Question 1

Given the triangle with angles $$(x-10)^{\circ}$$, $$(3x-155)^{\circ}$$, and $$\left(\frac{1}{4}x+22\$$right)^{\circ}$$, what is the value of x$?

Accepted Answer

$$x = 90$$

Question 2

Which graph correctly represents a circle with center $$(4, 3)$$ and radius $$3$$?

Accepted Answer

The circle centered at $$(4, 3)$$

Question 3

Given the table of values: $$\begin{array}{cc} x & y \ 0 & 0 \ -19 & 19 \ -41 & 41 \end{array}$$, does this relation represent a function? What are its domain and range?

Accepted Answer

Function; domain: $$\{0, -19, -41\}$$; range: $$\{0, 19, 41\}$$

Question 4

If $$g(x) = 6$$^{-x}$$ is graphed, how does its graph compare to y = 6^x$?

Accepted Answer

Reflected across the $$y-$$axis

Question 5

Determine the value of the expression $$-|9.4|.$$

Accepted Answer

$$-9.4$$

Question 6

Solve the quadratic equation $$2x^2 + 7x + 3 = 0$ using the zero-factor property.

Accepted Answer

$$x = -3, x = -\frac{1}{2}$$

Question 7

Calculate the product $$(2 - 3i)(2 + 3i)$$ and express your answer in standard form.

Accepted Answer

$$-13$$

Question 8

For an angle of $$8^{\circ}$$, what are the measures of its complement and supplement?

Accepted Answer

Complement: $$82^{\circ}$$, Supplement: $$172^{\circ}$$

Question 9

Which of the following sets of positive and negative angles is coterminal with $$270^{\circ}$$?

Accepted Answer

$$630^{\circ}$$ and $$-90^{\circ}$$

Question 10

Angles $$A$$ and $$B$$ are complementary, with $$A = 4x - 7$$ and $$B = 11x - 53. $$What are the measures of $$A$$ and $$B$$?

Accepted Answer

$$A = 33$$^{\circ}$$, B$$ = $$57^{\circ}$$

Question 11

Convert $$\frac{\pi}{5}$$ radians to degrees.

Accepted Answer

$$40^{\circ}$$

Question 12

A circle is centered at $$(-4, 3)$$ with radius $$3. $$Which equation represents this circle?

Accepted Answer

$$(x + 4)^2$ + (y - 3)^2$ = 9$$

Question 13

If the external pressure $$P_{ext} on a $$planet is given by $$P_{ext} = 1.153 - 0.012h$$, where $$h is $$the vertical distance in units of $$10,000$$ meters, what is the pressure at $$h = 8.3$$?

Accepted Answer

$$0.153$$ atm

Question 14

Which transformation occurs when the function $$f(x) is $$replaced by $$f(-x)$$?

Accepted Answer

Reflection across the $$y-$$axis

Question 15

A real-world application: A satellite orbits a planet in a circular path with center at $$(0, 0)$$ and radius $$r = 6. $$What is the equation of its orbit?

Accepted Answer

$$x^2$$ + $$y^2 = 36$

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