Q: If $$b = s - |l + xz|$$, and $$s = 10$$, $$l = -2$$, $$x = 3$$, $$z = -4$$, what is the value of $$b$$?

$$b = 10 - |-2 + 3 \times -4| = 10 - |-2 - 12| = 10 - | -14 | = 10 - 14 = -4$$

Q: If $$S = 2c + xz$$, and $$c = 5$$, $$x = -2$$, $$z = 3$$, what is the value of $$S$$?

$$S = 2 \times 5 + (-2) \times 3 = 10 - 6 = 4$$

Q: A car’s value depreciates according to $$V(t) = 20,000(0.85)^t$$, where $$t is $$the number of years after purchase. What is the value after 3 years?

$$V(3) = 20,000 \times (0.85)^3$ \approx 12,282.5$$

Question 1

Given the equation $$g = 4 - x^2$, which of the following best describes the graph of g$?

Accepted Answer

A parabola opening downwards with vertex at $$(0, 4)$$

Question 2

Suppose the population of a bacteria culture is modeled by $$P(t) = 800e$$^{0.2t}$$, where t$ is in hours. What is the population after 5 hours?

Accepted Answer

$$P(5) = 800e$$^{1}$$ \approx 2171.47$$

Question 3

If $$b = s - |l + xz|$$, and $$s = 10$$, $$l = -2$$, $$x = 3$$, $$z = -4$$, what is the value of $$b$$?

Accepted Answer

$$b = 10 - |-2 + 3 	imes -4| = 10 - |-2 - 12| = 10 - | -14 | = 10 - 14 = -4$$

Question 4

Which of the following equations represents a line with slope $$m = 2$$ and $$y-$$intercept $$b = -3$$?

Accepted Answer

$$y = 2x - 3$$

Question 5

A chemical reaction's temperature $$T (in $$Celsius) over time $$t (in $$minutes) is modeled by $$T = 25 + 10\sin(\frac{\pi}{30}t). $$What is the maximum temperature reached during the reaction?

Accepted Answer

$$35$$ degrees Celsius

Question 6

Solve for $$x if$$ $$6 - x^2$ = 4x.$$

Accepted Answer

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

Question 7

Which of the following is the solution set for $$|2x - 5| = 9$$?

Accepted Answer

$$x = 7 or$$ $$x = -2$$

Question 8

A company’s profit $$P (in $$thousands of dollars) is given by $$P = -2x^2$ + 8x - 3$$, where $$x is $$the number of units sold (in thousands). What is the maximum profit, and for how many units sold does it occur?

Accepted Answer

Maximum profit is $$5$$ thousand dollars at $$x = 2$$ thousand units

Question 9

If $$p + x = o + \frac{x}{c}$$, solve for $$x in $$terms of $$p$$, $$o$$, and $$c.$$

Accepted Answer

$$x = \frac{o - p}{1 - \frac{1}{c}}$$

Question 10

A projectile is launched from the ground with height $$h(t) = -16t^2$ + 64t. At $$what time $$t$$ does it reach its maximum height?

Accepted Answer

$$t = 2$$ seconds

Question 11

Which of the following is the correct solution to the system: $$\begin{cases} x + y = 5 \ 2x - y = 1 \end{cases}$$?

Accepted Answer

$$x = 2$$, $$y = 3$$

Question 12

If $$f(x) = x^2$ - 4x + 7$$, what is the minimum value of $$f(x)$$?

Accepted Answer

$$3$$

Question 13

A medication is administered and its concentration in the bloodstream is modeled by $$C(t) = 50e$$^{-0.3t}$$, where t$ is in hours. What is the concentration after 4 hours?

Accepted Answer

$$C(4) = 50e$$^{-1.2}$$ \approx 15.06$$

Question 14

Which of the following is the solution to $$2^{x} = 32$?

Accepted Answer

$$x = 5$$

Question 15

If $$S = 2c + xz$$, and $$c = 5$$, $$x = -2$$, $$z = 3$$, what is the value of $$S$$?

Accepted Answer

$$S = 2 	imes 5 + (-2) 	imes 3 = 10 - 6 = 4$$

Question 16

A car’s value depreciates according to $$V(t) = 20,000(0.85)^t$$, where $$t is $$the number of years after purchase. What is the value after 3 years?

Accepted Answer

$$V(3) = 20,000 	imes (0.85)^3$ \approx 12,282.5$$

Question 17

Which of the following is the solution to $$\log_{3}(x) = 4$$?

Accepted Answer

$$x = 81$$

Question 18

If $$g = 4 - x^2$ and g = 0$, what are the possible values of x$?

Accepted Answer

$$x = 2 or$$ $$x = -2$$

Question 19

A student invests $$1000 in an $$account that earns $$5\%$$ annual interest compounded yearly. What is the amount after $$3$$ years?

Accepted Answer

$$A = 1000(1.05)^3$ \approx 1157.63$$

Study Notes: Equations and Inequalities in College Algebra

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