Math help

Math 012 Spring 2019 Midterm

Page 1

1 Solve the equation below. Show all work following the methods discussed in class. If the equation has a unique solution, please show the complete check of your answer.

7(4x + 5) = −5 + 8(8x − 4)

2 Solve the equation below. Show all work following the methods discussed in class. If the equation has a unique solution, please show the complete check of your answer.

48 − 5(1− n) = 3(4 − 2n)− 2

3 Solve the equation below. Show all work following the methods discussed in class. If the equation has a unique solution, please show the complete check of your answer.

5( y + 4)− 2(1− 3y) =11y − 7

4 Solve the equation below. Show all work following the methods discussed in class. If the equation has a unique solution, please show the complete check of your answer.

17 m + 1 = 2 m + 29 5 3 5 6

5 If there are 435 Members of Congress and 57 more Republicans than Democrats, how many of each party are there, assuming that there are no Independents?

6 Janet set off on a bicycle trip at 6:30 am at an average rate of 24 miles per hour. Her husband, Bob, promised to bring her some lunch, and he set off by car 2 hours after Janet left, driving at an average speed of 40 miles per hour. At what time did Bob catch up with Janet?

7 Solve the inequality below. Write the solution set using interval notation and graph the solution set on a number line.

9x − 3 ≤17x −19

8 Solve the compound inequality below. Write the solution set using interval notation and graph the solution set on a number line.

−23 ≤ 7x − 2 <12

Math 012 Fall 2018 Midterm

Page 2

9 Find at least three ordered pairs that satisfy the following equation and graph the line through them. Show all work.

3x + 2 y =12

10 Find at least three ordered pairs that satisfy the following equation and graph the line through them. Show all work.

x − 2 y = 8

11 Draw the line through the point (4, 5) that is parallel to the y-axis. Write the equation of this line and state its slope.

12 Given the linear equation 7x − 5 y = −15 , find the slope and y-intercept of the line. Write the slope in simplest form and the y-intercept as an ordered pair. Show all work.

13 Given the points (-3, 5) and (6, -2):

a) Find the slope of the line through the points.

b) Write an equation in point-slope form of the line through the points.

c) Convert the equation to slope-intercept form.

d) Convert the equation to standard form, Ax + By = C, where A, B, and C are integers.

e) Graph the equation.

14 Write an equation in point-slope form of the line through the point (-5, 2) perpendicular to the line with equation 4x + 3y = 7.

15 The number of Starbucks stores in the US in 2005 was 8896. In 2014, there were 11,965

Starbucks stores in the US. Let y be the number of Starbucks stores in the US in the year x, where x = 0 represents the year 2005.

• Write a linear equation in slope-intercept form that models the growth in the number of Starbucks stores in the US in terms of x. [Hint: the line must pass through the points (0, 8896) and (9, 11965)].

• Use this equation to predict the number of Starbucks stores in the US in the year 2020.

Math 012 Fall 2018 Midterm

Page 3

16 Answer each of the questions below:

• Write the number in scientific notation: 2,354,107

• Write the number in scientific notation: 0.0512

2) 17 Simplify. Write the answer using positive exponents only.

(3x7 y8 ) (5x9 y12 ) =

18 Simplify. Write the answer using positive exponents only.

(2x5 y−3 ) 4 =

19 Perform the indicated operations and simplify:

(9x2 + 2x + 3) − (4x2 + 3x − 7) = 20 Perform the indicated operations and simplify:

(5x − 3) (8x2 − 4x +15) =