18. It would be the second graph. The third graph is eliminated as the boy takes a time period to shave, which means there should be a constant point (horizontal line) right after the first incline. The first one is eliminated as the boy takes a bath which requires another constant point in the graph.

19.

C

E

D

A

B

**Answer:**

**Step-by-step explanation:**

The given triangle is a right triangle. This is indicated by the box around one of the angles, signifying that the angle measure is (9) degrees. By its definition, a right triangle is a triangle with a (90) degree angle, thus the given triangle is a right triangle. In this situation, one can use right-angle trigonometry to find the value of the unknown side. In essence, right triangle trigonometry provides one with a series of ratios to describe the relationship between the sides and angles of the right trinagle. These ratios are the following,

Keep in mind that the way a side is named is relative to the angle it is being described from. Thus, the (opposite) and (adjacent) sides acquire different names based on the angle relative to them. However, the (hypotenuse) is the hypotenuse no matter the angle, as the hypotenuse is the side opposite the right angle.

Solve for (y) first. One is given the angle measure and the measure of the side opposite the angle measure. One is asked to find the measure of the side adjacent to the angle. Use the ratio of tangent (tan) to achieve this.

Substitute,

Inverse operations,

Simplify,

Now solve for the hypotenuse (x). One could use the Pythagorean theorem to do this, but since this is trigonometry, one might as well use the trigonometric ratios. One is given an angle, as well as the side opposite the angle, one is asked to find the hypotenuse. To do this, one can use the trigonometric ratio of sine (sin).

Substitute,

Inverse operations,

Simplify,

Answer 1) both have spent $30 on the 5th day

9514 1404 393

**Answer:**

D There is an infinite number of solutions to the system of equations

**Step-by-step explanation:**

When you put the first equation in standard form by dividing it by 2, you get ...

x -2y = 4

When you put the second equation in standard form by dividing it by 8, you get ...

x -2y = 4

These are the same equation, so describe the same line. There are an infinite number of (x, y) pairs that will satisfy this equation.

**There is an infinite number of solutions**.

**Answer:**

5 + (-5) and 8 + (-8)

**Step-by-step explanation:**

Sum of zero means when you add them you get 0

so the others are wrong

-5 + (-5) = -10 because you have -5 and you add another -5

-12 + (-12) = -24 you start with -12 and you add another -12

Think of positive and negative numbers like floors in a building. Positive numbers are the stories and the negative numbers are the basement and sub-basement, zero is the ground level. So for 5 + (-5) you go up 5 floors, then you go down 5 floors. you end up on the ground level, 0.