# Tutor profile: Corri I.

## Questions

### Subject: Trigonometry

Give a right triangle with legs 5 and 12 and an angle marked x acrodd from the side labeled 5. If tan(x) = 5/12, what is the value of sinx?

In order to compute the sinx, you need to know the hypotenuse length. We can use the pythagorean theorem to find the length of the hypotenuse: a^2+b^2=c^2. So we have, 5^2 + 12^2 = c^2. 25+144=c^2 169 = c^2 take the square root of both sides and c = 13. Thus, the side lengths are 5, 12 and 13 respectively. The sin x = 5/13.

### Subject: Basic Math

Solve the following equation for x and show all of your work: 4x-16=20

In order to solve an equation for x, you need to isolate x. We think of the numbers connected to x as what happened to x through his day - this particular x was multipled by 4 and then we subtracted 16 to arrive at 20. In order to get x by itself, we have to "undo" his day. We can think of this as rewinding - going backwards - undoing. Therefore, we need to complete these actions backwards and undo them. To undo subtraction, you add. We need to add 16 to both sides: 4x=36. To undo multiplication, we need to divide. We divide both sides by 4. x=9. Now, let's check our answer by plugging in x: 4(9) - 16 = 20 Use the order of operations (PEMDAS) to solve: 4*9 = 36 - 16 = 20! Yes we did it right! x=9

### Subject: Algebra

A quadratic function is given by f(x) = ax^2 +bx +c where a is not 0. Select all the statements that must be true about the graph of f. A. The y-intercept of the graph is at (0, c). B. The graph has an x-intercept at (c,0). C. When a<0, the graph opens downward. D. The graph has two x-intercepts. E. If b=0, then the vertex is on the y-axis

If a quadratic equation is written in standard form (ax^2+bx+c), then the y-intercept is always found by plugging in zero for x and solving the equation. By plugging in zero for x, you eliminate the ax^2 term and the bx term. You are left with y=c and therefore the y-intercept is located at (0, c) so you would select choice A. To find the x-intercepts of a quadratic formula, you can use many methods - factoring, quadratic formula, completing the square. When you factor, you are looking for factors of c that add up to b. Since you are spliting c into two values, you will not have an intercept at (c,0). You would not select choice B. The leading value of the quadratic function, a, tells you have the graph opens. When a>0 the graph opens upward. When a<0, the graph opens downward. Thus, choice C is true. The x-intercepts are referred to as the zeros. Many quadratic functions have two x-intercepts, but not all. Some graphs have a single x-intercept, some have none, and some have imaginary zeros. Therefore without values plugged in for a, b, and c you are unable to determine how many x-intercepts (zeros) this function has. Choice D does not get selected because it is not always true. If b=0, then the quadratic function becomes: f(x) = ax^2 + c. To find the vertex of the function you use the formula x = -b/2a. If b=0, then 0/2a is equal to 0. Therefore the vertex will be located at (0,c), which is the same location as the y-intercept. Choice E is correct. TRUE: A, C, E

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