7. Janelle and her friends are selling bracelets and headbands ahead of the school’s pep rally to support the team during homecoming. They figured they would sell the headbands for $4 and the bracelets for $2. They’d like to make more than $200 and sell no more than 100 items.

Question

Select one of the following combinations that Janelle can sell to make at least $200, but have no more than 100 items sold.
A) 20 bracelets, and 60 headbands
B) 70 Bracelets and 40 headbands
C) 45 Bracelets and 60 headbands
D) 50 Bracelets and 10 Headbands

8. Find the slope of a line that passes through (−10, −1) and (5, −4)
A) 1
B) -3
C) −1/5
D) 1/3

9. The pair of points (g, -1) and (2, 5) lie on a line with a slope of
3/2. What is the value of g? (1 point)
A) -5
B) 3
C) -2
D) 4

Answer 1

Let's go through each question one by one.

Question 7: Janelle wants to sell headbands for $4 each and bracelets for $2 each, aiming to make more than $200 while selling no more than 100 items.

• Let \( b \) be the number of bracelets and \( h \) be the number of headbands.
• The total income from selling bracelets and headbands is \( 2b + 4h \).
• The total number of items sold is \( b + h \).

The conditions to satisfy are:

1. \( 2b + 4h > 200 \)
2. \( b + h \leq 100 \)

Now, let's check each option.

A) \( b = 20, h = 60 \):

• Total income: \( 2(20) + 4(60) = 40 + 240 = 280 > 200 \)
• Total items: \( 20 + 60 = 80 \leq 100 \) ✔️

B) \( b = 70, h = 40 \):

• Total income: \( 2(70) + 4(40) = 140 + 160 = 300 > 200 \)
• Total items: \( 70 + 40 = 110 > 100 \) ❌

C) \( b = 45, h = 60 \):

• Total income: \( 2(45) + 4(60) = 90 + 240 = 330 > 200 \)
• Total items: \( 45 + 60 = 105 > 100 \) ❌

D) \( b = 50, h = 10 \):

• Total income: \( 2(50) + 4(10) = 100 + 40 = 140 < 200 \) ❌

The only option that satisfies both conditions is A) 20 bracelets and 60 headbands.

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Question 8: To find the slope \( m \) between points \( (−10, −1) \) and \( (5, −4) \): \[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-4 - (-1)}{5 - (-10)} = \frac{-4 + 1}{5 + 10} = \frac{-3}{15} = -\frac{1}{5} \]

Thus, the slope is C) −1/5.

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Question 9: The slope \( m \) between points \( (g, -1) \) and \( (2, 5) \) is given as \( \frac{3}{2} \): \[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{5 - (-1)}{2 - g} = \frac{6}{2 - g} \]

Setting the slopes equal to each other: \[ \frac{6}{2 - g} = \frac{3}{2} \]

Cross multiplying gives: \[ 6 \cdot 2 = 3(2 - g) \] \[ 12 = 6 - 3g \] \[ 12 - 6 = -3g \] \[ 6 = -3g \implies g = -2 \]

So the value of \( g \) is C) -2.

In summary: 7) A 8) C 9) C