The average rate of change of the function on the interval from x = 3 to x = 5 is 40.
What is meant by average rate of change?In mathematics, the average rate of change is a measure of how much a dependent variable (such as y) changes in proportion to a change in the independent variable (such as x). It is calculated by dividing the change in the dependent variable by the change in the independent variable during a certain time period. If the value of y rises by 5 units when the value of x rises by 2 units, the average rate of change is 5/2 Equals 2.5 per unit change in x. Calculus students frequently use this idea to compute the slope of a line on a graph or to calculate the rate at which a function changes. It is a crucial idea in several domains.
How to solve?
f(x) = 10(2)x,the interval is from x = 3 to x = 5
At x = 3, 10(2)3 = 80
at x = 5, 10(2)5 = 160
total change over the interval from x = 3 to x = 5 is 160 - 80 = 80.
the length of the interval is 5 - 3 = 2,
average rate of change is 80 / 2 = 40.
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what is the answer for
y=x−4y=−x+6
Answer: Your answers are Y = 1 and X = 5
Step-by-step explanation:
y=x-4 y=-x+6 Substitute x - 4 for y in y=-x+6 x-4=-x+6Add X on each side x-4+x =-x+6+x 2x - 4 = 6Add 4 on each side 2x-4+4 = 6+4 2x = 10Divide by 2 on each side 2x ÷ 2 = 10 ÷ 2 x = 5 Now we have X To find Y we substitute 5 for x in y= x-4 y = 5 - 4 y = 1 so you answers would be Y= 1 and x = 5 i hoped this helped:)
Kyle ran the width of a field, a distance of 35 meters. Then he ran the length of the field, a distance of 84 meters. Finally, he ran diagonally across it to get back to his starting point. How far did Kyle run?
The total distance travelled by Kyle is 210 m.
What is Pythagoras theorem?Pythagoras theorem states that in a right angled triangle, the sum of the squares of the perpendicular and base is equal to the square of the hypotenuse. It can be written as h² = p² + b².
The given length of the field is 84 m.
And, the width is 35 m.
Now, the diagonal of the field can be calculated using Pythagoras theorem as below,
Diagonal = √((84)² +(35)²)
= 91
Then, the total length is found by summing the length, width and the diagonal as below,
= 84 + 35 + 91
= 210
Hence, Kyle run for the distance of 210 m.
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What is the measure of angle b?
A. 36 degrees
B. 63 degrees
C. 144 degrees
D. 180 degrees
Answer:
A - 36 degrees
Step-by-step explanation:
117 - 81, to find another angle when given the outside of the triangle and another part of the triangle, all you have to do is subtract
Ezra works two summer jobs to save for a laptop that costs at least $1100. He charges $15/hr to mow lawns and $10/hr to walk dogs. This situation is modeled by: 15x + 10y ≥ 1100.
Suppose Ezra decides to also spend more than $80 on a printer. The inequality becomes
15x + 10y
.
The new inequality which represent Ezra's situation is 15x + 10y > 1180
How to write inequality?Cost of the laptop = at least $1100Amount Ezra charge to mow lawns per hour = $15Amount Ezra charge to walk dogs per hour = $10If
Hours spent to mow lawns = xHours spent to walk dogs = yThe inequality:
15x + 10y ≥ 1100
If Ezra decides to also spend more than $80 on a printer, that is, the amount spent on a printer is greater than $80
Adding an amount greater than $80 to the inequality,
It becomes 15x + 10y > 1180
Note the change in sign from greater than or equal to (≥) to greater than (>)
Therefore, the new inequality is given by 15x + 10y > 1180
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please help me with this
For the given quadratic equation we have:
a) F(-2) = 5
b) F(3) = 40
c) the solutions are:
t = -1
t = -1/3
How to evaluate the quadratic function?Here we have the following quadratic function:
F(t) = 3t^2 + 4t + 1
a) First, we want to determine the value of F(-2), to do so, we just need to replace the values of the variable, t, by the number -2, we will get:
F(-2) =3*(-2)^2 + 4*(-2) + 1
F(-2) = 3*4 - 8 + 1 = 5
F(-2) = 5
b) Now we want to find the value of the F(3), so this time we evaluate in x = 3.
