Q: A historical event is modeled by $$y = 9x - 4y = 9. If$$ $$x$$ represents years since 1900, what is the value of $$y$$ when $$x = 2$$?

$$y = \frac{9 - 9 \times 2}{4} = -\frac{9}{4}$$

Question 1

Solve the equation $$x - \frac{7}{8} = 3x + \frac{1}{10}. $$What is the value of $$x$$?

Accepted Answer

$$x = -\frac{39}{80}$$

Question 2

A chemical reaction is modeled by the equation $$-x = 1 - \frac{5(x-5)}{6}. $$What is the solution for $$x$$?

Accepted Answer

$$x = -93$$

Question 3

Solve the equation $$x + \frac{4}{5} = \frac{1}{7}x + \frac{1}{3}. $$What is the value of $$x$$?

Accepted Answer

$$x = \frac{49}{75}$$

Question 4

A business formula is given by $$4[3(x-13)-2(2x+2)- (x-6)-3(3x-4)] = 5. $$Solve for $$x.$$

Accepted Answer

$$x = \frac{131}{23}$$

Question 5

Given the function $$f(x) = \frac{8}{3}x - 8$$, find (a) the solution to $$f(x) = 0$$, (b) the $$x-$$intercept, and (c) the zero of $$f(x).$$

Accepted Answer

(a) $$x = 3$$; (b) $$x = 3$$; (c) $$x = 3$$

Question 6

A table shows $$f(x)$$ with $$x=6$$ and $$y_1=0$, and x=0$ and y_1$=-38. $$What is the $$x-$$intercept, $$y-$$intercept, and the solution to $$f(x)=0$$?

Accepted Answer

$$x-$$intercept: $$x=6$$, $$y-$$intercept: $$y=-38$$, solution: $$x=6$$

Question 7

A function $$f(x)$$ has a zero at $$x=40. $$Using the graph of $$y=f(x)$$, what is (a) the $$x-$$intercept and (b) the solution to $$f(x)=0$$?

Accepted Answer

(a) $$x=40$$; (b) $$x=40$$

Question 8

For the function $$f(x) = 190 + 20x$$, find (a) the zero of the function, (b) the $$x-$$intercept, and (c) solve $$f(x)=0.$$

Accepted Answer

(a) $$x = -9.5$$; (b) $$x = -9.5$$; (c) $$x = -9.5$$

Question 9

Solve the equation $$16x - 49 = 20 - 7x$$ using a graphical method. What is the value of $$x$$?

Accepted Answer

$$x = 3$$

Question 10

Solve the equation $$-4 = \frac{3t}{4} + \frac{8t-1}{3}$$ using a graphical method. What is the value of $$t$$?

Accepted Answer

$$t = -4$$

Question 11

Solve the formula $$G = P(1 + rt)$$ for $$t. $$What is the solution?

Accepted Answer

$$t = \frac{G - P}{Pr}$$

Question 12

Solve for $$x in $$the equation $$B + H = Mx. $$What is the solution for $$x$$?

Accepted Answer

$$x = \frac{M - Hy}{B}$$

Question 13

Solve for $$y in $$the equation $$9x - 4y = 9. $$What is the solution for $$y$$?

Accepted Answer

$$y = \frac{9 - 9x}{4}$$

Question 14

A company produces specialty golf hats. The profit function is $$P(x) = 20x - 2000. (a) $$How many hats must be produced and sold to earn a profit of $8000? (b) How many hats must be produced and sold to avoid a loss?

Accepted Answer

(a) $$500$$ hats; (b) $$100$$ hats

Question 15

Which of the following best describes the process for finding the $$x-$$intercept of a function $$f(x)$$?

Accepted Answer

Set $$f(x) = 0$$ and solve for $$x$$

Question 16

If a function $$f(x)$$ has an $$x-$$intercept at $$x=6$$, what does this mean in terms of the function's values?

Accepted Answer

$$f(6) = 0$$

Question 17

A medical dosage formula is $$D = C(1 + kt). If$$ $$D is $$the total dose, $$C is $$the initial concentration, $$k is $$the rate, and $$t is $$time, solve for $$t in $$terms of $$D$$, $$C$$, and $$k.$$

Accepted Answer

$$t = \frac{D - C}{Ck}$$

Question 18

A historical event is modeled by $$y = 9x - 4y = 9. If$$ $$x$$ represents years since 1900, what is the value of $$y$$ when $$x = 2$$?

Accepted Answer

$$y = \frac{9 - 9 	imes 2}{4} = -\frac{9}{4}$$

Step-by-Step Guidance for College Algebra: Solving Equations and Interpreting Functions

스터디 가이드 - 연습 문제

학습 가이드 - 플래시카드