# Tutor profile: Stefanie D.

## Questions

### Subject: Pre-Calculus

Use the trigonometric formulas to find the exact value of the expression. sin〖40°〗 cos〖10°〗- cos〖40°〗 sin〖10°〗

For the formula sin(A - B) = sinAcosB - cosAsinB we are working backwards from the expanded version sinAcosB - cosAsinB to the condensed version sin(A - B). In the problem A = 40 and B = 10 so we get sin(40 - 10) which becomes sin(30) and sin(30) is asking for y coordinate on the unit circle at the angle 30 degrees which is 1/2 Solution: 1/2

### Subject: Geometry

In a 30-60-90 triangle, the length of the hypotenuse is 6. What is the length of the shortest side

The shortest side (the side opposite from the 30 degree angle) is half the length of the hypotenuse (the side across from the 90 degree angle). Therefore, the shortest side is 6/2 = 3

### Subject: Algebra

For a volleyball match, 250 tickets were sold. Student tickets cost $5 each, and adult tickets cost $7 each. A total $1450 was collected from ticket sales. How many adult tickets were sold? How many student tickets were sold?

Define your variables a = number of adult tickets sold and s = number of student tickets sold. Setup a system of equations modeling the information in the problem. a + s = 250 7a + 5s = 1450 Solve the system by substitution or elimination method a + s = 250 -5a - 5s = -1250 2a = 200 a = 100 7a + 5s = 1450 7a + 5s = 1450 If there are a total of 250 tickets and 100 of them are adult tickets, then 250-100 = 150 student tickets. Solution: 100 adult tickets and 150 student tickets

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