Let f(x)=−1/2(x+2)^2+5 . What is the average rate of change for the quadratic function from x = −3 to x = 1? Enter your answer in the box.

Answers

Answer 1

Final answer:

The average rate of change of the function f(x) from x = -3 to x = 1 is -0.625, calculated using the values of f(-3) and f(1) in the average rate of change formula.

Explanation:

The average rate of change of a function f(x) from x = a to x = b is computed by finding the difference in function values at these points and dividing by the difference in x values, following the formula (f(b) - f(a)) / (b - a). To apply this to the quadratic function [tex]f(x) = -1/2(x + 2)^2 + 5[/tex] from x = -3 to x = 1, we evaluate f at both -3 and 1 and use these results in our formula.

First, find f(-3):
[tex]f(-3) = -1/2(-3 + 2)^2 + 5 = 4[/tex]

Then, find f(1):
[tex]f(1) = -1/2(1 + 2)^2 + 5 = 1.5[/tex]

Now, we calculate the average rate of change:
(f(1) - f(-3)) / (1 - (-3)) = (1.5 - 4) / (1 - (-3)) = -2.5 / 4 = -0.625

Therefore, the average rate of change of the function f(x) from x = -3 to x = 1 is -0.625.

Related Questions

PLS HURRY FIRST ANSWER IS MATKED BRAINLEST!!!

What is the volume of the piles of hay??

Answers

6 x 4 x 3 = 72

1 x 2 x 4 = 8

72 -8 = 64 cubic feet

9. A model of a building is made using a scale of 1 inch = 25 feet. What is the height of the actual building, in feet, if the height of the model is 12.5 inches?

*PLZ HELP* *DUE IN 1 HOUR* *EMERGENCY* *17 POINTS* *YOU WILL GET A COOKIE*

Answers

You can use the ratio to find the height of the actual building, 1 inch:25 feet.
We have to find y which is the actual height, 12.5 inches: y.
To find y, you have to multiply 12.5 by 25 to find the actual height.
12.5×25= 312.5
So the actual height of the building is 312.5 feet.

Answer:

312.5

Step-by-step explanation:

i wil get my cookie

Which relation is a function of x?

Answers

The correct awnset to that question would be D

Answer:

last option is correct.

Step-by-step explanation:

A relation is a function if each x value has a unique y value.

We'll use this concept to check whether the relation is a function or not.

For the first relation,

the x value 2 has two different values -9 and 8 . Hence, it is not a function.

For the second relation,

the x values -8 and 1 has different y values . Hence, it is not a function.

For the third relation

The x value -5 has different y values. Hence, it is not a function.

For the fourth relation

All the x values have unique y values. Hence, from the definition it is a function.

Therefore, last option is correct.

....................

Answers

The slope of LM is (-2 -(-4))/(3 -1) = 2/2 = 1, as is the slope of NK. The other two sides of the rectangle will be perpendicular, so their slopes will be -1/1 = -1.

Selection A is appropriate.

What is the answer for 20x21

Answers

The answer is 420. I hope that it is right and next time use a calculator.

20*21=420

21 groups of 20 is 21*2=42
42*10=420

Hope this helped☺☺

I have to translate these into algebraic expressions. three-fifths x subtracted from 4 times one-eighth w. the other one is 60% of the product of one-twelfth y and two-thirds z.

Answers

3/5x-4(1/8w)

0.6(1/12y*2/3z)

The final algebraic expressions are: [tex]\frac{1}{2} w - \frac{3}{5} x[/tex] and [tex]\frac{1}{30} yz[/tex]

Sure, let's break down each part of your question step-by-step to translate them into algebraic expressions.

Three-fifths x subtracted from 4 times one-eighth w

Let's identify the components first:

"Three-fifths x" is written as [tex]\frac{3}{5} x[/tex]."4 times one-eighth w" is written as [tex]4 \times \frac{1}{8} w[/tex] or simply [tex]\frac{4}{8} w[/tex].

Now, write the expression for "three-fifths x subtracted from 4 times one-eighth w":

[tex]\frac{4}{8} w - \frac{3}{5} x[/tex]

Simplifying [tex]\frac{4}{8} w[/tex] to [tex]\frac{1}{2} w[/tex], the algebraic expression becomes:

[tex]\frac{1}{2} w - \frac{3}{5} x[/tex]

60% of the product of one-twelfth y and two-thirds z

Let's identify the components first:

"One-twelfth y" is written as [tex]\frac{1}{12} y[/tex]."Two-thirds z" is written as [tex]\frac{2}{3} z[/tex]."Product of one-twelfth y and two-thirds z" is written as [tex]\frac{1}{12} y \times \frac{2}{3} z[/tex].

