Given the figure below, find the values of x and z

What is the solution to the equation 32x − 1 = 243? Question 18 options: A) x = 2 B) x = 3 C) x = 4 D) x = −2

Mama L [17]

Answer:

x = 4

Step-by-step explanation:

To solve this equation, first you want to write the whole thing out.

32x - 1 = 243

Next you want to get the variable by itself, so you are going to use inverse operations. in the equation, it is 32x - 1, so you are going to add one to both sides, getting you this:

32x = 244

Now for the final step you are going to get x alone, so you are going to use inverse operations once more and divide 32 on both sides getting you your answer.

x = 4

Now if you want to check your work simply plug in x, and if it is equal, you got the correct answer!

I hope this helped and good luck with your math!

I'm really sorry if I'm wrong though, even though I already finished this unit a while ago I struggled on this one even though it is so easy compared to the equations I have now.

5 0

3 years ago

Which function has an average rate of change of -4 over the interval [-2,2]?

kolbaska11 [484]

Only p(x) has an average rate of change of -4 over [-2, 2].

Find the average rate of change of each given function over the interval [-2, 2]]:

The average rate of change of m(x) over [-2, 2]:

<h3>What is the average rate?</h3>

The average rate of change = $\frac{m(b)-m(a)}{b-a}$

Where, a = -2, m(a) = -12

b = 2, m(b) = 4

Plug the values into the equation

The average rate of change

$=\frac{4-(-12)}{2-(-2)} =\frac{16}{4}$

The average rate of change = 4

The average rate of change of n(x) over [-2, 2]:

The average rate of change = $\frac{n(b)-n(a)}{b-a}$

Where, a = -2, n(a) = -6

b = 2, n(b) = 6

Plug the values into the equation

The average rate of change

$=\frac{6-(-6)}{2-(-2)} \\=\frac{12}{4}$

The average rate of change = 3

The average rate of change of q(x) over [-2, 2]:

The average rate of change = $\frac{q(b)-q(a)}{b-a}$

Where, a = -2, q(a) = -4

b = 2, q(b) = -12

Plug the values into the

The average rate of change = $\frac{-4-12}{2-(-2)}$

= $\frac{-16}{4}$

The average rate of change = -2

The average rate of change of p(x) over [-2, 2]:

The average rate of change = $\frac{p(b)-p(a)}{b-a}$

Where, a = -2, p(a) = 12

b = 2, p(b) = -4

Plug the values into the equation

The average rate of change = $\frac{-4-12}{2-(-2)}$

$=\frac{-16}{4}$

The average rate of change = -4

The answer is D.

Only p(x) has an average rate of change of -4 over [-2, 2].

To learn more about the average rate of visit:

brainly.com/question/8728504

#SPJ1

8 0

1 year ago

Complete the proportion to compare the first two triangles

lukranit [14]

12 and 13 because elmo

6 0

2 years ago

Your family is installing a new square pool in the backyard. The existing patio has a side length of 8 feet. How much of the pat

trasher [3.6K]

The question is an illustration of perimeters.

The amount of patio to remove to install the pool is 8 feet.

From the question, we have:

$\mathbf{Length\ of\ the\ pool = 8}$

$\mathbf{Length\ of\ walkway = 1}$

The perimeter of the patio is:

$\mathbf{P_p = 4 \times Length\ of\ the\ pool}$

$\mathbf{P_p = 4 \times 8}$

$\mathbf{P_p = 32}$

A 1ft walkway means that;

1ft would be subtracted from both sides of the patio before installing the pool

So, the perimeter of the patio in terms of the length of the pool is:

$\mathbf{P_p = 4 \times (x +2)}$

Equate both expressions

$\mathbf{P_p = P_p}$

$\mathbf{4 \times (x +2) = 32}$

Divide both sides by 4

$\mathbf{x +2 = 8}$

Subtract 2 from both sides

$\mathbf{x = 6}$

So, the perimeter of the pool is:

$\mathbf{P_{pool} = 4 \times 6}$

$\mathbf{P_{pool} = 24}$

The amount of patio to remove is:

$\mathbf{Amount = P_p - P_{pool}}$

So, we have:

$\mathbf{Amount = 32 - 24}$

$\mathbf{Amount = 8}$

Hence, 8ft of the patio would be removed to install the pool

<em>See attachment for illustration</em>