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Expressions, Equations, and Relationships

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Solve equations and inequalities and reason about geometric relationships and measurement.

Questions

125

Skill type

expressions and-equations

Study mode

Practice + review

Sample questions

Question

What is the area of a rectangle with length 8 cm and width 5 cm?

A.
26 cm²
B.
40 cm²
C.
45 cm²
D.
80 cm²

Question

$A fishbowl shaped like a sphere is filled with water. The fishbowl has a diameter of 16 inches. Which measurement is closest to the volume of water in the fishbowl in cubic inches?$ Open full-size question

A.
$Answer A: 2,144.66 in.3$
B.
$Answer B: 17,157.28 in.3$
C.
$Answer C: 5,461.67 in.3$
D.
$Answer D: 6,433.98 in.3$

Question

$Four plumbers estimated the length of the radius of a cylindrical pipe. The estimates made by the plumbers are listed. • Plumber W estimated that the radius had a length of inches.3 25 • Plumber X estimated that the radius had a length of inches.3 11 • Plumber Y estimated that the radius had a length of inches.9 100 • Plumber Z estimated that the radius had a length of inches.π 24 Which list shows these lengths in order from greatest to least?$ Open full-size question

A.
$Answer A: 9 π 24 3, 113 100 , 25 ,$
B.
$Answer B: 3 π 24 3 9, 100 11 , 25 ,$
C.
$Answer C: 9 3 25 , π 24 ,3 100 , 11$
D.
$Answer D: 3 3 25 , π 24 9, 11 , 100$

Question

$Jerry has a new job and earns a salary of $45,000. Victoria has a new job and earns a salary of $54,000. Jerry will receive a salary increase of $2,500 per year, and Victoria will receive a salary increase of $1,500 per year. Which equation can be used to find x, the number of years it will take Jerry to earn the same salary as Victoria?$ Open full-size question

A.
$Answer A: 45,000 x + 2,500 x = 54,000 x + 1,500 x$
B.
$Answer B: 45,000 x + 2,500 = 54,000 x + 1,500$
C.
$Answer C: 45,000 + 2,500 x = 54,000 + 1,500 x$
D.
$Answer D: 45,000 x + 2,500 x = 54,000 x + 1,500$

Question

$Natasha walked from the library to the grocery store and then to her house. The diagram shows the top view of the locations of these three places and their distances from each other. Library Grocery 1.7 mi store 0.9 mi Natasha’s house Which measurement is closest to the shortest distance in miles from Natasha’s house to the library?$ Open full-size question

A.
$Answer A: 2.6 mi$
B.
$Answer B: 1.9 mi$
C.
$Answer C: 1.4 mi$
D.
$Answer D: 2.3 mi$

Question

$A relation contains the points (1, 2), (2, −− 1), (3, 0), (4, 1), and (5, −− 1). Which statement accurately describes this relation?$ Open full-size question

A.
$Answer A: The relation does not represent y as a function of x, because each value of x is associated with a single value of y.$
B.
$Answer B: The relation represents y as a function of x, because one value of y is associated with two values of x.$
C.
$Answer C: The relation does not represent y as a function of x, because each value of y is associated with two values of x.$
D.
$Answer D: The relation represents y as a function of x, because each value of x is associated with a single value of y.$

Question

$In a museum there is a sculpture in the shape of a cylinder. The cylinder has a diameter of 12 feet and a height of h feet. Which equation can be used to find V, the volume of the cylinder in cubic feet?$ Open full-size question

A.
$Answer A: V = π(6)2 h$
B.
$Answer B: V = (6π h )2$
C.
$Answer C: V = π(12)2 h$
D.
$Answer D: V = π(12 h)2$

Question

$Julie started with 20 pieces of gum and gave away x pieces. Conrad started with 35 pieces of gum and gave away twice as many pieces as Julie did. How many pieces of gum did Julie give away if they had the same number of pieces of gum left?$ Open full-size question

