Q: Which of the following systems of equations has no solution?

$$\begin{cases} x - y = 2 \\ 2x - 2y = 5 \end{cases}$$

Q: Which of the following is the correct result of applying one step of Gauss-Jordan elimination to the augmented matrix $$\begin{bmatrix} 1 & 2 & | & 5 \\ 2 & 4 & | & 10 \end{bmatrix}$$?

$$\begin{bmatrix} 1 & 2 & | & 5 \\ 0 & 0 & | & 0 \end{bmatrix}$$

Question 1

Which of the following systems of equations has no solution?

Accepted Answer

$$\begin{cases} x - y = 2 \ 2x - 2y = 5 \end{cases}$$

Question 2

Solve the following system using the substitution method: $$\begin{cases} x + 2y = 7 \ 3x - y = 5 \end{cases}$$

Accepted Answer

$$x = 3,\ y = 2$$

Question 3

Which of the following is the correct result of applying one step of Gauss-Jordan elimination to the augmented matrix $$\begin{bmatrix} 1 & 2 & | & 5 \ 2 & 4 & | & 10 \end{bmatrix}$$?

Accepted Answer

$$\begin{bmatrix} 1 & 2 & | & 5 \ 0 & 0 & | & 0 \end{bmatrix}$$

Question 4

What is the sum of the complex numbers $$3 + 4i$$ and $$2 - 5i$$?

Accepted Answer

$$5 - i$$

Question 5

Which of the following is a solution to the quadratic equation $$x^2 - 6x + 13 = 0$?

Accepted Answer

$$x = 3 + 2i$$

Question 6

A ball is thrown upward from the ground with an initial velocity of $$32 ft/s. $$Its height $$h (in $$feet) after $$t$$ seconds is given by $$h = -16t^2$ + 32t. $$After how many seconds does the ball hit the ground again?

Accepted Answer

$$2$$ seconds

Question 7

Solve for $$x$$: $$\sqrt{x + 5} = 3$$

Accepted Answer

$$x = 4$$

Question 8

Which of the following equations is quadratic in form?

Accepted Answer

$$x^4$$ - $$5x^2 + 6 = 0$

Question 9

Solve the rational equation: $$\frac{2}{x} + 1 = 3$$

Accepted Answer

$$x = 1$$

Question 10

Which of the following is the solution set for $$|2x - 5| = 7$$?

Accepted Answer

$$\left\{ 6, -1 \right\}$$

Question 11

Find the distance between the points $$A(2, 3)$$ and $$B(8, 7).$$

Accepted Answer

$$2\sqrt{10}$$

Question 12

What is the equation of a circle with center at $$(3, -2)$$ and radius $$5$$?

Accepted Answer

$$(x - 3)^2$ + (y + 2)^2$ = 25$$

Question 13

Given the function $$f(x) = \frac{1}{x-2}$$, what is the domain of $$f$$?

Accepted Answer

$$(-\infty, 2) \cup (2, \infty)$$

Question 14

If $$f(x) = 2x + 1$$ and $$g(x) = x^2$, what is (f$$ \circ g)(3)$$?

Accepted Answer

$$19$$

Question 15

Which of the following describes a function that is decreasing on its entire domain?

Accepted Answer

$$f(x) = -2x$$

Question 16

A quadratic equation models the height $$h (in $$meters) of a projectile: $$h = -4.9t^2$ + 19.6t + 2. $$What is the maximum height reached by the projectile?

Accepted Answer

$$21.6$$ meters

Question 17

Which of the following relations is NOT a function?

Accepted Answer

$$\{ (1,2), (2,3), (1,4) \}$$

Question 18

Solve for $$x$$: $$x^{2/3} = 16$

Accepted Answer

$$x = 64$$

Question 19

Which of the following best describes the range of the function $$f(x) = |x|$$?

Accepted Answer

$$[0, \infty)$$

Question 20

Given the points $$A(-1, 4)$$ and $$B(3, -2)$$, what is the midpoint of $$AB$$?

Accepted Answer

$$(1, 1)$$

College Algebra: Key Concepts and Methods Study Guide

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