Question

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1. justine signed up for a gym membership. the gym charges a one - time fee of $59 plus a monthly fee. justine determines that she will pay a total of $557 for her gym membership after one year. how much does the gym charge per month?

1. determine the value of each square root or cube root.

a. \\(\sqrt{1}=\underline{1}\\)
b. \\(\sqrt{81}=\underline{9}\\)
c. \\(\sqrt{144}=\underline{}\\)
d. \\(\sqrt3{- 64}=\underline{4}\\)
e. \\(\sqrt3{512}=\underline{8}\\)
f. \\(\sqrt3{8000}=\underline{20}\\)

solve for x. include all answers.

1. \\(x^{2}+11 = 60\\)
2. \\(2x^{2}=72\\)
3. \\(3x^{3}-100=-19\\)

Explanation:

Problem 8

Step1: Define variables and total cost

Let $m$ = monthly fee. Total cost = one-time fee + 12×monthly fee:
$$557 = 59 + 12m$$

Step2: Isolate the monthly fee term

Subtract 59 from both sides:
$$557 - 59 = 12m$$
$$498 = 12m$$

Step3: Solve for monthly fee

Divide both sides by 12:
$$m = \frac{498}{12}$$

Step1: Evaluate square roots

a. $\sqrt{1}$: Find $x$ where $x^2=1$
b. $\sqrt{81}$: Find $x$ where $x^2=81$
c. $\sqrt{144}$: Find $x$ where $x^2=144$

Step2: Evaluate cube roots

d. $\sqrt[3]{-64}$: Find $x$ where $x^3=-64$
e. $\sqrt[3]{512}$: Find $x$ where $x^3=512$
f. $\sqrt[3]{8000}$: Find $x$ where $x^3=8000$

Step1: Isolate $x^2$ term

Subtract 11 from both sides:
$$x^2 = 60 - 11$$
$$x^2 = 49$$

Step2: Solve for $x$

Take square root of both sides:
$$x = \pm\sqrt{49}$$

Answer:

$\$41.50$

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Problem 9