(a) at a= 2 is 9.

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Answer:

y = -3x + 3

[tex]y=\frac{1}{3}x-7[/tex]

Step-by-step explanation:

Slope of a line passing through two points ([tex]x_1, y_1[/tex]) and [tex](x_2, y_2)[/tex] is determined by the formula,

Slope = [tex]\frac{(y_2-y_1)}{(x_2-x_1)}[/tex]

If these points are (0, 3) and (3, -6),

Slope of the line passing through these lines = [tex]\frac{3+6}{0-3}[/tex] = (-3)

Equation of the line which passes through (0, 3) and slope = (-3),

y - y' = m(x - x')

y - 3 = (-3)(x- 0)

y - 3 = -3x

y = -3x + 3

Now slope of another line that passes through (3, -6) and (0, -7),

m' = [tex]\frac{(-6+7)}{(3-0)}[/tex]

m' = [tex]\frac{1}{3}[/tex]

Equation of the line that passes through (0, -7) and slope = [tex]\frac{1}{3}[/tex]

y - (-7) = [tex]\frac{1}{3}(x-0)[/tex]

y + 7 = [tex]\frac{1}{3}x[/tex]

y = [tex]\frac{1}{3}x-7[/tex]

Therefore, system of linear equations are,

y = -3x + 3

[tex]y=\frac{1}{3}x-7[/tex]

Answer:

f(x) = -3x + 4

Step-by-step explanation:

Step 1: Write it in slope-intercept form

9x + 3y = 12

3y = -9x + 12

y = -3x + 4

Step 2: Replace y with f(x)

f(x) = -3x + 4

In math, function f(x) is equal to the variable y.

=======================================================

Work Shown:

Substitute y = 1 into the first equation. Basically we replace every y with 1. From here we solve for x

3x+y = 7

3x+1 = 7

3x+1-1 = 7-1 .... subtracting 1 from both sides

3x = 6

3x/3 = 6/3 .... dividing both sides by 3

x = 2

We have x = 2 pair up with y = 1. The two equations intersect at (2,1)

As a check, plugging (x,y) = (2,1) into the first equation should lead to a true statement

3x+y = 7

3(2)+1 = 7

6+1 = 7

7 = 7 and it does lead to a true statement

The graph is shown below.

Answer:

15 is the answer to the question

Answer:

15, which for some reason does not seem to be an option.

Step-by-step explanation:

Product means to multiply to numbers, items etc.

5 times 3, as you should know, is 15.

Hope this helps.

Answer:

a = 30

b = 6/7

Step-by-step explanation:

The number of yeast cells after t hours is modeled by the following equation:

[tex]f(t) = a(1 + be^{-0.7t})[/tex]

In which a is the initial number of cells.

At time t = 0 the population is 30 cells

This means that [tex]a = 30[/tex]

So

[tex]f(t) = 30(1 + be^{-0.7t})[/tex]

And increasing at a rate of 18 cells/hour.

This means that f'(0) = 18.

We use this to find b.

[tex]f(t) = 30(1 + be^{-0.7t})[/tex]

So

[tex]f(t) = 30 + 30be^{-0.7t}[/tex]

Then, it's derivative is:

[tex]f'(t) = -30*0.7be^{-0.7t}[/tex]

We have that:

f'(0) = 18

So

[tex]f'(0) = -30*0.7be^{-0.7*0} = -21b[/tex]

Then

[tex]-21b = 18[/tex]

[tex]21b = -18[/tex]

[tex]b = -\frac{18}{21}[/tex]

[tex]b = \frac{6}{7}[/tex]

Answer:

0.0179 = 1.79% probability that the mean of this sample is less than 15.99 ounces of water.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

When the distribution is normal, we use the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this question, we have that:

[tex]\mu = 16.15, \sigma = 0.45, n = 35, s = \frac{0.45}{\sqrt{35}} = 0.0761[/tex]

What is the probability that the mean of this sample is less than 15.99 ounces of water?

This is the pvalue of Z when X = 15.99. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{15.99 - 16.15}{0.0761}[/tex]

[tex]Z = -2.1[/tex]

[tex]Z = -2.1[/tex] has a pvalue of 0.0179

0.0179 = 1.79% probability that the mean of this sample is less than 15.99 ounces of water.

