What is the average rate of change of f(x) = −2x + 1 from x = −5 to x = 1?

Answers

Answer 1

[tex]\bf slope = {{ m}}= \cfrac{rise}{run} \implies \cfrac{{{ f(x_2)}}-{{ f(x_1)}}}{{{ x_2}}-{{ x_1}}}\impliedby \begin{array}{llll} average\ rate\\ of\ change \end{array}\\\\ -------------------------------\\\\ f(x)=-2x+1 \qquad \begin{cases} x_1=-5\\ x_2=1 \end{cases}\implies \cfrac{f(1)-f(-5)}{-5-1} \\\\\\ \cfrac{[-2(1)+1]~~-~~[-2(-5)+1]}{-6}\implies \cfrac{[-1]~~-~~[11]}{-6} \\\\\\ \cfrac{-12}{-6}\implies 2[/tex]

Related Questions

The function f(x) is graphed on the coordinate plane. What is f(−4) ?

Answers

For this type of problem, plug the -4 into the graph for x. So where is the line at x = -4??
y = 4 where x = -4.
That's the same as saying: "what is the y-value when x = -4?)
f(-4) = y = 4

Complete the equation of the line through (4,-8) and (8,5).
Use exact numbers.

y=_______ Topic:
Slope-intercept from two points.

Answers

slope = (5+8)/(8-4) = 13/4

y = mx + b
b= y - mx
b = -8 - (13/4) (4)
b = -8 -13
b = -21

equation
y = 13/4x - 21

The equation of the line that passes through (4, -8) and (8, 5) in slope intercept form is y = 13 / 4 x - 21

Slope intercept form of a line

The slope intercept form of a line is represented as follows;

y = mx + b

where

m = slopeb = y-intercept

Therefore,

(4, -8) and (8, 5)

m = 5 + 8 / 8 - 4

m = 13 / 4

Therefore, using (8, 5)

5 = 13 / 4(8) + b

5 = 26 + b

b = 5 - 26

b = -21

Hence, the equation is as follows:

y = 13 / 4 x - 21

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What is the length of the hypotenuse of an isosceles right triangle with an area of 32?

Answers

[tex] \int\limits^a_b {x} \, dx [/tex]

Astronauts use a tool in space that weigh 5 ounces on Earth. How many grams does the tool weigh? Round your answer to the nearest hundredth.

Answers

First you need to find how many grams is 1 ounce. 1o z.is 28.35 g, then you need to multiply 28.35 g by 5 which is 141.75. you need to round it to the nearest hundred so it is about 142 grams.
the key here would be
1 oz. = 28.35g or 1 oz. = 28 g

Answer: 141.75

Step-by-step explanation: Yw future edge users

Solve the equation the square root of the quantity x minus 6 plus 2 equals 6 for the variable. Show each step please. Remember the X - 6 is under a square root sign

Answers

sqrt (x-6) + 2 = 6

sqrt(x-6) = 4

sqrt(x-6) squared = 4 squared

x-6 = 16

x = 10

Karen's penny bank is 1/3 full. After she removes 240 pennies, it is 1/9 full. How many pennies can Karen's bank hold?

Answers

the difference between 1/3 and 1/9 is: 3/9-1/9=2/9
2/9 of the capacity if 240 pennies
2/9 * x=240
x=240*(9/2)=1080
the penny bank can hold 1080 pennies

Final answer:

The difference between the bank being 1/3 and 1/9 full equals 240 pennies, so 1/9 of the bank's capacity equals 120 pennies. So, Karen's bank can hold a total of 1080 pennies.

Explanation:

This is a mathematics problem dealing with fractions and subtraction. From the problem, we understand that after Karen removes 240 pennies, the bank is 1/9 full from previously being 1/3 full. So, the difference between 1/3 and 1/9, which is 2/9, accounts for the 240 pennies that were removed.