F(3) =3*3^2 + 4*3 + 1
F(3) = 27 + 12 + 1 = 40
F(3) = 40
c) Last, we want to solve:
F(t) = 0
So we need to solve the quadratic equation:
3t^2 + 4t + 1 = 0
Using the quadratic formula we will get the two solutions:
[tex]t = \frac{-4 \pm \sqrt{4^2 - 4*3*1} }{2*3} \\\\t = \frac{-4 \pm 2}{6}[/tex]
Then the two solutions are:
t = (-4 + 2)/6 = -2/6 = -1/3
t = (-4 - 2)/6 = -1
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OB. 7,418÷33=R
What is the answer
Solve the equation (1+3)³-(2)2 + 4 =
Answer:
64
Step-by-step explanation:
We can solve this using PEMDAS (Parentheses, Exponents, Multiplication, Division, Addition, Subtraction). We do parentheses first, then exponents, all the way down to subtraction:
1. Parentheses
(1 + 3)³ -(2)2 + 4
4³ - (2)2 + 4
(By the way, (2)2 is considered multiplication not parentheses).
2. Exponents
4³ - (2)2 + 4
64 - (2)2 + 4
3. Multiplication
64 - (2)2 + 4
64 - 4 + 4
4. Division
None.
5. Subtraction
(Even though PEMDAS is labeled as addition before subtraction, in the MD | AS part, whichever one comes first in either section of the equation goes first):
64 - 4 + 4
60 + 4
6. Addition
60 + 4
64
Solution:
64
I hope my answer helped you! If you need more information or help, comment down below and I will be sure to respond if I am online. Have a wonderful rest of your day!
-7+4/(-2)
follow the order of operations to simplify the following expression
Answer: The answer is -9
Order of operations/PEMDAS:
Parenthesis, Exponents, Multiplication,
Division, Addition, Subtraction
Here is why:
using the order of operations,
do 4/-2 First
4/-2 = -2
Then do -7 + (-2)
-7 + (-2) = -2
When adding a negative plus a negative, it stays negative,
so the expression -7 +(-2) is like 7+2, it will equal 9, but because it is a negative plus a negative, the answer is negative.
On the coordinate plane, point F is located at (x, 8) and point G is located at (1, 4). The
distance between points F and G is √ √52 units.
What are the two possible locations of point F?
Answer:
Step-by-step explanation:
[tex]a^{2} + b^{2} = c^{2} \\4^{2} +b^{2} = (\sqrt{52} )^{2} \\16 + b^{2} = 52\\b^{2} =36\\\sqrt{b^2} =\sqrt{36} \\b=6\\[/tex]
One of the possible x-values of point F will be 6 units to the right of point G. So, the x-value of point F could be 7, since 1+6=7. That means one possible location of point F is (7,8).
The other possible x-value of point F will be 6 units to the left of point G. So, the x-value of point F could be -5, since 1–6=–5. That means the other possible location of point F is (–5,8).
So the answer is:
(7,8) and (-5,8)
find the exact value of n in 9⅓ ×27^n = 27⅘ and express it in fraction . Its urgent
Answer:
n = 26/45
Step-by-step explanation:
If the 9⅓ and 27⅘ are supposed to be [tex]9^{1/3}[/tex] and [tex]27^{4/5}[/tex], then
[tex]9^{1/3}[/tex] × [tex]27^{n}[/tex] = [tex]27^{4/5}[/tex]
=> [tex](3^{2})^{1/3}[/tex] × [tex](3^3)^{n}[/tex] = [tex](3^3)^{4/5}[/tex]
=> [tex]3^{2/3}[/tex] × [tex]3^{3n}[/tex] = [tex]3^{12/5}[/tex]
=> [tex]3^{3n+\frac{2}{3}}[/tex] = [tex]3^{12/5}[/tex]
=> 3n+2/3 = 12/5
=> 45n + 10 = 36
=> 45n = 26
=> n = 26/45
If using the method of completing the square to solve the quadratic equation x 2 + 14 x − 1 = 0 which number would have to be added to "complete the square"?
The values of x after solving the quadratic equation x²+14x-1 , using completing the square method is -√50-7 or +√50-7.
What is a quadratic equation?
A Quadratic equations is second-degree algebraic expressions and is of the form ax² + bx + c = 0.
Uisng the method of completing the square to solve the equation below, we following the steps.