Answer:

The probability that a group of 15 randomly selected skiers will overload the gondola = (3.177 × 10⁻⁵¹)

(almost zero probability showing how almost impossible it is to overload the gondola, therefore showing how very safe the gondola is)

Step-by-step explanation:

Complete Question

A ski gondola carries skiers to the top of the mountain. If the Total weight of an adult skier and the equipment is normally distributed with mean 200 lb and standard deviation 40 lb.

Consider the ski gondola from Question 3. Suppose engineers decide to reduce the risk of an overload by reducing the passenger capacity to a maximum of 15 skiers. Assuming the maximum load limit remains at 5,000 lb, what is the probability that a group of 15 randomly selected skiers will overload the gondola.

Solution

For 15 people to exceed 5000 lb, each person is expected to exceed (5000/15) per skier.

Each skier is expected to exceed 333.333 lb weight.

Probability of one skier exceeding this limit = P(x > 333.333)

This becomes a normal distribution problem with mean = 200 lb, standard deviation = 40 lb

We first standardize 333.333 lbs

The standardized score for any value is the value minus the mean then divided by the standard deviation.

z = (x - μ)/σ = (333.333 - 200)/40 = 3.33

To determine the required probability

P(x > 333.333) = P(z > 3.33)

We'll use data from the normal distribution table for these probabilities

P(x > 333.333) = P(z > 3.33) = 1 - P(z ≤ 3.33)

= 1 - 0.99957

= 0.00043

So, the probability that 15 people will now all be above this limit = (probability of one person exceeding the limit)¹⁵ = (0.00043)¹⁵

= (3.177 × 10⁻⁵¹)

(almost zero probability showing how almost impossible it is to overload the gondola, therefore showing how very safe the gondola is)

Hope this Helps!!!

26.

Step-by-step explanation:

To figure out the missing side of a right triangle, we will use the Pythagorean theorem. This is...

[tex]a^2+b^2=c^2[/tex]

With this Pythagorean theorem, a and b will always be the legs and the c will always be the hypotenuse, no matter what. Now knowing this, we can plug the legs into the equation.

[tex]10^2+24^2=c^2[/tex]

[tex]100+576=c^2[/tex]

Add the legs together.

[tex]676=c^2[/tex]

Now, since c is squared we will have to find the square root of 676.

[tex]\sqrt{676}[/tex]

= 26

Answer:

[tex]\frac{1}{12}[/tex]

Step-by-step explanation:

The number with the smallest denominator is the larger number and [tex]\frac{1}{12}[/tex] is the number with the smallest denominator out of [tex]\frac{1}{12} , \frac{1}{32} , \frac{1}{48} , \frac{1}{18}[/tex].

Answer:

1/12

Step-by-step explanation:

Start with a number, for example 100.

Now divide 100 by several numbers which are greater and greater:

100/1 = 100

100/2 = 50

100/4 = 25

100/10 = 10

100/100 = 1

As you divide the same number, 100, by a greater number, the result becomes smaller.

As we divide 100 by 1, then by 2, then by 4, etc., we are always dividing 100 by a greater and greater number. The result is smaller and smaller, 100, 50, 25, etc. If you always divide the same number by other numbers, the larger the number you divide by, the smaller the result.

Numbers in order from greatest to smallest:

1/12, 1/18, 1/32, 1/48

Answer: The greatest number is 1/12

Answer:

A linear equation is an equation with two variables whose graph is a line. The graph of the linear equation is a set of points in the coordinate plane that all are solutions to the equation. If all variables represent real numbers one can graph the equation by plotting enough points to recognize a pattern and then connect the points to include all points.If you want to graph a linear equation you have to have at least two points, but it's usually a good idea to use more than two points. When choosing your points try to include both positive and negative values as well as zero

Step-by-step explanation:

Answer:

The answer would be C because the y-intercept is when x is equal to 0

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The graph of the compound inequality can be seen at the end.

Here we have two inequalities that depend on p, these are:

4p + 1 > -15

6p + 3 < 45

First, we need to isolate p on both inequalities.

4p + 1 > -15

4p > -15 - 1

p > -16/4

p > - 4

6p + 3 < 45

6p < 45 - 3 = 42

p < 42/6 = 7

So we have the compound inequality:

p > -4

p < 7

or:

-4 < p < 7

Then this represents the set (-4, 7) where the values -4 and 7 are not included, so we should graph them with open circles.

The graph of the inequality is something like the one below.

