Question

test prep

1. jose starts a savings account with $80. at the end of 6 months, the account has $350. assuming there is a constant rate, how much did jose save per month?

a $270
b $72
c $60
d $45

1. camille wants to set up a hot chocolate stand to raise money. she spends $40 on hot chocolate and $0.25 for each paper cup. she uses the equation $y = 0.25x + 40$ to keep track of her spending. if camille has $60 in donations to spend, what is the maximum number of paper cups she can buy?

a 5 cups
b 80 cups
c 240 cups
d 400 cups

1. admission to a carnival costs $15. each game costs $2 to play. which statements about the function modeling the cost to attend the carnival are true? select all that apply.

a the slope is positive.
b the initial value is $15.
c the rate of change is $15.
d the graph has a y-intercept of 2.
e the graph passes through the origin.
spiral review

1. solve $4x - 12 = -7x - 111$.
2. calculate the slope of the line that passes through (3, 2) and (-7, 4).
3. the table shows a proportional relationship. complete the table.

x	y
2
3	12
5	20

Explanation:

Problem 7:

Step1: Calculate total saved

$\$350 - \$80 = \$270$

Step2: Divide by months

$\frac{\$270}{6} = \$45$

Problem 8:

Step1: Set y equal to donations

$60 = 0.25x + 40$

Step2: Isolate the x-term

$60 - 40 = 0.25x$
$20 = 0.25x$

Step3: Solve for x

$x = \frac{20}{0.25} = 80$

Problem 9:

Step1: Define cost function

Let $x$ = number of games, $C(x) = 2x + 15$

Step2: Analyze function properties

Slope = 2 (positive), initial value/y-intercept = 15.

Problem 10:

Step1: Collect x terms on left

$4x + 7x - 12 = -111$
$11x - 12 = -111$

Step2: Isolate the x-term

$11x = -111 + 12$
$11x = -99$

Step3: Solve for x

$x = \frac{-99}{11} = -9$

Problem 11:

Step1: Use slope formula

Slope $m = \frac{y_2 - y_1}{x_2 - x_1}$, where $(x_1,y_1)=(3,2)$, $(x_2,y_2)=(-7,4)$

Step2: Substitute values

$m = \frac{4 - 2}{-7 - 3} = \frac{2}{-10} = -\frac{1}{5}$

Problem 12:

Step1: Find proportionality constant

$k = \frac{y}{x} = \frac{4}{1} = 4$, so $y=4x$

Step2: Calculate missing y-value

For $x=2$, $y=4\times2=8$

Answer:

1. D. $45
2. B. 80 cups
3. A. The slope is positive., B. The initial value is $15.
4. $x=-9$
5. $-\frac{1}{5}$

12.

x	y
2	8
3	12
5	20