To find out the total capacity of the penny bank, you need to consider that 1/9 (the fraction representing the bank's fill level after removal of the 240 pennies) is equivalent to 120 pennies (half of 240, as 2/9 of the capacity is 240 pennies). This means that the total capacity of the bank (comparable to 9/9 of the fraction) is 120 pennies times 9, which equals to 1080 pennies.

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A rectangle has length x+9 and width 2x-1 what are the areas of the rectangle

Answers

Area=l*w

a=(x+9)(2x-1) <--- Use FOIL

a=2x²-x+18x-9
a=2x²+17x-9

Hope I helped :)

During the 2005 football season, Team Tackle beat Team Sack by 5 points. If their combined scores totaled 89, find the individual team scores.

Answers

42 and 47 for Team Tackle and 42 fro Team Sack as team Tackle had 5 points more.

Consider the equation below. log4 (x+3)=log2 (2x). Which system of equations can represent the equation?

Answers

Note that
[tex]log_{4} (x+3) = \frac{log_{2} (x+3)}{log_{2}4} [/tex]

Therefore, given
log₄(x+3) = log₂(2x), obtain
[tex] \frac{log_{2}(x+3)}{log_{2}4}=log_{2} (2x) \\ log_{2}(x+3) = log_{2}4 log_{2}(2x) \\ x+3 = (2x)^{log_{2}4} [/tex]
Because
log₂4 = log₂ 2² = 2 log₂ 2 = 2, therefore
x + 3 = (2x)² = 4x²
4x² - x - 3 = 0
This factorizes into
(4x + 3)(x - 1) = 0

Answer:
4x² - x - 3 = 0
or
4x + 3 = 0, and
x - 1 = 0

Full problem. The reason people can't answer the question is because ya'll don't post all the information.

N a contest, a total of $12,000 was divided among the first, second, and third-place winners in the ratio of 3 to 2 to 1, respectively. how much did the first-place winner receive

Answers

You will divide the ratio by the total and then multiply into 12,000
The first Winner
3/6 × 12,000 = $6,000
The Second Winner
2/6 × 12,000 = $ 4,000
The Third Winner
1/6 × 12,000 = $2,000

After 6 years, what is the total amount of a compound interest investment of $35,000 at 4% interest, compound quarterly?
Round to the nearest cent.

Answers

1.06^6 * 35000 = $49648.20
1.06 is the mutiplier.

A=P(1+r/100)^6
A=35000(1+1/100)^4×6
A=$44440.7127
A=$44441

A triangle has three different integer side lengths and a perimeter of 20 units. What is the max length of any one side?

Answers

Final answer:

Using the Triangle Inequality Theorem and given a perimeter of 20 units for a triangle with integer side lengths, the maximum length of one side is found to be 15 units.

Explanation:

To determine the maximum length of one side of a triangle with integer side lengths and a perimeter of 20 units, we must apply the Triangle Inequality Theorem. This theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. Given a perimeter of 20 units, if we denote the longest side as x, and the other two sides as y and z, we must satisfy two conditions:

x + y + z = 20 (perimeter condition)

x < y + z (Triangle Inequality Theorem)

Since the triangle has different integer side lengths, the largest x can be is when y and z are consecutive integers because this allows for the largest possible x. If we try the smallest integers, 1 and 2, for y and z, their sum is 3. To satisfy the triangle inequality, the largest possible integer for x would be 20 - 1 - 2 = 17. However, this does not satisfy the inequality x < y + z, because 17 is not less than 3.

Next, we increase y and z to 2 and 3, respectively, which sums up to 5. Thus, for x, we have 20 - 2 - 3 = 15. Since 15 is less than 2 + 3, it satisfies the condition required by the Triangle Inequality Theorem. Therefore, the maximum length of any one side of the triangle is 15 units.

Please help me asap
It's due tomorrow

Answers

You have 3n. You want n, so divide all three sides by 3.

-15 < 3n <= 6

-5 < n <= 2

n is an integers and must be greater than -5 and can be as great as 2.
n can be -4, -3, -2, -1, 0, 1, 2

Which point is an x-intercept of the quadratic function
f(x) = (x – 8)(x + 9)?

