In Problems 1-15, Find the Slope, the Equation of the Line, Or X-And Y-Intercepts
Math 060 Final Exam Review
In problems 1-15, find the slope, the equation of the line, or x-and y-intercepts.
1. Find the slope of a line passing through and
2. Find the slope of a line passing through and .
3. Write the equation of the line in slope-intercept form that passes through the points and .
4. Find the equation of the line passing through and . Write your answer in slope-intercept form if possible.
5. Find the equation of the line passing through and . Write your answer in slope-intercept form if possible.
6. Write the equation of the line in point-slope form that passes through and is perpendicular to the line .
7. Find the equation of the line that passes through the point and is parallel to the line . Write your answer in slope-intercept form.
8. Find the equation of the line that passes through the point and is perpendicular to the line .
9. Graph the line by using the x- and y-intercepts.
10. Graph the line using the slope and y-intercept.
11. Graph the line with x-intercept – 2 and slope = .
12. State the slope, -intercept, and -intercept of . Then graph the line.
13. State the slope, -intercept, and -intercept of . Then graph the line.
14. State the slope, -intercept, and -intercept of . Then graph the line.
15. The cost to rent a car for a day is $53 plus $0.62 for each mile driven. The total cost, , is given by the equation , where represents the total number of miles driven.
a) How much will it cost to drive the car 50 miles?
b) If you have $75.32 to spend on renting the car, how far will you be able to drive it?
In problems 16- 35, perform the given operation. Make sure to simplify your answers. Write your final answers with positive exponents.
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34. long division
35. long division
In problems 36 - 40, simplify the given expression. Write the answer in scientific notation.
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In problems 41 – 79, factor completely. If it cannot be factored, state that it’s prime.
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In Problems 80-88, perform the indicated operations with rational expressions and simplify your answers as much as possible.
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In problems 89 – 94, solve the system of equations using the indicated method. Write answers as an ordered-pair (x,y). If there are infinitely many solutions or no solution, state this.
89. Solve by graphing.
90. Solve by graphing.
91. Solve by using substitution.
92. Solve by using elimination.
93. Solve by either substitution or elimination.
94. Solve by either substitution or elimination.
In problems 95 – 110, solve the given equation. Remember to check your answers for possible extraneous solutions, when necessary.
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109. Solve for C:
110. Solve for y:
In problems 111- 115, solve each inequality, graph it, and write the solution set using interval notation.
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In Problems 116-130, solve each word problem by setting up the equation first.
116. When 30 is subtracted from seven-eighths of a number, the result is equal to one-half of the number. What is the number?
117. Peanuts sell for $4.00 per pound. Almonds sell for $6.50 per pound. How many pounds of each type should be mixed together to make a 5-pound mixture that sells for $5 per pound?
118. Two cars travel the same route, both leaving from the same point. The slower car averages 40 miles per hour, and the faster car averages 50 miles per hour. If the faster car leaves 2 hours after the slower car, in how many hours will the faster car overtake the slower car?
119. Two cities are 400 miles apart. A car leaves one of the cities traveling toward the second city at 45 miles per hour. At the same time, a bus leaves the second city at 35 miles per hour. How long will it take for them to meet?
120. A passenger jet took three hours to fly 1800 miles in the direction of the jet stream. The return trip against the jet-stream took four hours. What was the jet's speed in still air and the jet-stream’s speed?
121. How many liters of a 50% alcohol solution must be added with 80 liters of a 20% alcohol solution to make a 40% alcohol solution?
122. How many milliliters of pure water must be added to 100 ml of a 7% iodine solution to make a 2% iodine solution?
123. Find the measure of the three interior angles of a triangle if the second is 9 degrees more than five times the first and the third is three times the measure of the first.
124. The sum of twice one number plus second number is fourteen. The first number plus three times the second number is twenty-two. Find these numbers.
125. Find the measure of two supplementary angles such that the larger angle is 5 degrees more than 4 times the smaller angle.
126. The length of a rectangular garden is 5 feet longer than the width. The area of the rectangle is 300 square feet. Find the length and the width.
127. Henry has $10,000 to invest. He invests the money in two different accounts, one expected to return 5% and the other expected to return 8%. If he wants to earn $575 for the year, how much should he invest at each rate?
128. The width of a rectangular carpet is 7 meters shorter than the length, and the diagonal is 1 meters longer than the length. What are the length and the width of the carpet?
129. A painter can paint a fence around a house in 6 hours. Working alone, the painter’s apprentice can paint the same fence in 10 hours. How many hours would it take them to do the job if they worked together?
130. Paul can paddle a kayak 15 miles upstream in the same amount of time it takes him to paddle a kayak 27 miles downstream. If the current is 2mph, what is Paul’s speed as he paddled downstream?