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Answer:

The mode would not change

Step-by-step explanation:

Mode is the frequency of 1 number. In this case, the mode is 3. If we add 8, the frequency of 3 would not change; there would still be 4 3's, and 3 would still have the most of itself.

Answer:

The x intercepts are (7,0) and (-4,0)

Step-by-step explanation:

y = x^2 – 3x - 28

Set y=0

0 = x^2 – 3x - 28

Factor.  What 2 numbers multiply to -28 and add to -3

-7*4 = -28

-7+4 = -3

0 = (x-7)(x+4)

Using the zero product property

0 = (x-7)      0 = x+4

x=7              x = -4

The x intercepts are (7,0) and (-4,0)

Answer:

C. Yes, because A does not have a pivot position in every row.

Step-by-step explanation:

The pivot position in the matrix is determined by entries in non zero rows. The pivot position may be in the row or a column. By Invertible Matrix Theorem the equation Axequalsb has non trivial solution. A has fewer pivot positions therefore A is not invertible. Ax will map RSuperscript into real numbers for n times. A has pivot position if left parenthesis bold x right parenthesis.

Answer: H - 46

Step-by-step explanation:

Primeter = 2(l + w)

50 = 2{(3m+2) + (m-5)}

25 = 3m+2 +m -5

25 = 4m -3

m = 28/4 = 7

l = 3m+2 = 23 cm

w = m-5 = 2 cm

Area = l x b

= 23 x 2 = 46 sq. cm.

Answer:

the answer is 157

Step-by-step explanation:

7 +10= 17

17+20=37

37+40=77

77+80=157

157+160=317

At the beginning you add +10. Every sequence, you need to multiply that number x2. For example: 10 x 2=20...

Answer:

different slope same intercept

Step-by-step explanation:

g(x)= 3x+3

this means they both intercept the y axis at 3 but the incline of g is much greater then f since the slope is much larger.Hope this is what you were looking for

Answer: time = 20 seconds

Step-by-step explanation:

h(t) = -16t² + 316t + 80

The shape of this graph is an upside parabola ∩.  

It lands on the ground when height (h) = 0

Set the equation equal to zero, factor, and solve for t.

0 =  -16t² + 316t + 80

0 =  4t² - 79t - 20              divided both sides by -4

0 = (4t + 1)(t - 20)               factored the equation

t = -1/4      t = 20              Applied Zero Product Property and solved for t

Since we know time cannot be negative, disregard t = -1/4

The only valid solution is: t = 20

Answer:

csc 270° is the answer.

Answer:

Step-by-step explanation:

Let x be a random variable representing the number of U.S. adults who think that political correctness is a problem in America today. This is a binomial distribution since the outcomes are two ways. The probability of success, p = 78/100 = 0.78

The probability of failure, q would be 1 - p = 1 - 0.78 = 0.22

n = 6

a) Mean = np = 6 × 0.78 = 4.68

b) Variance = npq = 6 × 0.78 × 0.22 = 1.0

c) Standard deviation = √npq = √(6 × 0.78 × 0.22) = 1.0

d) The standard deviation is used to express the spread of the data from the mean. Therefore, most samples of 6 adults would differ from the mean by no more than 1.0

Answer:

D.

Step-by-step explanation:

Deus ex machina is the plot device of using something very improbable to resolve a situation.

Answer:

Step-by-step explanation: [tex]\frac{5}{3}[/tex]÷[tex]\frac{1}{3}[/tex] =

(Decimal: 0.555556)

Answer:

12.5% probability that when a couple has three​ children, there are exactly 0 girls.

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

Possible outcomes:

b for boy, g for girl

g - g - g

g - g - b

g - b - g

g - b - b

b - g - g

b - g - b

b - b - g

b - b - b

8 outcomes, one of which (b - b - b) with exactly 0 girls.

So

1/8 = 0.125

12.5% probability that when a couple has three​ children, there are exactly 0 girls.

The probability that when a couple has three​ children, there are exactly 0 girls is 12.5%

Here we assume b for boy, g for girl

Now the probability conditions are

g - g - g

g - g - b

g - b - g

g - b - b

b - g - g

b - g - b

b - b - g

b - b - b

There are 8 outcomes, one of which (b - b - b) with exactly 0 girls.