A.
$Answer A: 18$
B.
$Answer B: 5$
C.
$Answer C: 15$
D.
$Answer D: 8$

Question

$Trapezoid PQRS is rotated 180° about the origin to form trapezoid PQ′′R′S′. y 9 8 7 6 5 P 4 Q 3 2 1 −9 −8 −7 −6 −5 −4 −3 −2 −1 −1 x 1 2 3 4 5 6 7 8 9 S −2 −3 R −4 −5 −6 −7 −8 −9 Which statement is true?$ Open full-size question

A.
$Answer A: The sum of the angle measures of trapezoid PQRS is 180° less than the sum of the angle measures of trapezoid PQRS.′′′′$
B.
$Answer B: Trapezoid PQRS is not congruent to trapezoid PQRS.′′′′$
C.
$Answer C: The area of trapezoid PQRS is less than the area of trapezoid PQRS.′′′′$
D.
$Answer D: The angle measures of trapezoid PQRS are equal to the corresponding angle measures of trapezoid PQRS.′′′′$

Question

$Which function is best represented by this graph? y 9 8 7 6 5 4 3 2 1 −9 −8 −7 −6 −5 −4 −3 −2 −1 −1 2 3 4 5 6 7 8 9x 1 −2 −3 −4 −5 −6 −7 −8 −9$ Open full-size question

A.
$Answer A: y = x1 + 8 4$
B.
$Answer B: y = x1 −− 2 4$
C.
$Answer C: y = 4 x −− 2$
D.
$Answer D: y = 4 x + 8$

Question

$In each diagram, line k is parallel to line l , and line t intersects lines k and l . 113° k k 127° 113° 127°l l t t k 79° k l x° l t t Based on the diagrams, which statement is true?$ Open full-size question

A.
$Answer A: The value of x is 79, because the two angles shown in each diagram are congruent.$
B.
$Answer B: The value of x is 101, because the two angles shown in each diagram are supplementary.$
C.
$Answer C: The value of x is greater than 90, because the two angles shown in each diagram are obtuse angles.$
D.
$Answer D: The value of x is 11, because the two angles shown in each diagram are complementary.$

Question

$A hot-air balloon is released at ground level, and it rises into the air at a constant rate. After 5 seconds the height of the balloon is 20 feet. The balloon continues to rise at the same rate. Which table shows the relationship between the time in seconds, x, and the height of the balloon in feet, y? F Balloon H Balloon Time, x (sec) Height, y (ft) Time, x (sec) Height, y (ft) 10 2.5 10 40 20 5.0 20 60 30 7.5 30 80 40 10.0 40 100 50 12.5 50 120 G Balloon J Balloon Time, x (sec) Height, y (ft) Time, x (sec) Height, y (ft) 10 25 10 40 20 35 20 80 30 45 30 120 40 55 40 160 50 65 50 200$ Open full-size question

A.
$Answer A: Answer F (see image)$
B.
$Answer B: Answer G (see image)$
C.
$Answer C: Answer H (see image)$
D.
$Answer D: Answer J (see image)$

Question

$Rudolfo has 15 toys in his toy box, and he adds 2 new toys every month. Based on this information, which representation best shows this relationship between the number of toys Rudolfo has in his toy box, y, and the number of months that have passed, x? Rudolfo’s Toys Rudolfo’s Toys x y x y F 4 8 H 1 17 6 12 4 68 11 22 7 119 13 26 11 187 y Rudolfo’s Toys y Rudolfo’s Toys 50 100 40 80 30 60 G J 20 40 10 20 0 12345678910 x 0 12345678910 x Number of Months Number of Months$ Open full-size question

A.
$Answer A: Answer F (see image)$
B.
$Answer B: Answer G (see image)$
C.
$Answer C: Answer H (see image)$
D.
$Answer D: Answer J (see image)$

