Question 1

Solve the equation $$|5x + 8| = |3 - x|. $$Which of the following is a solution?

Accepted Answer

$$x = -\frac{11}{6}$$

Question 2

Solve the inequality $$|6x + 5| \u003e 3$$ and express the solution in interval notation.

Accepted Answer

$$(-\infty, -\frac{4}{3}) \cup (-\frac{1}{3}, \infty)$$

Question 3

Given the quadratic equation $$5x^2 + 3x - 1 = 0$, what is the value of the discriminant, and what does it tell you about the solutions?

Accepted Answer

Discriminant is $$29$$, so there are two real solutions.

Question 4

Solve the quadratic equation $$5x^2 + 3x - 1 = 0$ and choose the correct exact solution.

Accepted Answer

$$x = \frac{-3 \pm \sqrt{29}}{10}$$

Question 5

A weight measured in kilograms $$x is $$proportional to a weight measured in pounds $$y$$, with $$1 kg$$ $$= 2.20 lb. $$Which equation correctly relates $$x$$ and $$y$$?

Accepted Answer

$$y = 2.20x$$

Question 6

Using the conversion $$y = 2.20x$$, how many kilograms is $$164$$ pounds? (Round to two decimal places.)

Accepted Answer

$$74.55 kg$$

Question 7

Find the equation of the line passing through $$(4, -3)$$ and $$(-8, 2) in $$standard form.

Accepted Answer

$$5x + 12y = 8$$

Question 8

A laboratory is monitoring cell growth with $$P(t) = 300e$$^{0.32t}$$. How many days will it take for there to be 880$ cells? (Round to one decimal place.)

Accepted Answer

$$t = 3.4$$ days

Question 9

Solve for $$x in$$ $$\ln(4x) - \ln(x - 10) = 7. $$Round your answer to two decimal places.

Accepted Answer

Question 10

Simplify $$(x + 20i)(x - 20i)$$ and write your answer in the form $$a + bi.$$

Accepted Answer

$$x^2 - 400$

Question 11

Which of the following best describes the solution set to $$|6x + 5| \u003e 3$$?

Accepted Answer

All $$x$$ such that $$x  -\frac{1}{3}$$

Question 12

If $$P(t) = 300e$$^{0.32t}$$ models cell growth, which equation would you solve to find the time t$ when there are N$ cells?

Accepted Answer

$$N = 300e$$^{0.32t}$$

Question 13

Given $$\ln(4x) - \ln(x - 10) = 7$$, which of the following is the correct first algebraic step to isolate $$x$$?

Accepted Answer

$$\ln\left(\frac{4x}{x - 10}\right) = 7$$

Question 14

Which of the following is the correct discriminant for the quadratic equation $$5x^2 + 3x - 1 = 0$?

Accepted Answer

$$3^2 - 4$$ \cdot 5 \cdot (-1) = 29$$

Question 15

If $$|5x + 8| = |3 - x|$$, which of the following is a possible value for $$x$$?

Accepted Answer

$$x = -\frac{11}{6}$$

Question 16

A patient’s medication dosage is proportional to their weight in kilograms. If a patient weighs $$164$$ pounds, what is their weight in kilograms? (Use $$1 kg$$ $$= 2.20 lb$$, round to two decimal places.)

Accepted Answer

$$74.55 kg$$

Question 17

Which of the following is the standard form of the equation of the line passing through $$(4, -3)$$ and $$(-8, 2)$$?

Accepted Answer

$$5x + 12y = 8$$

Step-by-Step Guidance for MAT 2240 Section 1.2 Homework (Precalculus/Algebra)

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