Question 1

Which of the following is the correct solution to the linear equation $$2x + 3 = 0$$?

Accepted Answer

$$x = -\dfrac{3}{2}$$

Question 2

A chemist needs to dilute a solution so that the final concentration is 5%. If she has 100 mL of a 20% solution, how much water should she add to achieve the desired concentration? (Let $$x be $$the amount of water added in mL.)

Accepted Answer

$$x = 300$$

Question 3

Solve for $$x in $$the equation $$\dfrac{3x - 6}{8} = 5 - \dfrac{1}{4}(x - 4).$$

Accepted Answer

$$x = 8$$

Question 4

A patient is prescribed a medication that requires the dosage to be calculated by the formula $$D = 2w + 5$$, where $$D is $$the dosage in mg and $$w is $$the patient's weight in kg. If the patient weighs 70 kg, what is the correct dosage?

Accepted Answer

$$D = 145 mg$$

Question 5

Which of the following is the solution to the equation $$\dfrac{4x + 3}{4} = 2x - x$$?

Accepted Answer

$$x = -3$$

Question 6

A business has fixed costs of $$\500$ and variable costs of $$\$$20$$ per unit produced. If the total cost is $$\900$, how many units were produced?

Accepted Answer

$$20$$

Question 7

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

Accepted Answer

Question 8

Which of the following is the correct solution to the quadratic equation $$x^2 - 6x + 8 = 0$?

Accepted Answer

$$x = 2 or$$ $$x = 4$$

Question 9

A car rental company charges a flat fee of $$\50$ plus $$\$$0.20$$ per mile driven. If a customer paid $$\90$, how many miles did they drive?

Accepted Answer

$$200$$

Question 10

Solve for $$x in $$the equation $$x^2 = 3x + 18$.

Accepted Answer

$$x = 6 or$$ $$x = -3$$

Question 11

A biologist is studying a population that doubles every year. If the initial population is 100, after how many years will the population reach 800?

Accepted Answer

$$4$$

Question 12

Which of the following is the correct solution to $$x^2 - 4x - 5 = 0$?

Accepted Answer

$$x = 5 or$$ $$x = -1$$

Question 13

A pharmacist needs to mix a 10% saline solution with a 30% saline solution to obtain 100 mL of a 25% solution. How many mL of the 30% solution should be used?

Accepted Answer

$$75 mL$$

Question 14

Solve for $$x in $$the equation $$x^2 + 3x - 18 = 0$.

Accepted Answer

$$x = 3 or$$ $$x = -6$$

Question 15

A company’s revenue $$R (in $$dollars) is given by $$R = 50x - 200$$, where $$x is $$the number of units sold. If the company wants to break even (i.e., $$R = 0$$), how many units must be sold?

Accepted Answer

Question 16

Which of the following is the correct solution to $$x^2 + 3x - 18 = 0$?

Accepted Answer

$$x = 3 or$$ $$x = -6$$

Question 17

A student borrows $$\500$ at an annual simple interest rate of 6%. How much will the student owe after 3 years?

Accepted Answer

$$\590$

Question 18

Solve for $$x in $$the equation $$\dfrac{2x + 3}{4} = \dfrac{x - 2}{2}.$$

Accepted Answer

$$x = 7$$

Question 19

A rectangle has a length that is 3 times its width. If the perimeter is 48 units, what is the area of the rectangle?

Accepted Answer

$$216$$

Question 20

Which of the following is the correct solution to $$x^2 - 9 = 0$?

Accepted Answer

$$x = 3 or$$ $$x = -3$$

Solving Linear and Quadratic Equations

Guida di studio - Domande di pratica

Study guide - Flashcard