Question 1

Which of the following is a linear equation in one variable?

Accepted Answer

$$x + 5 = 0$$

Question 2

A chemist needs to prepare 100 mL of a solution that is 30% acid by mixing a 20% acid solution and a 50% acid solution. Let $$x be $$the amount (in mL) of the 20% solution used. Which equation models this situation?

Accepted Answer

$$0.2x + 0.5(100-x) = 30$$

Question 3

Solve the equation $$2x - 5 = 9.$$

Accepted Answer

$$x = 7$$

Question 4

Which of the following steps is NOT a valid operation for producing an equivalent equation?

Accepted Answer

Multiplying both sides by zero

Question 5

A box is to be made by cutting equal squares from each corner of a square piece of metal with side $$x$$ meters and folding up the sides. If the box must have a volume of $$500 m$^3$$ and the height is $$5 m$$, what equation must $$x$$ satisfy?

Accepted Answer

$$5(x-5)^2 = 500$

Question 6

Which of the following quadratic equations has no real solutions?

Accepted Answer

$$x^2 + x + 1 = 0$

Question 7

If $$x^2 - 6x + 9 = 0$, what is the solution set?

Accepted Answer

$$\{3\}$$

Question 8

A worker is paid $$1.5$$ times the regular hourly wage for overtime and double time for Sundays. If she worked $$40$$ regular hours, $$6$$ overtime hours, and $$4$$ Sunday hours for a total of $$\1083$, what is her regular hourly wage?

Accepted Answer

$$\19.00$

Question 9

Solve the quadratic equation $$x^2 - 5x = 0$ by factoring.

Accepted Answer

$$x = 0 or$$ $$x = 5$$

Question 10

Which of the following is the correct quadratic formula for solving $$ax^2 + bx + c = 0$?

Accepted Answer

$$x = \frac{-b \pm \sqrt{b^2$ - 4ac}}{2a}$$

Question 11

What is the solution set for $$x^2 = -25$ in the complex number system?

Accepted Answer

$$\{-5i, 5i\}$$

Question 12

Which of the following statements about complex numbers is TRUE?

Accepted Answer

The product of a complex number and its conjugate is always a real number.

Question 13

What is the standard form of $$\frac{2 + 3i}{1 - i}$$?

Accepted Answer

$$\frac{5}{2} + \frac{7}{2}i$$

Question 14

If $$i is $$the imaginary unit, what is $$i^{23}$$?

Accepted Answer

$$-i$$

Question 15

Which of the following best describes the solutions to the equation $$x^2 + 2x + 6 = 0$?

Accepted Answer

Two complex conjugate solutions

Question 16

Convert $$68^{\circ}F$ to Celsius using the formula C$$ = \frac{5}{9}(F - 32)$$. What is the result?

Accepted Answer

$$20^{\circ}C$

Question 17

Which of the following is the principal square root of $$-36$$?

Accepted Answer

$$6i$$

Question 18

If $$z = 3 + 4i$$, what is $$z \cdot \overline{z}$$?

Accepted Answer

$$25$$

Question 19

Which of the following best describes the discriminant $$b^2 - 4ac$ of a quadratic equation ax^2$ + bx + c = 0$$?

Accepted Answer

All of the above are correct.

College Algebra: Equations and Inequalities – Study Notes

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