Question 1

A chemist plots the temperature (in °C) versus time (in minutes) for a reaction. The data point (15, 60) is on the graph. What does this point represent?

Accepted Answer

At 60 minutes, the temperature was 15°C.

Question 2

A line passes through the points $$(2, 3)$$ and $$(6, 11). $$What is the equation of the line in slope-intercept form?

Accepted Answer

$$y = 2x - 1$$

Question 3

A business tracks its profit using the equation $$y = 5x + 200$$, where $$y is $$profit in dollars and $$x is $$the number of products sold. What is the $$y-$$intercept, and what does it represent?

Accepted Answer

$$200$$, representing the initial profit when no products are sold.

Question 4

Solve the linear equation for $$x$$: $$\frac{2x}{3} - 4 = 6$$

Accepted Answer

$$x = 15$$

Question 5

A medical researcher uses the formula $$C = 2A + 3B to $$calculate a patient's risk score. Solve for $$A in $$terms of $$C$$ and $$B.$$

Accepted Answer

$$A = \frac{C - 3B}{2}$$

Question 6

Add the complex numbers: $$(4 + 3i) + (2 - 5i)$$

Accepted Answer

$$6 - 2i$$

Question 7

Multiply the complex numbers: $$(2 + 3i) 	imes (1 - 4i)$$

Accepted Answer

$$14 - 5i$$

Question 8

Solve the quadratic equation by factoring: $$x^2 - 5x + 6 = 0$

Accepted Answer

$$x = 2 or$$ $$x = 3$$

Question 9

Solve the quadratic equation by completing the square: $$x^2 + 6x + 5 = 0$

Accepted Answer

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

Question 10

Use the quadratic formula to solve $$2x^2 - 4x - 6 = 0$.

Accepted Answer

$$x = 3 or$$ $$x = -1$$

Question 11

A quadratic equation $$x^2 + 4x + 4 = 0$ has a discriminant of 0$. What does this mean about its solutions?

Accepted Answer

There is one real solution.

Question 12

Solve the radical equation: $$\sqrt{x + 5} = 4$$

Accepted Answer

$$x = 11$$

Question 13

A company wants to find the intersection of the intervals $$[2, 8]$$ and $$[5, 10]. $$What is the intersection?

Accepted Answer

$$[5, 8]$$

Question 14

Solve the linear inequality: $$3x - 7 \u003c 8$$

Accepted Answer

$$x \u003c 5$$

Question 15

A biologist models the population of bacteria with $$P = 1000 + 50t$$, where $$t is $$time in hours. After how many hours will the population reach $$1500$$?

Accepted Answer

$$t = 10$$

Question 16

Divide the complex numbers: $$\frac{6 + 2i}{2 - i}$$

Accepted Answer

$$2 + 2i$$

Question 17

A car rental company charges according to the equation $$C = 40d + 100$$, where $$C is $$the total cost and $$d is $$the number of days rented. If the total cost is $$220$$, how many days was the car rented?

Accepted Answer

$$d = 3$$

Question 18

Solve the quadratic equation by any method: $$x^2 - 8x + 16 = 0$

Accepted Answer

$$x = 4$$

Question 19

A scientist measures the concentration of a solution over time and finds it follows the equation $$C = 5t + 20. $$What is the $$x-$$intercept of this equation?

Accepted Answer

$$t = -4$$

Chapter 1 Study Guide: Equations, Graphs, and Complex Numbers

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