Equation ⇒ x²+14x-1 = 0
Step 1:
Take the constant to the other side of the equation
x²+14x = 1Step 2:
Find half the coefficient of x, square, and add it to both side of the equation.
Coefficient of x = 14Half coefficient of x = 14/2 = 7square of half the coefficient of x = 7²There,
x²+14x+7² = 1+7²x²+14x+7² = 50Step 3:
Express the trinomial on the left side as a square of binomial
(x+7)² = 50Step 4:
Take the square root of both side.
√(x+7)² = √50x+7 = ±√50Step 5:
Make x the subject of the equation by moving 7 to the other side of the equation
x = ±√50-7Step 6:
Seperate the expression for each value of x
Either x = -√50-7or x = +√50-7Hence, the value of x is -√50-7 or +√50-7.
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please help it’s due tomorrow
[x + y = -4
[x - y = 2
Answer:
which one substitution or elimination
Step-by-step explanation:
Substitution: (-1,-3 )
Elimination: (-1,-3)
i hope this helps you :)
Please mark me brainlest
h(x)=x^2-1 what is the average rate of change of h over the interval -3 x -1
For the given function, h(x) = x² - 1, over the interval -3 ≤ x ≤ -1, the average rate of change is 4.
What is function?A function is a combination of different types of variable and constants in which for the different values of x the value of function y is unique.
The given function is,
h(x) = x² - 1, and the interval is -3 ≤ x ≤ -1.
To find average rate of change for the function,
Use formula,
Average rate of change = [tex]\frac{h(b)- h(a)}{b-a}[/tex]
h(b) = h(-1) = (-1)² - 1 = 0
h(a) = h(-3) = (-3)² - 1 = 8
Rate of change = [tex]\frac{8 - 0 }{-1 - (-3)}[/tex]
= 8 / 2
= 4
The average rate of change is 4.
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Please help, quick!!
Answer:
Step-by-step explanation:
First one is C
Second is B
third i cant see all of the answers
HELP ASAP PLSS!!
I think it’s b I’m not so sure
Answer:
Step-by-step explanation: I think it is 'b' too (sorry if wrong)
"A toy rocket is shot vertically into the air from a launching pad 7 feet above the ground with an initial velocity of 72 feet per second. The height in feet, of the rocket above the ground at t seconds after launch is given by the function h(t)=-16 t²+72 t+7. How long will it take the rocket to reach its maximum height? What is the maximum height?
The rocket reaches its maximum height at second(s) after launch.
(Simplify your answer.)
The maximum height reached by the object is feet.
(Simplify your answer.)"
Answer:
2.25 seconds ; 88 feet
Step-by-step explanation:
the maximum height of the rocket is the vertex of the parabola
x coordinate = -72/2(-16)
-72/-32 = 2.25 seconds
y coordinate = -16(2.25)^2 + 72(2.25) + 7
-81 + 162 + 7
-81 + 169
88 feet
A movie theater sells popcorn in a reusable bucket for $3.50. They offer refills for $2.50 each.
Write an equation in slope-intercept form to model the cost in dollars, y, for x refills.
The equation in slope-intercept form to model the cost in dollars, y, for x refills is 3.50 = 2.50x + b.
What is an equation?
An equation is an expression that shows the relationship between two or more numbers and variables.
We have been given that movie theater sells popcorn in a reusable bucket for $3.50. They offer refills for $2.50 each.
The value of y is popcorn cost = $3.50
The slope will be $2.50
Therefore, the equation is y = mx + b
Plug the values; y = 3.50 and m = 2.50
3.50= 2.50x + b
Hence, the equation in slope-intercept form to model the cost in dollars, y, for x refills is 3.50= 2.50x + b.
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SOLVE FOR T
t+3/2 = -2
T =
Answer:[tex]t= -\frac{7}{2}[/tex]
Step-by-step explanation:
[tex]=t+\frac{3}{2}=-2\\=t=-2-\frac{3}{2} \\=t=-\frac{7}{2}[/tex]
in a rectangle, if an area
[tex]\textit{area of a rectangle}\\\\ A=Lw ~~ \begin{cases} L=length\\ w=width\\[-0.5em] \hrulefill\\ A=12\sqrt{30}\\ w=3\sqrt{5} \end{cases}\implies 12\sqrt{30}=L3\sqrt{5}\implies \cfrac{12\sqrt{30}}{3\sqrt{5}}=L \\\\\\ 4\cdot \cfrac{\sqrt{30}}{\sqrt{5}}=L\implies 4\cdot \sqrt{\cfrac{30}{5}}=L\implies 4\sqrt{6}=L[/tex]
am i shadowbanned why aren't people answering my questions
Answer:
no
Step-by-step explanation:
your questions are so tricky to pass
A 0.8-liter bottle of Mexican wine costs 99 pesos. At thatprice, how much would a half-gallon jug of the same wine cost indollars?
