Question 1

A scientist records the mass of a sample as $$0.000045$$ grams. Express this mass in scientific notation.

Accepted Answer

$$4.5 	imes 10$$^{-5}$$

Question 2

Which of the following is the result of $$(3x^2 - 2x + 5$$) + $$(4x^2 + x - 3$$)$$?

Accepted Answer

$$7x^2 - x + 2$

Question 3

A pharmaceutical company needs to factor the polynomial $$x^2 - 9x + 20$ to determine the optimal dosage formula. What is the correct factorization?

Accepted Answer

$$(x - 4)(x - 5)$$

Question 4

Simplify the rational expression $$\frac{6x^2$}{3x}.$$

Accepted Answer

$$2x$$

Question 5

A medical researcher combines two solutions. The concentrations are represented by $$\frac{2}{x}$$ and $$\frac{3}{x}. $$What is the sum of these concentrations?

Accepted Answer

$$\frac{5}{x}$$

Question 6

Solve the linear equation for $$x$$: $$5x - 7 = 3x + 9.$$

Accepted Answer

$$x = 8$$

Question 7

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

Accepted Answer

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

Question 8

Use the quadratic formula to solve $$x^2 + 4x - 5 = 0$.

Accepted Answer

$$x = 1$$ and $$x = -5$$

Question 9

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

Accepted Answer

$$8 - 2i$$

Question 10

Solve the equation by factoring: $$x^2 - 16 = 0$.

Accepted Answer

$$x = 4$$ and $$x = -4$$

Question 11

A company needs to ensure a safety margin for a chemical reaction. If the inequality $$2x - 5 \u003c 9$$ must be satisfied, what is the range of possible values for $$x$$?

Accepted Answer

$$x \u003c 7$$

Question 12

Find the equation of the line passing through $$(2, 3)$$ with slope $$m = 4$$ using the point-slope form.

Accepted Answer

$$y - 3 = 4(x - 2)$$

Question 13

Given the line $$y = 2x + 5$$, what is the equation of a line parallel to it passing through $$(1, -3)$$?

Accepted Answer

$$y + 3 = 2(x - 1)$$

Question 14

Given the line $$y = -\frac{1}{2}x + 4$$, what is the equation of a line perpendicular to it passing through $$(0, 2)$$?

Accepted Answer

$$y - 2 = 2x$$

Question 15

A biologist needs to multiply two rational expressions: $$\frac{x}{x+2} 	imes \frac{x+2}{x-3}. $$What is the simplified result?

Accepted Answer

$$\frac{x}{x-3}$$

Question 16

Subtract the rational expressions: $$\frac{5}{x} - \frac{2}{x}.$$

Accepted Answer

$$\frac{3}{x}$$

Question 17

A chemical engineer needs to factor $$x^2 - 25$ to determine the volume of a container. What is the correct factorization?

Accepted Answer

$$(x - 5)(x + 5)$$

Question 18

Solve for $$x in $$the quadratic equation $$2x^2 - 8x = 0$ by factoring.

Accepted Answer

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

Question 19

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

Accepted Answer

$$8 - i$$

Question 20

A business needs to solve the inequality $$3x + 2 \geq 11 to $$determine minimum production levels. What is the solution?

Accepted Answer

$$x \geq 3$$

College Algebra: Review and Foundations Study Notes

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