The question describes a ramp that forms a triangle, the length of which is the hypotenuse of the triangle. The height of the ramp (3 feet) is the length of the side of the triangle opposite the 35° angle. In general for some angle θ, sin θ =​\( \frac{opposite}{hypotenuse} \)​ . In the question, this corresponds to sin 35° =​\( \frac{opposite}{hypotenuse} \)​ = ​\( \frac{3}{length of ramp} \)​→ length of ramp =​\( \frac{3}{35°} \)​ . This is (D).

This question requires evaluating both equations to determine the values of a and b. You could begin by solving either of the two equations for a or b, and then substituting the solution into the other equation. But note that the question asks for the value of a + b, so check to see if there’s a faster way: Could you stack and add (or subtract) the equations? If you stack and add the equations, you get 7a + 7b = 77. Now divide both sides of the equation by 7, resulting in a + b = 11. This is (D).

When a function f(x) is transformed into a function of the form f(ax), where a is a constant, if a > 0, the function will be compressed horizontally by a factor of a. Here, y = x² + 4 can be represented as the parent function, and y = 3x² + 4 as the transformed function compressed horizontally versus the parent function, and thus narrower, by a factor of 3. This is (D). If you’re not sure, try plugging values into each equation to construct a rough graph of each equation and compare them.

Rearranging and factoring the expression provided in the question, we have t² – 4t – 90 = 6 → t² – 4t – 96 = 0 → (t – 12)(t + 8) = 0. Therefore, t – 12 = 0 and t + 8 = 0. t must then equal 12 or -8. If t represents the number of tickets Steven buys, then only t = 12 is consistent with the context of the question. If each ticket costs $80, Steven must have spent $80*12 = $960. This is (C).

We must find values of c and d by solving the system of equations in order to determine the value of 4c – 4d. There are several ways to go about this. One way is to multiply the terms of the equation 2c + 3d = 17 by -3 to get -6c – 9d = -51 . If you stack and add this equation with the second equation, the result is -4d = -12, which solves to d = 3. Plug this value for d into the equation 6c + 5d = 39 to get 6c + 15 = 39, so 6c = 24 and c = 4. Therefore, 4c – 4d = 4(4) – 4(3) = 16 – 12 = 4. This is (C).