math

MATH 1314 – College Algebra Graded Homework 2 (Sections 2.1-2.7)

Due Friday, October 1, 2021

Write your solutions neatly on your own paper with your name at the top of the first page. Show all work to obtain full credit. Scan your work using a scanner or scanning application and save as a PDF. Submit the PDF via the ”Submit Assignments” folder in eLearning. 1. Answer the following parts using the figure below:

a) Determine the coordinates for points A, B, and C. b) Name the quadrant in which the points A, B, and C would be located. If the point is on an axis, name the axis. c) Find the distance between points A and C. d) Find the midpoint of the line segment that joins the points A and B.

2. Solve the following equations for x. State if there are any excluded values from the solution set.

a) 2𝑥(6𝑥 − 1) + 21 = 8𝑥 − 𝑥(3 − 12𝑥)

b) 5

𝑥 + 1 +

1

𝑥 − 3 =

−6

𝑥 2 − 2𝑥 − 3

3. Use the information below to find the equation of the line. Write all the final equations using the slope-intercept form, if possible.

a) passes through the points (-5, 7) and (1, -11)

c) parallel to 9𝑥 + 2𝑦 = 1 and passes through the point (6, -1)

d) perpendicular to 9𝑥 + 2𝑦 = 1 and passes through the point (6, -1)

e) the slope is undefined and it passes through the point (2, 3) 4. Perform the indicated operation and express the result as a simplified complex number. a) (−11 + 7𝑖)𝑖 7 − (−3 + 5𝑖)𝑖 8

b) (−8 + 3𝑖)(6 − 𝑖)

c) 5 − 4𝑖

2 + 7𝑖

5. Solve the following equations. a) 𝑥 2 − 4𝑥 − 20 = 3𝑥 + 24

b) 2𝑥 2 − 11𝑥 = −32

c) 𝑥 2

3 − 5𝑥 1

3 + 6 = 0

d) √1 + 3𝑥 = 4 + √5 − 𝑥 e) |3 − 4𝑥| = 10 6. Solve the following inequalities for x. a) 7𝑥 + 2(4 − 𝑥) < 12 − 3(5 + 6𝑥) b) 2𝑥 + 3 < 5𝑥 − 2 < 3𝑥 + 8 c) |2 − 7𝑥| ≥ 20 d) |4𝑥 + 2| < 9