Question 1

Solve for $$x in $$the equation $$23x - 5 = 12x - 3. $$Write your answer in solution set notation.

Accepted Answer

$$\{x = \frac{2}{11}\}$$

Question 2

Solve the formula $$E = z \cdot sn$$ for $$n.$$

Accepted Answer

$$n = \frac{E}{z s}$$

Question 3

Solve by factoring and using the Zero-Product Property: $$12x^2 - 41x + 24 = 0$. Which of the following is the correct solution set?

Accepted Answer

$$\left\{ x = \frac{8}{3},\ x = \frac{3}{4} \right\}$$

Question 4

Find the real solutions, if any, to the equation $$2x^2 - 6x + 1 = 0$ using the Quadratic Formula. Write your answer in solution set notation.

Accepted Answer

$$\left\{ x = \frac{6 \pm \sqrt{28}}{4} \right\}$$

Question 5

Use the discriminant to determine the nature of the solutions for $$4x^2 + 12x + 9 = 0$.

Accepted Answer

A repeated real solution

Question 6

Use the discriminant to determine the nature of the solutions for $$3x^2 - 2x + 10 = 0$.

Accepted Answer

No real solution

Question 7

Solve for $$x in $$the equation $$2x + 5 = x - 5. $$Write your answer in solution set notation.

Accepted Answer

$$\{x = -10\}$$

Question 8

Solve by factoring: $$3x^4$$ - $$48x^2 = 0$. Write your answer in solution set notation.

Accepted Answer

$$\{x = 0,\ x = 4,\ x = -4\}$$

Question 9

Solve the inequality $$-4x + 2 \geq 3x + 20. $$Write your answer in interval notation.

Accepted Answer

$$(-\infty, -\frac{18}{7}]$$

Question 10

Solve for $$x in $$the equation $$2x - 3 = 11. $$Write your answer in set notation.

Accepted Answer

$$\{x = 7\}$$

Question 11

Solve the inequality $$3x + 5 \u003c 17. $$Write your answer in interval notation.

Accepted Answer

$$(-\infty, 4)$$

Question 12

A chemical reaction requires the temperature $$T (in$$ $$^\circC) to $$satisfy $$2T - 3 \u003e 11$$ for the reaction to proceed safely. What is the minimum integer temperature at which the reaction can proceed?

Accepted Answer

$$T = 7$$

Question 13

A company’s profit $$P is $$modeled by $$P = 12x^2$ - 41x + 24$$, where $$x is $$the number of units sold (in thousands). For what values of $$x$$ does the company break even?

Accepted Answer

$$x = \frac{8}{3} or$$ $$x = \frac{3}{4}$$

Question 14

A ball is thrown upward and its height $$h (in $$meters) after $$t$$ seconds is given by $$h = -4.9t^2$ + 6t + 1. $$Use the discriminant to determine if the ball will ever reach the ground ($$h = 0).$$

Accepted Answer

The ball will reach the ground at two different times.

Question 15

A population model is given by $$P = 3x^4$ - 48x^2$. For which values of x$ is the population zero?

Accepted Answer

$$x = 0,\ x = 4,\ x = -4$$

Question 16

A student solves $$2x + 5 = x - 5$$ and gets $$x = 10. $$What mistake did the student most likely make?

Accepted Answer

Added $$5 to $$both sides instead of subtracting $$5$$ from both sides.

Question 17

A quadratic equation $$ax^2 + bx + c = 0$ has a discriminant b^2$ - 4ac = 0. $$What does this tell you about the solutions?

Accepted Answer

There is one repeated real solution.

Precalculus Test I: Step-by-Step Guidance and Solutions

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