An expression is shown below.

Place a check next to each equivalent expression.

Work Shown:

f(x) = 4x^(-2) + (1/4)x^2 + 4

f ' (x) = 4*(-2)x^(-3) + (1/4)*2x .... power rule

f ' (x) = -8x^(-3) + (1/2)x

f ' (2) = -8(2)^(-3) + (1/2)*(2)

f ' (2) = 0

Finding the derivative, we have that f'(2) = 0, option D.

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[tex](x^n)^{\prime} = nx^{n-1}[/tex]

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The function is:

[tex]f(x) = 4x^{-2} + \frac{x^2}{4} + 4[/tex]

The derivatives are:

[tex](4x^{-2})^{\prime} = -2 \times 4x^{-2 -1} = -8x^{-3}[/tex]

[tex](\frac{x^2}{4})^{\prime} = \frac{2x}{4}[/tex]

[tex](4)^{\prime} = 0[/tex]

Thus, the derivative of the function is:

[tex]f^{\prime}(x) = -8x^{-3} + \frac{2x}{4} = -\frac{8}{x^3} + \frac{2x}{4}[/tex]

At x = 2:

[tex]f^{\prime}(2) = -\frac{8}{2^3} + \frac{2(2)}{4} = -1 + 1 = 0[/tex]

Thus f'(2) = 0, option D.

A similar problem is given at https://brainly.com/question/10037173

Answer: The answer is 2

Step-by-step explanation:

Given A and B are vertical angles with m ∠A = 20x + 10 and m ∠B =30x - 10, the value of x is 2

From the Vertical angle theorems, we have that

Two opposite vertical angles formed when two lines intersect each other are always equal to each other.

Now, from the question, we are given that A and B are vertical angles

That means

A = B

Also, from the question

measure of angle A = 20x + 10 and measure of angle B = 30x - 10

To determine the value of x, we will equate the two equations to each other  

A = 20x + 10

B = 30x - 10

Since, A = B

∴ 20x + 10 = 30x - 10

To solve for x,

20x + 10 + 10 = 30x - 10 +10

We get

20x + 20 = 30x

20x - 20x + 20 = 30x - 20x

20 = 10x

That is,

10x = 20

∴ x = 20 ÷ 10

x = 2

Hence, given A and B are vertical angles with m ∠A = 20x + 10 and m ∠B =30x - 10, the value of x is 2

Learn more here: https://brainly.com/question/5719544

Answer:

[tex] \huge \boxed{x = 8}[/tex]

Step-by-step explanation:

f(x) = 70 + 11x

To find the value of x when f(x) =158 , equate f(x) to 158

We have

[tex]70 + 11x = 158 \\ 11x = 158 - 70 \\ 11x = 88[/tex]

Divide both sides by 11

[tex] \frac{11x}{11} = \frac{88}{11} \\ [/tex]

We have the final answer as

Hope this helps you

Answer:

Step-by-step explanation:

Yes

Answer:

15

Step-by-step explanation:

I'm assuming that b3 is the variable b times 3. So if you plug in 5 for the b variable you'd get (5)3 which is 5 times 3, or 15.

Answer:

(-1.6)(3 + 0.1)

Step-by-step explanation:

Sidney applied the steps to find the product of two numbers (3.1) and (-1.6),

Step 1,

(3.1)(-1.6) = (-1.6)(3.1)

Step 2,

(-1.6)(3.1) = (-1.6)(3 + 0.1)

Step 3,

(-1.6)(3 + 0.1) = -4.8 + (-0.16) [Distributive property]

Step 4,

-4.8 + (-0.16) = -4.96

Therefore, expression that correctly fits in step 2 will be,

(-1.6)(3 + 0.1)

Answer:

it might be D

Step-by-step explanation:

sorry is im wrong

EDIT

on edge im right!!!!!!!!!!!!!!

Answer:

the left column is the statement and Right column is the reason. The statement is the steps of how are you going to solve the problem

-3(n+6)+10=-8

Use distributive property:

-3n -18 +10 = -8

Combine like terms:

-3n -8 = -8

Add 8 to both sides:

-3n = 0

Divide both sides by -3:

n = 0

Answer:

n=0

Step-by-step explanation:

I know this is in fraction form because it says out of. A fraction will say out of, for example: 3 out of 4. The number 62 boys out of 100 students can be represented as 0.62, 0.62 of 1 (100) whole number.

Hope this helps!

The longest side is always the hypotenuse

Answer:

x=-1

Step-by-step explanation:

Answer:

X = -1

Step-by-step explanation:

Answer:

1. x = 5

Remember that all angles add up to 180, and because you know that one of the angles = 90, you can add the other two angles like so.

6x + 15 + 10x - 5 = 90

2.

Angle 1 = 43 degrees

Angle 3 = 32 degrees

Answer:

16 hours

Step-by-step explanation:

trust me its rsm principal test rite? lol u just divide the hours by 2 cuz there are only half the pumps

Answer:

64 hours

Step-by-step explanation:

Answer:

=7bx3−6b+6

Step-by-step explanation:

6−7b+7bx3+b

=6+−7b+7bx3+b

=6+−7b+7bx3+b

=(7bx3)+(−7b+b)+(6)

=7bx3+−6b+6

Answer:43b

Step-by-step explanation:7+7 x3 +b = 43b

Answer:

$4.00 per pound

Step-by-step explanation:

A grocery store sells cashew nuts at $8.00 per pound and peanuts at $4.00 per pound. They want to mix 10 pounds of the cashews with peanuts to create a mixture that will sell at $6.50 per pound

Answer:

Step-by-step explanation:

The ratio for cashews to raisins is 2:16 and you can simplify that by 2 because they are factors of 2. When you simplify you get 1:8.

The ratio for dates to peanuts is 3:24 and you can simplify that by 3 since they are factors of 3. When you simplify by 3, you get 1:8 which is the same ratio for cashews to raisins.

Answer:

what?

Step-by-step explanation:

Answer:

I am cunfushion

Step-by-step explanation:

Answer:

<4 ~= <5 - Consecutive Interior Angles Theorem

<4 ~= <2 - Vertical Angles Theorem

<6 ~= <2 - Corresponding Angles Theorem

line I || line m - Transitive Property

Answer:

I believe the exact value is -265

The last one the answer is ( number ) 40 degrees

Answer:

-8+3x

Step-by-step explanation:

7 – 9x – 15 + 12x

We cannot solve since there is no equals sign, we can only simplify

Combine like terms

7 -15   -9x+12x

-8          +3x

Answer:

3x - 8

Hope that was the answer you were looking for :D

Answer:

15

Step-by-step explanation:

pls rate and thank me so i can get the points, thanks

Answer:

he can fit 15 stickers...............................

Step-by-step explanation:

Answer:

25

Step-by-step explanation:

multiply 3 1/2 by 6

add the answer 4 times

I THINK

Answer:

y=-2x-1

Make sure to have no spaces in your answer.( if your test said that remember to not put space between them)

Step-by-step explanation:

Answer:

y= -7

Step-by-step explanation:

A line that has a slope of zero is a horizontal line

Horizontal lines are of the form

y=

The y coordinate is -7

y= -7

Step-by-step explanation:

1.)i always eat salad

2.)you ate rice

3.)She has a lot of children

4.)He drank tea

5.)i still drink wine

6.)you are students of the French language

(thanks, sorry and hope I helped)