NC Math 3 EOC released #18-30

Which function does not have the set of all real numbers as its domain?

An equation is shown below.

$$9^{\left(-3x+2\right)}=48$$

What is the value of x to the nearest ten-thousandth?

The diagram below shows an angle, θ, graphed in the xy-coordinate plane. Segment RT is the initial side of the angle, and segment RM is the terminal side. Segments RT and RM are radii of the unit circle centered at the origin R(0, 0).

The x-coordinate of point M is $$-\frac{1}{2}$$ . What is the measure of θ to the nearest thousandth of a radian?

A function, f(x) = Asin(Bx) + H, has the following properties:

- a period of 6

- a minimum value of 2

- f(2.5) = 5

- A, B, and H are all positive constants

Place the correct values into the appropriate cells below that will create this function.

A = ​ (a)   B= ​ (b)   H= ​ (c)  

The vertices of a triangle are at (0, 0), (6, 6), and (9, 3). What is the volume, in cubic units, of the figure created by rotating the triangle about y = x?

In parallelogram MNPT, m<M = (6x+10) ° and m<N = (5x+10.5) ° .

How many degrees is ∠T ?

In rectangle FGHI, diagonals FH and GI intersect at E.

• IE = 3x + 4

• EG = 5x – 6

What is the length of FH ?

Triangle PMT is shown

mGH = x+ 3

mPG = 4x+1

mGJ = 2x-1

What is the measure of segment PG?

What is the length of a radius of the circle represented by the equation

$$x^2+y^2-4x-4y+4=0$$

David plans to cover the floor of his room with new material.

• The floor is an isosceles trapezoid whose bases are 16 feet and 26 feet and sides are 13 feet in length.

• Each piece of new material has an area of 2.5 square feet.

Assuming the pieces of new material can be cut as needed, how many pieces does David need?