First, calculate the product:

[tex]\frac{1}{12} y \times \frac{2}{3} z = \frac{2}{36} yz = \frac{1}{18} yz[/tex]

Now, we need "60% of that product":

60% can be written as [tex]0.60[/tex], so the expression becomes:

[tex]0.60 \times \frac{1}{18} yz = \frac{3}{90} yz = \frac{1}{30} yz[/tex]

So, the algebraic expression for "60% of the product of one-twelfth y and two-thirds z" is:

[tex]\frac{1}{30} yz[/tex]

What is the median of the following data set? {6, 3, 9, 1, 7} 3 6 8 9

Answers

The median of a data set is the number in the very middle.
Your answer would be 9.

Answer:

Step-by-step explanation:

Find x. Round to the nearest hundredth.

Answers

X = 11 x tan(64)

x = 22.55

The table below represents a linear function f(x), and the equation represents a function g(x): X) -1, 0, 1 F(x) -5, -1, 3 G(x)=2x+8
Part A. Wrote a sentence to compare the slope of the two functions and shows the steps you used to determine the slope of f(x) and g(x)

Part B which functions has greater y-intercept. Justify

Answers

f(x) = 4x - 1. You can get this by using the slope formula and then point-slope form.

1. The slope of f(x) is twice as steep as that of g(x).

2. The y intercept of g(x) is much greater than that of f(x) because 8>-1

How many 53/4 pieces of yarn can be cut from a roll that is 60 inches long? please i really need help

Answers

Divide the total length by the length of the pieces.

x= number of 53/4 pieces

x= 60 ÷ 53/4
to divide by the fraction, multiply by the reciprocal/inverse of 53/4
x= 60 * 4/53
x= (60*4)/53
x= 240/53
x= 4 28/53 or 4.528

ANSWER: The roll can be cut into 4 pieces with a 28/53 piece leftover.

Hope this helps! :)

Uniforms are sold in packages of 8 - the stores 127 employees will be given 3 uniforms

Answers

you need 48 packages for each employee to have 3 uniforms

100 dL = how many L exp lane please and answer

Answers

Hello there!

100 deciliter is equal to 10 liter

Details down below....

There are 0.1 liters in a deciliter.

We can use that information to find how many liter are there in 100 deciliter.

So, it should look like this:

0.1 L...........1 dl
x L................100 dl

Cross multiply

1 * x = 100 * 0.1

x = 10

You got it? See how easy that was :)

Math is an interesting beautiful subject. We just need to know the formulas and understand when and how to use them.

I hope this answer helps! As always, it is my pleasure to help students like you!

Which describes the correct way to convert minutes to hours?

Answers

Every 60 minutes equals an hour.

60m = 1h

m = minutes | h =hour

60m + 60m = 120m = 2h

Hope this helped!

James cut 1 1/4 dozen flower for a bouquet. Gwen added 1 2/4 dozen flowers to the bouquet. How many dozen flowers are there altogether?

Answers

3 and 3/4 of a dozen

Flower cut for a bouquet by James =[tex] 1\frac{1}{4} [/tex]

Flower cut for a bouquet by Gwen=[tex] 1\frac{2}{4} [/tex]

Flower cut for a bouquet by James and Gwen is the sum of flowers cut by both.

Flower cut for a bouquet by James and Gwen=[tex] 1\frac{1}{4} +1\frac{2}{4} =(1+1)+(\frac{1}{4} +\frac{2}{4} =(2)+\frac{3}{4} =2\frac{3}{4} [/tex]

Flower cut for a bouquet by James and Gwen =[tex] 2\frac{3}{4} [/tex]

What are three two dimensional shapes that could result from slicing a cube

Answers

Any 3 of ...
triangle, square, rectangle, trapezoid, parallelogram, pentagon, hexagon.

A deep-sea diver must descend and ascend in short steps to equalize pressure on his body. If the diver rises toward the surface too fast, he may suffer from a physical condition called "the bends." Suppose the diver started at 82 feet below the surface and rose in 5 steps of 15 feet each. Use an integer to describe his new position in relation to the water surface.

Answers

Start by multiplying 15 by 5, and you get 75. then subtract that from 82, and you get 7. Since you are below the surface, the number is negative. So you get -7.

Answer:

-7 feet

Step-by-step explanation:

The total distance the diver rose is 5*15 = 75 feet

If we take the zero at the water surface, then the initial position, that is, 82 feet below the surface has to be considered as -82. The 75 feet risen by the diver is a positive quantity, then his new position, in relation to the water surface, is -82 + 75 = -7 feet, i. e. 7 feet below the surface.

