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weqwewe [10]
3 years ago
6

Mrs. Bryant's homeroom students are collecting boxtops. Each student is responsible for collecting 4% of the class's overall goa

l. Kevin has already collected 37.5% of his collection requirements. If the class's goal is to collect 800 boxtops, how much is each student responsible for collecting, and how many boxtops does Kevin currently have?
(Solving Percent Problem using algebra)
Mathematics
1 answer:
galina1969 [7]3 years ago
8 0

Answer:

Each student; 32

Kevin; 12

Step-by-step explanation:

4% of 800 is 32. Each student is responsible for colleting 32 box tops.

The next step is to figure out what 37.5% of the 32 is 12.

Hope that this helps! Have a good day and good luck!

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3 years ago
A telephone pole has a wire to its top that is anchored to the ground. The distance from the bottom of the pole to the anchor po
Bumek [7]

Answer:

The height of the pole is 105ft,

Step-by-step explanation:

Let us call h the height of the pole, then we know that the distance from the bottom of the pole to the anchor point is 49, or it is h - 49.

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Thus we get a right triangle with hypotenuse d= y+14, perpendicular  h, and base h-49; therefore, the Pythagorean theorem gives

(h-49)^2+h^2 = (h+14)^2

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h^2-98h+2401 = h^2+28h+196

further simplification gives

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Since the first solution h =21ft will give the triangle base length of 21ft-49ft = -28ft which is negative; therefore, we disregard it and pick the solution h = 105ft.

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3 0
3 years ago
Express p in terms of q if
Irina-Kira [14]

p=x^2+\dfrac{1}{x^2}\\\\p=\dfrac{x^4}{x^2}+\dfrac{1}{x^2}\\\\p=\dfrac{x^4+1}{x^2}\qquad(*)

q=x+\dfrac{1}{x}\\\\q=\dfrac{x^2}{x}+\dfrac{1}{x}\\\\q=\dfrac{x^2+1}{x}\qquad\text{square both sides}\\\\q^2=\left(\dfrac{x^2+1}{x}\right)^2\\\\q^2=\dfrac{(x^2+1)^2}{x^2}\qquad\text{use}\ \ (a+b)^2=a^2+2ab+b^2\\\\q^2=\dfrac{(x^2)^2+2(x^2)(1)+1^2}{x^2}\\\\q^2=\dfrac{x^4+2x^2+1}{x^2}\\\\q^2=\dfrac{x^4+1}{x^2}+\dfrac{2x^2}{x^2}\\\\q^2=\dfrac{x^4+1}{x^2}+2\qquad\text{subtract 2 from both sides}\\\\q^2-2=\dfrac{x^4+1}{x^2}\\\\\text{From (*) we have}\\\\\boxed{p=q^2-2}

8 0
2 years ago
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