A gallon of Mexican wine have a price of 433.13 Mexican pesos.
How much does a half-gallon jug of Mexican wine cost?
Herein we know that 0.8 liters of Mexican wine have a cost of 99 pesos and we need to determine the price for a gallon of the same beverage, that is, 3.5 liters. The price for a gallon can be determined by cross multiplication:
x = 99 MXN × (3.5 L / 0.8 L)
x = 433.13 MXN
A price of 433.13 Mexican pesos must be paid for a gallon of Mexican wine.
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If I work from 4:30pm to 9:00pm how many hours did I work?
Answer:
4 hours and 30 minutes.
Step-by-step explanation:
You count, 4, 5, 6, 7, 8, then you take the 30 from 4:30 and add another 30 to it to make it five. 5+4=9 or 4.5 + 4.5=9. (In this case, 30 is half of an hour, hence the 4.5 instead of 4.3).
Answer:
5 hours and 10 minutes.
Step-by-step explanation:
9:00 minus 4:30 = 4:70.
4:70 = 5 hours and 10 minutes.
Coach Rogers listed the number of the different types of balls in the storage room. What is the ratio of baseballs to all of the balls?
Group of answer choices
1 : 5
1 : 4
1 : 10
1 : 50
Answer:
1:4
Step-by-step explanation:
Ratio of 40 to 10 = 40:10 = 4:1 (after reducing 40:10 to lowest form). Hence, ratio of 40 to 10 is 4:1.
One year, the population of a city was 209,000. Several years later it was 217,360. Find the percent increase.
The percentage of the increase in population is 4%
How to determine the percentage of the increase?From the question, we have the following parameters that can be used in our computation:
Initial population = 209000
New population = 2017360
The percentage of the increase is then calculated using the following percentage equation
Percentage increase = (New population - Initial population )/Initial population * 100%
Substitute the known values in the above equation, so, we have the following representation
Percentage increase = (217360 - 209000)/209000 * 100%
Evaluate
Percentage increase = 4%
Hence, the increase percentage is 4%
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I have four number cards. The median is 8.
If the range is 10, what are the missing numbers?
Answer:
Below
Step-by-step explanation:
I think you will need to be more specific, but it could be
3 8 8 12 or something like 2 8 8 11 or 1 8 8 10 etc
PYTHAGORAS THEOREM
How do i find the n
Answer:
and data pro is the best solution assumption that you are a very important thing to me and I am not sure what to do with my
Answer:
this is the answer
Step-by-step explanation:
c² = a² + b²
c = √a²+b²
Katherine is younger than Alexandra. Their ages are consecutive integers.
square of Katherine's age and 5 times
Find Katherine's age if the sum of the
if the sum of the
Alexandra's age is 109.
Using equations to solve the word problem, Katherine's age is 8 years
Word ProblemWord problem are often mathematical problem that are represented in words and sometimes can be solved using an equation.
To solve this problem, we have to represent the problem using mathematical equations;
Let;
Katherine's age = x²
Alexandra = 5(x + 1)
Sum of their age = 109
5(x + 1) + x² = 109
5x + 5 + x² = 109
x² + 5x - 104 = 0
Solving for the equation; x = 8
Katherine's age is 8
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Your parents debt ratio increased, causing their credit score to drop from excellent rate of 5.75% to good rating of 6.20%. How much interest are they being charged during the first month on their mobile home loan of $74,860.00 Group of answer choices $358.70 $346.77 $374.30 $386.78
$336.87 is the interest they being charged during the first month on their mobile home loan of $74,860.00
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
Given,
Debt ratio increased, causing their credit score to drop from excellent rate of 5.75% to good rating of 6.20%.
We need to find interest they being charged during the first month on their mobile home loan of $74,860.00.