The quantity demanded x for a product is inversely proportional to the cube of the price p for p > 1. When the price is $10 per unit, the quantity demanded is 64 units. The initial cost is $150 and the cost per unit is $2. What price will yield a maximum profit?

Answers

q(p) = k/p^3 . . . . . . . . we want to find k
q(10) = k/10^3 = 64
k = 64,000

Revenue = q(p)*p = 64000/p^2
Cost = 150 +2q = 150 +2*64000/p^3

Profit = Revenue -Cost = 64000/p^2(1 -2/p) -150

Differentiating to find the maximum profit, we have
.. dProfit/dp = -2(64000/p^3) +6(64000/p^4) = 0
.. -1 +3/p = 0
.. p = 3

A price of $3 per unit will yield a maximum profit.

During a 5-year period, 32% of snowstorms in a certain city caused power outage Fifty-one of the snowstorms did not cause power outages. Find the total number of snowstorms in this city over the 5-year period.

Answers

To answer this question you will consider that if 32% of the storms did cause outages, then 100% (all of them)-32%= 68% did NOT produce a power outage. We can say that 68% of the total is 51.

This can be written as 0.68 x = 51 where x is the total number of snowstorms. Divide both sides by 0.68 to solve for x. X = 75 snowstorms. Another way to do this is to use Ratios. See the attached page for the strategy.

Answer:
Total number of snowstorms = 75 storms

Explanation:
We are given that:
32% of the snowstorms caused power outage
This means that we can get the percentages of the snowstorms that did not cause power outage as follows:
% of storms not causing outage = 100% - 32% = 68%

Now, we are given that the number of snowstorms that did not cause power outage is 51
Assuming that the total number of storms is x, the equation would be as follows:
68% * x = 51
0.68x = 51
x = 51 / 0.68
x = 75 storms

Hope this helps :)

translate the verbal phrase into a algebraic expression pls

Answers

2 × (x + 3) < 5
...................................................................

How do u do #10? Plz show on paper

Answers

Reflection across the line y=x simply swaps the x and y coordinates.
K'(-2, -5), A'(1, -4), I'(-1, 0), J'(-4, -2)

Paige works at a department store and has a commission rate of 3 percent. Her sales for the quarter were $4,596. If she earns $50 per day and she worked 30 days in the quarter, what is the total amount she earned?

Answers

Here's what the equation would look like:

30(50) + 0.03(4596)

1500 + 137.88

Paige earned $1637.88.

Answer:

Paige earned $1637.88.

Step-by-step explanation:

i did it enginuity

what is eleven less than 7 times a number is at least 2 what is the inequality

Answers

----------------------------------------------------------
Define x.
----------------------------------------------------------
Let the number be x.

----------------------------------------------------------
Construct inequality
-----------------------------------------------------------
7x - 11 ≥ 2

----------------------------------------------------------
Add 11 to both sides.
----------------------------------------------------------
7x ≥ 13

----------------------------------------------------------
Divide by 7 on both sides.
----------------------------------------------------------
[tex]x \geq \dfrac{13}{7} [/tex]

----------------------------------------------------------
[tex]\bf \text{ Answer: } x \geq \dfrac{13}{7} [/tex]
----------------------------------------------------------

Hence, the inequality is [tex]x\geq \frac{13}{7}[/tex].

What is an inequality?

A relationship between two expressions or values that are not equal to each other is called 'inequality.

Here given that,

Eleven less than [tex]7[/tex] times a number is at least [tex]2[/tex].

Let the number be [tex]x[/tex]. Construct the inequality

[tex]7x - 11 \geq 2[/tex]

Now add [tex]11[/tex] to both sides.

[tex]7x\geq 2+11\\7x\geq 13[/tex]

Now, divide by [tex]7[/tex] both sides, we get

[tex]x\geq \frac{13}{7}[/tex].

Hence, the inequality is [tex]x\geq \frac{13}{7}[/tex].

To know more about inequality

https://brainly.com/question/23575974

#SPJ2

Anyone? please i need help

Answers

Answer:
y = 5x - 7

Explanation:
The general form of the linear line in slope-intercept form is:
y = mx + c
where:
m is the slope
c is the y-intercept

1- getting the slope:
The slope of the line can be calculated using the following formula:
m = [tex] \frac{y_{2}-y_{1}}{x_{2}-x_{1}} [/tex]

We are given the points:
(3,8) representing (x₁,y₁)
(2,3) representing (x₂,y₂)
Substitute with the givens in the above equation to get the slope as follows:
m = [tex] \frac{3-8}{2-3} [/tex] = 5

Therefore, the equation now became:
y = 5x + c

2- getting the y-intercept:
To get the value of the c, we will use any of the given points, substitute in the equation we got in part 1 and solve for c. I will use point (2,3) as follows:
y = 5x + c
3 = 5(2) + c
3 = 10 + c
c = 3 - 10
c = -7

Based on the above, the equation of the line is:
y = 5x - 7

Hope this helps :)

Answer:

[tex]y= 5x-7[/tex]

Step-by-step explanation:

Using slope-intercept form:

The equation of line is given by:

[tex]y=mx+b[/tex] .....[1]

where,

m is the slope of the line

b is the y-intercept.

