Question

question 12 (1 point) (01.05 mc) shiloh has to earn at least $200 to meet her fundraising goal. she has only 100 cakes that she plans to sell at $5 each. which inequality shows the number of cakes, x, shiloh can sell to meet her goal?
options:
a) ( 20 leq x leq 200 )
b) ( 40 leq x leq 100 )
c) ( 100 leq x leq 200 )
d) ( 20 leq x leq 100 )

question 13 (1 point) (01.06 lc) mukayla is taking a math course and is working with the perimeter of rectangles. she knows the perimeter and length of her rectangle but wants to solve for the width. rearrange the following equation for ( w ), where ( p ) is the perimeter, ( l ) is the length, and ( w ) is the width of the rectangle. ( p = 2l + 2w ).
options:
a) ( w = 2p - 2l )
b) ( w = \frac{p}{2} - 2l )
c) ( w = \frac{p - 2l}{2} )
d) ( w = 2p + 2l )

Explanation:

Question 12

Step 1: Determine the inequality from the problem

Shiloh needs to earn at least $2000, and each cake is sold for $5. So the total money earned from selling \( x \) cakes is \( 5x \). The inequality for "at least" is \( 5x \geq 2000 \). Also, she has only 100 cakes, so \( x \leq 100 \).

First, solve \( 5x \geq 2000 \):
Divide both sides by 5: \( x \geq \frac{2000}{5} = 40 \).

So the combined inequality is \( 40 \leq x \leq 100 \).

Step 1: Start with the perimeter formula

We have the formula for the perimeter of a rectangle: \( P = 2L + 2W \).

Step 2: Isolate the term with \( W \)

Subtract \( 2L \) from both sides of the equation:
\( P - 2L = 2W \)

Step 3: Solve for \( W \)

Divide both sides by 2:
\( W = \frac{P - 2L}{2} \) or \( W = \frac{P}{2} - L \) (which can also be written as \( W = \frac{P}{2}-2L\) if we consider the form in the options, maybe a typo in the option but the correct rearrangement is as above). Wait, looking at the options, option c is \( W=\frac{P - 2L}{2} \) and option b is \( W=\frac{P}{2}-2L \)? Wait, no, let's check again. Wait the options:

a. \( W = 2P - 2L \)

b. \( W=\frac{P}{2}-2L \)

c. \( W=\frac{P - 2L}{2} \)

d. \( W = 2P + 2L \)

Starting from \( P = 2L + 2W \)

Subtract \( 2L \): \( P - 2L = 2W \)

Divide by 2: \( W=\frac{P - 2L}{2} \), which is option c. Wait, but let's check the arithmetic.

Wait, \( P = 2L + 2W \)

Subtract \( 2L \): \( P - 2L = 2W \)

Divide both sides by 2: \( W=\frac{P - 2L}{2}=\frac{P}{2}-L \). But in the options, option c is \( W=\frac{P - 2L}{2} \), which is correct.

Answer:

b. \( 40 \leq x \leq 100 \)

Question 13