Question 1

Which of the following is the correct interval notation for the solution set of the inequality $$2x - 5 \leq 7$$?

Accepted Answer

$$(-\infty, 6]$$

Question 2

A function $$f is $$defined as $$f(x) = 3x^2$ - 2x + 5. $$What is $$f(-2)$$?

Accepted Answer

$$f(-2) = 17$$

Question 3

Which of the following equations represents a line parallel to $$y = -2x + 3$$ and passing through the point $$(1, 4)$$?

Accepted Answer

$$y = -2x + 6$$

Question 4

Solve the system of equations: $$\begin{cases} 2x + 3y = 7 \ x - y = 1 \end{cases}$$

Accepted Answer

Question 5

Which of the following is the simplified form of the expression $$\dfrac{2x^2$ - 8}{4x}$$ for $$x 
eq 0$$?

Accepted Answer

$$\dfrac{x - 2}{2}$$

Question 6

A chemist needs to mix a $$20\%$$ saline solution with a $$50\%$$ saline solution to obtain $$10$$ liters of a $$30\%$$ solution. How many liters of the $$20\%$$ solution should be used?

Accepted Answer

$$6.67$$ liters

Question 7

Which of the following is the correct solution to the equation $$|3x - 2| = 7$$?

Accepted Answer

$$x = 3,\ x = -\dfrac{5}{3}$$

Question 8

Simplify the expression $$\sqrt{50} + 2\sqrt{8}.$$

Accepted Answer

$$5\sqrt{2} + 4\sqrt{2} = 9\sqrt{2}$$

Question 9

Which of the following is the correct factorization of $$x^2 - 9x + 20$?

Accepted Answer

$$(x - 4)(x - 5)$$

Question 10

Solve for $$x$$: $$\dfrac{3}{x} + 2 = 5$$

Accepted Answer

Question 11

Which of the following is the solution to the quadratic equation $$x^2 + 4x + 5 = 0$?

Accepted Answer

$$x = -2 \pm i$$

Question 12

A piecewise function is defined as $$f(x) = \begin{cases} x + 2 & x \u003c 0 \ 2x - 1 & x \geq 0 \end{cases}. $$What is $$f(-3) + f(2)$$?

Accepted Answer

$$(-3) + 2 + 2(2) - 1 = -1 + 3 = 2$$

Question 13

Which of the following is the simplified form of $$\dfrac{5x^2$y}{10xy^2$}$$ for $$x, y 
eq 0$$?

Accepted Answer

$$\dfrac{x}{2y}$$

Question 14

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

Accepted Answer

$$f(g(3)) = 2 \cdot 9 + 1 = 19$$

Question 15

Which of the following is the correct solution to the radical equation $$\sqrt{x + 5} = x - 1$$?

Accepted Answer

Question 16

A quadratic function models the height $$h (in $$meters) of a ball $$t$$ seconds after it is thrown: $$h(t) = -4.9t^2$ + 14t + 2. $$What is the maximum height reached by the ball?

Accepted Answer

$$h = 22$$ meters

Question 17

Simplify the expression $$(2 + 3i)(1 - 4i)$$, where $$i is $$the imaginary unit.

Accepted Answer

$$2 - 8i + 3i - 12i^2$ = 2 - 5i + 12 = 14 - 5i$$

Question 18

Which of the following is the correct solution to the inequality $$x^2 - 4x$$ \u003e 0$$?

Accepted Answer

$$x  4$$

Question 19

Which of the following is the correct simplified form of $$(x^{1/2}y$$^{1/3}$$)^6$$?

Accepted Answer

$$x^3y^2$

Intermediate Algebra Syllabus and Course Structure Study Guide

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