Expressions and Equations
Which expressions below are equivalent to
2(2x + 1)? Select all that apply.
A. 4x + 2
B. 2(1 + 2x)
C. 2(2x) + 1
D. 2x + 1 + 2x + 1
E. x + x + x + x + 1 + 1
A, B, D, E
Fill in the blanks:
Vertical angles are always __________.
Adjacent angles share a common ________ and ______.
Vertical angles are always congruent.
Adjacent angles share a common vertex and side.
A crew of highway workers paved 2/15 mile in 20 minutes. If they work at the same rate, what portion of a mile will they pave in one hour?
2/5
Mount Ojos del Salado is the highest mountain in Chile, with a peak at about 6900 meters above sea level. The Atacama Trench, just off the coast of Chile, is about 8100 meters below sea level (at its lowest point).
What is the difference in elevations between Mount Ojos del Salado and the Atacama Trench?
15,000 meters
The Lions won 16 games last year. This year the Lions won 20 games. What is the percent increase in the number of games the Lions won from last year to this year?
25%
Solve for x.
0.5𝑥 + 78.2 = 287
417.6
Fill in the blanks:
Angles of a triangle add up to be ______ degrees.
Angles of a quadrilateral add up to be ________ degrees.
Angles of a triangle add up to be 180 degrees.
Angles of a quadrilateral add up to be 360 degrees.
Betty makes pies. To make 6 pies, she uses 7 1/2 cups of flour. How many cups of flour are needed to make 1 pie?
1 1/4
What is the value of the expression shown below?
8 – (-5.5)
13.5
Donte bought a computer that was 20% off the regular price of $1,080. If an 8% sales tax was added to the cost of the computer, what was the total price Donte paid for it?
$933.12
Max is taking a cab in New York City. The fare is calculated as a base charge of $3.00 plus an additional $2.00 per mile traveled. It is also customary to leave a $2 tip.
If Max wants to spend exactly $20, how many miles can he travel?
7.5 miles
Angles T and V are complementary. Angle T has a measure of (2x + 10) degrees. Angle V has a measure of 48 degrees.
What is the value of x?
x = 16
Ms. Robinson gave her class 12 minutes to read. Carrie read 5 ½ pages in that time. At what rate, in pages per hour, did Carrie read?
27 1/2
What is the value of the expression shown below?
−7 3/4 + 3 1/2
-4 1/4
At Juicy Deals grocery store, 4 oranges cost $7.00. You can buy 7 oranges for $12.50. Is the relationship between the number of oranges and their price proportional? Explain.
No, the relationship between the cost and the number of oranges is not constant. You can use cross products property to determine the answer.
Rewrite the expression below as the sum of one constant and one variable term:
2(𝑥 − 4) + 6𝑥 − 5𝑥 ∙ 3
-7x - 8
The circumference of a circle is 188 meters. What is the approximate radius of the circle? (Round to the nearest whole number. You may use a calculator).
30 meters
A bathtub fills at a constant rate. The amount of water in the tub increases by 1/2 gallon every 1/10 minute. What is the unit rate at which the bathtub fills?
5 gal./min. or 0.2 min./gal.
Determine if each fraction is a terminating decimal or a repeating decimal.
-7/9
42/50
-7/9 is repeating.
42/50 is terminating.
What is the solution to the inequality −3𝑥 − 42 > 3?
x < -15
Phillip bought a used car for x dollars. One year later the value of the car was 0.88x.
Which expression is another way to describe the change in the value of the car?
A. 0.12% decrease
B. 0.88% decrease
C. 12% decrease
D. 88% decrease
D
If angle QPS is a right angle and the measurement of QPR = 71 degrees, what is the measurement of angle RPS?
19 degrees
Laura jogs at a rate of 2 miles every 2/5 hour. What is her unit rate?
5 miles/hour
Jason’s checking account balance was $345. Jason withdrew $160 three times. What is his current balance?
$-135.00
Mr. Smith earns $200 per week working at a clothing store. In addition, he earns 3% commission on all of his sales. Last week, he sold $1,800 worth of clothes. What was Mr. Smith’s total income for that week?
$254