Answers

x-intercept means f(x) = 0

(x-8)(x+9) = 0 ⇒ x = 8 or x = - 9

There are two points which are x-intercepts. They are (8,0) and (-9,0).

factor the trinomial x^2 - 16x +63

Answers

Factor the following:
x^2 - 16 x + 63
The factors of 63 that sum to -16 are -7 and -9. So, x^2 - 16 x + 63 = (x - 7) (x - 9):
Answer: (x - 7) (x - 9)

Doris put $4000 in a 2-year CD paying 6% interest, compounded monthly. After 2 years, she withdrew all her money. What was the amount of the withdrawal?
a. 4000.00
B. $4214.41
C. $4508.64
D. $4448.13

Answers

Your answer is going to be C

Your answer is C I hope it helps you

Emma read the statement “the quotient of six and a number, x, is the same as negative two times the difference of x and 4.5.” She translated it as shown below.

Answers

Emma should have used division to represent the quotient of six and x, and she should have used parentheses to show that -2 is multiplied by (4.5 - x). Hence the correct options are 1 and 5.

Emma made two errors in translating the statement "the quotient of six and a number, x, is the same as negative two times the difference of x and 4.5." First, instead of representing the quotient of six and x, she incorrectly wrote 6x, which implies multiplication rather than division. The correct representation should be 6/x.

Second, Emma failed to use parentheses to show that -2 is multiplied by the difference of x and 4.5. The correct expression should be -2(x - 4.5) to ensure proper order of operations. These errors impact the accuracy of the translated equation, and correcting them would yield a more faithful representation of the original statement. Hence the correct options are 1 and 5.

Complete question:

Emma read the statement "the quotient of six and a number, x, is the same as negative two times the difference of x and 4.5." She translated it as shown below 6x=-2x-4.5 What errors did Emma make? Select two options

She should have used division to represent the quotient of six and x.

She should not have included an equal sign.

She should have used parentheses to show that -2 is multiplied by (x-4.5).

She should have subtracted the difference (x-4.5) from -2.

She should have used parentheses to show that -2 is multiplied by (4.5-x).

Emma made the following errors in her translation:

E. She should have used parentheses to show that -2 is multiplied by (x-4.5). Emma’s equation, 6x = -2x - 4.5, lacks parentheses around the expression (x-4.5). To correctly represent the difference of x and 4.5 being multiplied by -2, she should have written -2(x-4.5).

D. She should have subtracted the difference (x-4.5) from -2. Emma’s equation does not correctly account for the subtraction of the difference (x-4.5) from -2. The correct equation should be 6x = -2(x-4.5).

The other options are not relevant to Emma’s specific errors in translating the statement.

Emma made the following errors in her translation:

E. She should have used parentheses to show that -2 is multiplied by (x-4.5). Emma’s equation,

6x = -2x - 4.5, lacks parentheses around the expression

(x-4.5). To correctly represent the difference of x and 4.5 being multiplied by -2

, she should have written

-2(x-4.5)

.D. She should have subtracted the difference(x-4.5) from -2

. Emma’s equation does not correctly account for the subtraction of the difference

(x-4.5)

from

-2

The correct equation should be

6x = -2(x-4.5)

Complete question:

A. She should have used division to represent the quotient of six and x.

B. She should not have included an equal sign.

C. She should have used parentheses to show that -2 is multiplied by (x-4.5).

D. She should have subtracted the difference (x-4.5) from -2.

E. She should have used parentheses to show that -2 is multiplied by (4.5-x).

Which graph represents the inequality y<−1+2x?

Answers

C, because the equation of the line matches the equation in the question & the shaded region is under the line, representing that it is less that the equation.

A: The y-intercept is negative, therefore the line must touch -1 on the y axis. With this information, you can eliminate B and D. Since the sign is less than, you shade down.

