Show:
Inequalities
Midpoint/Distance
Simplifying Radicals
Solving Equations
Linear Equations/Slope
100
Solve: x/2 + 3 ≥ 3x/2 - 5
8 ≥ x or x ≤ 8
100
What is the distance from 29/7 to 4/3? Round answer to the nearest hundredth.
2.81
100
Round the following numbers to the nearest hundredth then place in order from least to greatest. 9.526, 9.993, 9.091, 9.996, 9.523, 9.097
9.09, 9.10, 9.52, 9.53, 9.99, 10.00
100
Solve: 2(y+7) = (9y+8)/2
y=4
100
What is the slope of the line determined by the equation 9x+3y =12 ?
-3
200
Solve and graph the following compound inequality: 3x/4 +6.5 < 2 or 7x - 1 - 2x ≥ x - 5.
x < 6 or x ≥ -1 (See Graph.)
200
Point A is located at (-3,6) and point B is located at (5,22). What is the midpoint of AB?
(1, 14)
200
Evaluate the cube root of 26. Round answer to the nearest hundredth.
2.96
200
5. Harry is renting a U-Haul truck to move furniture from one place to another. There is an initial rental fee of $19.99, and an additional charge of $1.75 per mile that the truck is driven. This situation can be modeled by the equation C=1.75m + 19.99, where C represents the total cost of renting the truck, and m represents the number of miles Harry drives it. If Harry ends up paying a total of $81.24, how many miles did he drive the truck?
35 miles
200
What is the slope of the line determined by the points (-3, -6) and (5, -4)?
1/4
300
6. A shipping company charges a $4.25 flat fee in addition to $1.10 per pound. Hannah can spend no more than $20 on shipping a present to her aunt. This situation can be modeled by the inequality 1.10p + 4.25 ≤ 20, where p is the weight of the package in pounds. Rounded to the nearest hundredth of a pound, how heavy can the package be without exceeding Hannah’s spending limit?
14 lbs.
300
Point X is located at (2, -4) and point M is located at (6, 2). Point M is the midpoint of XY. What are the coordinates of Y?
(10, 8)
300
Simplify completely 2x sqrt(800 x^3 y^5)
40 x^2 y^2 sqrt(2xy)
300
The volume of a cone with a radius of 4 inches and a height of h inches is V = (π 4^2 h)/3 What is the height of the cone, in inches, when the volume is 48π inches ?
9
300
Jane is competing in a bicycle race. She rides at a pace of 3.9 minutes per mile. During the race, she stops and takes a break for 3 minutes. Write an equation to model this situation, where T represents the time spent biking, and m represents the number of miles Jane bikes.
T = 3.9m + 3
400
3(2/3)x - 9/2 > 6(2/3)x + 3/2
x < -2
400
Point R is located at (4a, b+3), point T is located at (a-2, 2b), and point S is located at (4, 6). Point S is the midpoint of RT. What are the values of a and b?
a=2 b=3
400
Evaluate 3 sqrt2 (4 - 2sqrt16)
-12 sqrt2
400
Nikola pays a monthly bill for electricity in his home. The cost of the monthly bill can be represented by the equation B=5.49 + 0.07u, where B represents the total bill and u represents the number of units of electricity used that month. Use the equation to fill in the missing information in the table.
July: B = $73.95 August: u = 914 September: u = 383
400
Ryan is planning a trip across the country. He has budgeted $300 for car rental. The cost of car rental is $25 per day and a service fee of $30. Write an inequality that models Ryan’s car rental expenses. What is the maximum number of days Ryan can afford to rent a car?
300 ≥ 25d + 30 10 days
500
6. Heather is going to the United Center to see a Bulls game. She has $75 in her pocket. Her ticket costs $59. Jumbo pretzels (which are Heather’s favorite snack inside the building) cost $5.99 each. Write an inequality that represents how many pretzels (p) Heather can buy inside the building if she has $75 and needs to buy a ticket first. And how many whole pretzels is Heather able to buy with the money she has and still have enough to buy a ticket?
75 ≥ 59 + 5.99p & 2 pretzels
500
What is the distance from (12, 9) to (7, -3)?
13
500
Simplify the following by rationalizing the denominator. 3/(5 + 2 sqrt3)
(15-6 sqrt3)/13
500
Solve for h: 4v/6h = 2mv/3
1/m
500
Ginny sells three flavors of ice cream cones in the park: vanilla, chocolate, and strawberry. Chocolate, the most popular flavor, sells for $1.29 per cone. Vanilla sells for $1.09 per cone, and strawberry sells for $0.75 per cone. Write an equation that represents the total amount of money made, with T representing total sales, c representing the number of chocolate cones sold, v representing the number of vanilla cones sold, and s representing the number of strawberry cones sold. Ginny makes $101.48 in total sales after one day. She sold twice as many chocolate cones as strawberry cones, and eight fewer vanilla cones than chocolate cones. How many chocolate cones did Ginny sell?
T = 1.29c + 1.09v + 0.75s 20 Strawberry 40 Chocolate 32 Vanilla