Question 1

A biologist is studying the population of bacteria in a petri dish. The population is estimated to be $$3.2 	imes 10^7$ at noon and 1.6$$ 	imes $$10^8 at 6 PM. $$What is the ratio of the population at 6 PM to that at noon, expressed in scientific notation?

Accepted Answer

$$5 	imes 10^0$

Question 2

Which of the following is the correct result of $$\$$left(2x^2$$ - 3x + 4\right) + \$$left(5x^2$$ + 7x - 6\right)$$?

Accepted Answer

$$7x^2 + 4x - 2$

Question 3

A chemical company needs to factor the polynomial $$6x^2 - 11x - 10$ to determine the possible concentrations of a solution. Which of the following is the correct factorization?

Accepted Answer

$$(2x + 5)(3x - 2)$$

Question 4

Simplify the following rational expression: $$\dfrac{3x^2$}{4y} \div \dfrac{9x}{2y^2$}$$

Accepted Answer

$$\dfrac{2x}{3y^2$}$$

Question 5

A pharmacist needs to combine two solutions. Simplify the sum: $$\dfrac{2}{x} + \dfrac{3}{x+1}$$

Accepted Answer

$$\dfrac{2(x+1) + 3x}{x(x+1)}$$

Question 6

Solve for $$x$$: $$5x - 3 = 2x + 9$$

Accepted Answer

$$x = 4$$

Question 7

A projectile's height is modeled by $$h(t) = t^2$ - 5t + 6. At $$what times $$t$$ does the projectile hit the ground? (Solve by factoring.)

Accepted Answer

$$t = 2$$ and $$t = 3$$

Question 8

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

Accepted Answer

$$x = 3,\ x = -1$$

Question 9

Simplify $$(-3 + 4i) + (2 - 7i).$$

Accepted Answer

$$-1 - 3i$$

Question 10

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

Accepted Answer

$$11 - 2i$$

Question 11

Solve by factoring: $$x^2 - 7x + 12 = 0$

Accepted Answer

$$x = 3,\ x = 4$$

Question 12

Solve the inequality: $$2x - 5 \u003c 7$$

Accepted Answer

$$x \u003c 6$$

Question 13

Find the equation of the line passing through $$(2, 5)$$ with slope $$-3 ($$point-slope form).

Accepted Answer

$$y - 5 = -3(x - 2)$$

Question 14

Find the equation of the line parallel to $$y = 2x - 7$$ that passes through $$(1, 4).$$

Accepted Answer

$$y = 2x + 2$$

Question 15

Find the equation of the line perpendicular to $$y = -\dfrac{1}{2}x + 3$$ and passing through $$(4, -1). $$Write your answer in slope-intercept form.

Accepted Answer

$$y = 2x - 9$$

Question 16

A medical researcher is analyzing the concentration of a drug, modeled by $$C(t) = \dfrac{5t}{t+2}. $$What is $$C(2)$$?

Accepted Answer

$$5$$

Question 17

Simplify the expression: $$\dfrac{x^2$ - 9}{x^2$ - 6x + 9}$$

Accepted Answer

$$\dfrac{(x + 3)(x - 3)}{(x - 3)^2$}$$

Question 18

A company’s profit $$P is $$given by $$P = 2x^2$ - 8x. $$Factor the expression to find the values of $$x$$ for which the profit is zero.

Accepted Answer

$$x = 0$$ and $$x = 4$$

Question 19

A student is asked to multiply $$\dfrac{2x}{x+1} \cdot \dfrac{x+1}{3x}$$ and simplify the result.

Accepted Answer

$$\dfrac{2}{3}$$

Question 20

Solve for $$x$$: $$x^2 + 2x + 5 = 0$

Accepted Answer

$$x = -1 \pm 2i$$

College Algebra: Review and Foundations Study Notes

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