Explain how to write and evaluate an algebraic expression that represents the situation. The blueberries were divided equally into six bowls. Evaluate when b = 210.

Answers

The variable is the number of blueberries, the operation is division, and the constant is 6. Write the division expression as the fraction, b/6 . To evaluate, substitute 210 in for the variable, b, and simplify. 210 divided by 6 is 35. So each bowl has 35 blueberries.

The algebraic expression can be written in terms of the variable b and and evaluated as b/6 = 210/6 = 35

According to the question;

The blueberries were divided equally into six bowls;

Hence, the algebraic expressions is;

b/6

where, b = total number of blueberries

Hence, when b= 210

The number of blueberries in each bowl is; 210/6 = 35

Read more on Algebraic expressions;

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How to solve nonlinear equations using iteration method?

Answers

this is a definition and an example of it

A bakery makes donuts at the rate of 225 per hour. How long will it take the bakery to fill an order of 500 donuts?

Answers

If I understood your question properly, it would take 2 hours for the company to fill an order of 500 donuts.

I hope you found this helpful! C:

500 / 225 = 2.22 repeating

It will take them ~2.22 hours to make 500 donuts.

The admission fee at an amusement park is $2.00 for children and $5.60 for adults. On a certain day, 352 people entered the park, and the admission fees collected totaled 1280 dollars. How many children and how many adults were admitted?

Answers

this is harder than it looks I cant figure it out

How to find slope when there is the y intercept and x-intercept?

Answers

First graph your x and y intercept then pick any two points on the line.
[tex] \frac{rise}{run} = \frac{y2 - y1}{x2 - x1} [/tex]
that's the equation used to find your slope

Example:

(4,2) (8,6) let's say those are the points you pick from the line

so then you subtract 6-2=4 (6 is your y2 and 2 is your y1)

then subtracts 8-4=4 (8is your x2 and 4 is your x1)

then your left with
[tex] \frac{2}{4} [/tex]
if you can reduce the reduce in this case you can which leaves you with
[tex] \frac{1}{2} [/tex]
and that's how you find the slope

What is the maximum length possible for her blanket?

Answers

can you please explain your question
It looks like you are missing some information

Answer: c: 60

Step-by-step explanation:

i did the test

How to find the distance between two lines in 3d?

Answers

use graph paper, draw the 3d shape and count the squares as one unit each

Answer:

Step-by-step explanation:

What would '6 meters to 60 meters' be in a ratio

Answers

because you van turn 6 into 60 so they are in common. Hope that helps

Which inequality represents this sentence? Ten minus three is greater than one plus two.

Answers

Ten minus three ⇒ 10 - 3
One plus two ⇒ 1 + 2

Greater than use the symbol >

Ten minus three greater than one plus two
10 - 3 > 1 + 2
7 > 3

According to question we have: (10-3) which is equal to 7 i.e (10-3) = 7 ......eq.(1) also (1+2) is equal to 3 i.e (1+2) = 3 ......eq.(2) now from eq(1) and (2) we have 7>3 ..........(applying greater than symbol) so (10-3) > (1+2) hence, Ten minus three is greater(>) than one plus two.

Vectors...

Let u = <-3, -5>, v = <-3, 1>. Find u + v.

Answers

-3 + -3 = 0
-5 + 1 = -4
vector = < 0,-4 >

Answer:

u + v = <-3 + -3, -5 + 1> = <-6 , -4>

u + v = <-6 , -4>

Step-by-step explanation:

I hope this helped you.

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Have a great day!!!!!!!!!!!

Which ordered pairs lie on the graph of the exponential function f(x)=4(5)2x?

Select each correct answer.
(−1,4/25)
(0,0)
(1,4)
(2,2500)

Answers

(-1, 4/25) and (2,2500)

A pizza parlor sold 38mc005-1.jpg pizzas during a dinner hour. If each pizza contained 8 slices, how many slices of pizza were sold?

The options are

Answers

38 pizzas times 8 slices each =

38 *8 = 304 slices total

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