As per the statement:

The points (3, 8) and (2, 3) fall on a particular line.

Using slope(m) formula:

[tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex]

Substitute the given points we have;

[tex]m = \frac{3-8}{2-3}=\frac{-5}{-1}=5[/tex]

⇒m = 5

Put m = 5 in [1] we have;

[tex]y=5x+b[/tex]

Substitute the point (3, 8) we have;

8 = 5(3)+b

8 = 15+b

Subtract 15 from both sides we have;

[tex]-7 = b[/tex]

b = -7

Then we have;

[tex]y= 5x-7[/tex]

Therefore, the equation of line in slope intercept form is, [tex]y= 5x-7[/tex]

the pyramid arena in memphis tennessee is a square pyamid that is 321 feet tall. the base has 600 foot sides. find the volume of the pyramid

Answers

38,520,000 [tex] ft^{3} [/tex]

The volume of a pyramid is represented by

V = [tex] \frac{l * w* h}{3} [/tex]

The sides are 600 and the height is 321 so by filling in the values in the formula, you can get to your final answer. This is represented in the attached image.

-2x+y=1.3 2(0.5x-y)=4.6

Answers

1 Solve for yy in -2x+y=1.3−2x+y=1.3How?
y=1.3+2xy=1.3+2x
2 Substitute y=1.3+2xy=1.3+2x into 2(0.5x-y)=4.62(0.5x−y)=4.6How?
2(-1.5x-1.3)=4.62(−1.5x−1.3)=4.6
3 Solve for xx in 2(-1.5x-1.3)=4.62(−1.5x−1.3)=4.6How?
x=-2.4x=−2.4
4 Substitute x=-2.4x=−2.4 into y=1.3+2xy=1.3+2xHow?
y=-3.5y=−3.5
5 Therefore,
x=-2.4x=−2.4
y=-3.5y=−3.5

passing through (1,9),slope=2

Answers

Passes through (1, 9) with a slope of 2.

Assuming that we want this in slope intercept form, which is y=mx+b (m=slope, b=y-intercept) then we need to find the y-intercept! :)

To find the y-intercept (or b!!) you simply need to plug everything into slope intercept form using our given points.

y = mx + b

Plug everything in.

9 = 2(1) + b

Simplify.

9 = 2 + b

Subtract 2 from both sides.

9 - 2 = b

b = 7

Therefore, our y-intercept is 7! :)

Now that we have both the y-intercept and the slope, we can finally plug this into a new equation, using slope intercept form.

y = mx + b

y = 2x + 7

~Hope I helped!~

y = ax + b

Here the slope is 2.

Then, y = 2x + b

The line is passing through (1;9).

We just have to substitute that in the equation.

9 = 2*1+ b
b = 9 - 2
b = 7

That's the intercept.

Eventually, the equation is : y = 2x + 7

Hope this helps !

Photon

4/5 of the books in a library of fiction books. What percentage of the books or fiction books?

Answers

4/5 is equivalent to 80%.

Are similar this triangles

Answers

Yes.

Both triangles have sides in the ratios 9 : 11 : 13.

Kerry cut an 8 foot long board into 6 pieces that are equal in length. Represent this problem as a fraction

Answers

The answer is 8/6. Hope this helped! God bless :)

8/6 which is simplified to 4/3

PLZ!!! HELP!!!!!!!!!

This figure is 14 of a circle.

What is the best approximation for the perimeter of the figure?

Use 3.14 to approximate pi.

A.7.85 in.
B.12.9 in.
C. 17.9 in.
D. 31.4 in.

The file is the picture of the quarter or 1/4 circle

Answers

The answer is c with a side of bacon hope that helps. :)

Answer:

C. 17.9

Step-by-step explanation:

Formula: 1/4 π x d

d = diameter

d = 2r

1/4 π x 10 = 10/4 π

Add the 2 non-curve sides

5 + 5 = 10

10/4 x (3.14 = π) x 10

= 17.9

I hope this helps! :)

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The second florist bought 8 flower bouquets and 2 vases for a total of 29.00 Let b represent the cost of one flower bouquet and v represent the cost of one vase. Write and solve a system of equations to find the price of each type of arrangement. SHOW ALL WORK!