The difference is percentage is 6.0-5.75
0.45%
0.45% of $74,860.00
0.45/100×74,860.00
336.87
Hence, $336.87 is the interest they being charged during the first month on their mobile home loan of $74,860.00
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Write a linear function f with f(-3)=1 and f(13)=5.
Answer:
0.25x+1.75
Step-by-step explanation:
A linear equation is of the form ax+b. Set a up a system of equation with -3 and 13 substituted in to ax+b. We get -3a+b=1 and 13a+b=5. Solving tis gives us a,b=(0.25,1.75)
Answer:
f(x) = [tex]\frac{1}{4}[/tex] x + [tex]\frac{7}{4}[/tex]
Step-by-step explanation:
a linear function has the form
f(x) = ax + b ( a and b have to be found )
given f(- 3) = 1 and f(13) = 5 , then by substitution
- 3a + b = 1 → (1)
13a + b = 5 → (2)
subtract (2) from (1) term by term to eliminate b
- 3a - 13a = 1 - 5
- 16a = - 4 ( divide both sides by - 16 )
a = [tex]\frac{-4}{-16}[/tex] = [tex]\frac{1}{4}[/tex]
substitute a = [tex]\frac{1}{4}[/tex] into (1) and solve for b
- 3( [tex]\frac{1}{4}[/tex] ) + b = 1
- [tex]\frac{3}{4}[/tex] + b = 1 ( add [tex]\frac{3}{4}[/tex] to both sides )
b = 1 [tex]\frac{3}{4}[/tex] = [tex]\frac{7}{4}[/tex]
f(x) = [tex]\frac{1}{4}[/tex] x + [tex]\frac{7}{4}[/tex] ← is the linear function
or
f(x) = 0.25x + 1.75
explain what an exponential function is. please do not palgraize
As below it is described what is exponential function with some examples.
What is Function ?A function is simply a “mapping” between 2 sets of objects (usually numbers but they could really be anything) such that, every object in the first set (the domain) is mapped to a single object in the second set. What you usually see as examples of functions (e.g. f(x)=x²) actually define the relationship between the sets. This is what I mean by “mapping”. Often, we don’t explicitly state what the sets are, because it’s understood from the context, but technically, it’s not a function unless we state the sets. E.g., instead of saying f(x)=x², we should say f:x↦x²|x∈ℂ (pronounced “f maps x to x² such that x is a complex number”), meaning that we map the complex numbers to themselves using the rule that we square each input. You can define it differently, so that, for example, we map complex to reals. However, and this is important, that would be a different function, even though the “rule” for turning inputs into outputs is the same.
Exponential Function:
Exponential functions are functions of the form f(x) = b^x where b is a constant.
The real mathematical importance of exponential functions is in their being proportional to their derivatives meaning the bigger x is, the steeper the slope of the function. This means they grow extremely fast: exponentially fast.
A common example of exponential growth is a bacterial population. Since bacteria reproduce rapidly by mitosis, for every bacterium in a culture, there will, before long be two bacteria. Thus, if I have 10 bacteria to start, one minute later I will have 20, and in another minute, each of those twenty will have reproduced and I will have 40; one minute later the same will have happened again and before long, the culture will be overrun with bacteria. The more bacteria there are, the more bacteria there are to make even more bacteria the next minute.
All exponential functions are proportional to their derivatives, but the function f(x) = e^x (where e = 2.718281828459…) is actually equal to its derivative meaning the y value of the function at a particular x value is equal to the slope of the curve at that same x value. Thus when dealing with exponential functions in calculus, e becomes a very natural number to use as a base. This is why e is such a big deal and why teachers try to introduce the number early on in Algebra 2, even though it doesn’t have much use at that point in one’s mathematical education.
When plotting an exponential curve by hand, one ought to simply pick whole number x values and multiply the base by itself an x number of times to calculate the corresponding y value. This will give a rough plot of the graph of the curve, although a calculator is requires to plot the points not on whole number x values. The curve of simple exponential functions is always increasing and concave up, or vice versa for b^-x. For a positive exponential function like f(x) = e^x, as x approaches ∞, f(x) approaches ∞, and as x approaches -∞, f(x) approaches 0. The curve has no absolute maximum or minimum value and has a horizontal asymptote at y = 0.
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