Akilah S.

Senior at Connecticut College

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Pre-Calculus

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Question:

Find the inverse of the function y=34x-365.

Akilah S.

Answer:

To find the inverse of the function, you will need to switch the x and y values. That becomes: x=34y-365. Then you will need to solve for y. To do that, the first thing you will need to do is add 365 to both sides of the equation: x+365=34y-365+365. And this will then become: x+365=34y. To continue to solve for y, you want to divide both sides of the equation by 34: (x+365)/34=(34y)/34. And that will become (x+365)/34=y. This is now the inverse of the function y=34x-365 and to write is as such you will say y^(-1)=(x+365)/34.

Trigonometry

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Question:

In the right triangle ABC, side AB=5, side AC=15, and side BC=10. What is the sin of the angle C being that side AB is it's opposite and BC is it;s adjacent side.?

Akilah S.

Answer:

The definition of sin is the length of the side opposite of the angle over the hypotenuse of the right triangle. In this example, the side AB is opposite of the angle, and that measurement is 5 and the length of the hypotenuse is 15. With that being said sin C= (5/15) which is then equal to sin C=1/3.

Algebra

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Question:

Solve the equation 3(7x-4)=12+2x

Akilah S.

Answer:

First, on the left side of the equation, we distribute the 3 throughout the parenthesis, leaving us with 21x-12=12+2x. Then, we subtract 2x from both sides of the equation which would look something like this: 21x-12-2x=12+2x-2x. And that will give us: 19x-12=12. Similar to what we did with 2x, we are going to take 12 and add it to both sides of the equation: 19x-12+12=12+12. And that will give us 19x=24. Now all that is left to do is divide both sides of the equation by 19: 19x/19=24/19. And this will give you your answer: x=24/19 or x=1.26

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