So

[tex]= 1\div 8[/tex]

= 0.125

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Answer:

[tex] P(X>1)= 1-P(X \leq 1)= 1- [P(X=0) +P(X=1)][/tex]

And if we use the probability mass function we got:

[tex]P(X=0)=(4C0)(0.6)^0 (1-0.6)^{4-0}=0.0256[/tex]  

[tex]P(X=1)=(4C1)(0.6)^1 (1-0.6)^{4-1}=0.1536[/tex]  

And replacing we got:

[tex] P(X>1) =1- [0.0256 +0.1536]= 0.8208[/tex]

Step-by-step explanation:

Let X the random variable of interest, on this case we now that:  

[tex]X \sim Binom(n=4, p=0.6)[/tex]  

The probability mass function for the Binomial distribution is given as:  

[tex]P(X)=(nCx)(p)^x (1-p)^{n-x}[/tex]  

Where (nCx) means combinatory and it's given by this formula:  

[tex]nCx=\frac{n!}{(n-x)! x!}[/tex]  

We want to find the following probability:

[tex] P(X >1)[/tex]

And for this case we can use the complement rule and we got:

[tex] P(X>1)= 1-P(X \leq 1)= 1- [P(X=0) +P(X=1)][/tex]

And if we use the probability mass function we got:

[tex]P(X=0)=(4C0)(0.6)^0 (1-0.6)^{4-0}=0.0256[/tex]  

[tex]P(X=1)=(4C1)(0.6)^1 (1-0.6)^{4-1}=0.1536[/tex]  

And replacing we got:

[tex] P(X>1) =1- [0.0256 +0.1536]= 0.8208[/tex]

Answer:

(a)650 ways

(b)650 ways

(c)676 ways

Step-by-step explanation:

There are 26 red and 26 black cards.

If a card is dealt to each of 2 players, we want to find out how many different ways this can be done.

(a)Both cards are red

If both cards are red:

The first red card can be dealt in 26 ways.

The second red card can be dealt in 25 ways.

Therefore: Both Red cards can be dealt in: 26 X 25 = 650 ways

(b)Both cards are black

If both cards are black:

The first black card can be dealt in 26 ways.

The second black card can be dealt in 25 ways.

Therefore: Both black cards can be dealt in: 26 X 25 = 650 ways

(c)One card is black and the other is red.

The red card can be dealt in 26 ways.

The black card can be dealt in 26 ways.

Therefore: Both cards can be dealt in: 26 X 26 = 676 ways

Answer: The mean difference is between 799586.3 and 803257.9.

Step-by-step explanation: To estimate the mean difference for confidence interval:

Find the statistic sample:

For the traffic count, mean = 1835.8 and s = 1382607.3

The confidence interval is 90%, so:

α = [tex]\frac{1-0.9}{2}[/tex]

α = 0.05

The degrees of dreedom are:

df = n - 1

df = 10 - 1

df = 9

Using a t-ditribution table, the t-score for α = 0.05 and df = 9 is: t = 1.833.

Error will be:

E = [tex]t.\frac{s}{\sqrt{n} }[/tex]

E = 1.833.([tex]\frac{1382607.3}{\sqrt{10} }[/tex])

E = 801422.1

The interval is: mean - E < μ < E + mean

1835.8 - 801422.1 < μ < 1835.8+801422.1

-799586.3 < μ < 803257.9

The estimate mean difference in trafic count between 6th and 13th using 90% level of confidence is between 799586.3 and 803257.9.

Answer:

908360.67 lb-ft

Step-by-step explanation:

height of tank= 6 ft

diameter of the tank = 4 ft

density of water p = 62.4 lbs/ft

A is the cross sectional area of the tank

A = [tex]\pi r^{2}[/tex]

where r = diameter/2 =  4/2 = 2 ft

A = 3.142 x [tex]2^{2}[/tex] = 12.568 ft^2

work done = force x distance through which force is moved

work = F x d

Force  due to the water = pgAh

where g = acceleration due to gravity = 32.174 ft/s^2

Force  = 62.4 x 32.174 x 12.568 x 6 =  151393.44 lb

work done = force x distance moved

work = 151393.44 x 6 = 908360.67 lb-ft

Answer:

A.   minus 10,

Step-by-step explanation:

The distance travelled must be positive.

Therefore minus 10 would not be a reasonable answer.

Answer:

The 1st graph

Step-by-step explanation:

The quickest and easiest way is to just graph y < x² + 4x + 5. When you do so you should be able to see your answer.