Question

$A gym charges a membership fee plus an additional fee per yoga class. The table shows the linear relationship between the number of yoga classes taken and the total cost including the membership fee. Yoga Classes Number of Cost Yoga Classes Total 6 $67.50 8 $75.00 10 $82.50 14 $97.50 20 $120.00 Which statement is true?$ Open full-size question

A.
$Answer A: The additional fee per yoga class is $3.75.$
B.
$Answer B: The additional fee per yoga class is $8.25.$
C.
$Answer C: The membership fee is $35.00.$
D.
$Answer D: The membership fee is $42.50.$

Question

$Pentagon VWXYZ is shown on the coordinate grid. A student reflected pentagon VWXYZ across the x-axis to create pentagon VW′ ′XY′′′Z. y 7 6 5 4 3 2 1 x −7 7−6 −5 −4 −3 −2 −11 2 3 V 54 6 −1 −2 −3 −4 Z W −5 −6 −7 Y X Which rule describes this transformation?$ Open full-size question

A.
$Answer A: (, xxy) → (, − − y)$
B.
$Answer B: (,xy →) xy+ 8) (,$
C.
$Answer C: (,xy) → (−− yx, )$
D.
$Answer D: (,xy) → (−− xy, )$

Question

$Which list shows these numbers in order from least to greatest? 37 26 5−− 5.17, 33 , −− 6 ,$ Open full-size question

A.
$Answer A: −− ,26 37 −− 5.17, 33 5 6 ,$
B.
$Answer B: −− 5.17, 26−− , 37 33 5 6 ,$
C.
$Answer C: −− ,26 − 5.17, 33 , 37 5 − 6$
D.
$Answer D: −− 5.17, 26−− ,5 33 , 376$

Question

$Snacks at a county fair are sold in containers shaped like a cone or a cylinder. The dimensions of each container are shown in the drawing. 4 in. 3 in. 12 in. 8 in. Which statement about the volumes of the cone and the cylinder is true?$ Open full-size question

A.
$Answer A: The volume of the cylinder is about 377 cubic inches greater than the volume of the cone.$
B.
$Answer B: The volume of the cylinder is about 377 cubic inches less than the volume of the cone.$
C.
$Answer C: The volume of the cylinder is about 25 cubic inches greater than the volume of the cone.$
D.
$Answer D: The volume of the cylinder is about 25 cubic inches less than the volume of the cone.$

Question

$Which situation can be represented by this equation? 7 x + 1 = 10x$ Open full-size question

A.
$Answer A: Brody ran at a constant rate of 7 miles per hour in a race. Candice ran at a constant rate of 10 miles per hour in a race and started 1 mile in front of the starting point. What is x, the number of hours that Brody and Candice would have to run in order for their distance to be the same?$
B.
$Answer B: Brody played a game where he scored 8 points per hour. Candice played the game and scored 10 points per hour. What is x, the number of hours that Brody and Candice would each have to play the game in order for their scores to be the same?$
C.
$Answer C: Brody went to two different amusement parks. The first park charged $7 per hour and gave a 1% discount for showing a student ID. The other park charged $10 per hour. What is x, the number of hours that Brody would have to stay at each park to have to pay the same amount?$
D.
$Answer D: Brody rode his bicycle on two different days. The first day he rode 7 miles per hour and started 1 mile from his house. The second day he started from his house and rode 10 miles per hour. What is x, the number of hours that Brody would have to ride his bicycle to travel the same distance on both days? Pa g e 2 6$

Question

$The coordinates of the endpoints of QR are Q (8, 2) and R (5, 7). y 9 8 R 7 6 5 4 3 2 Q 1 0 123456789 x Which measurement is closest to the length of QR in units?$ Open full-size question

A.
$Answer A: 5.8 units$
B.
$Answer B: 5 units$
C.
$Answer C: 4 units$
D.
$Answer D: 3.9 units Pa g e 2 7$

Question

$The ticket sales for a concert started at 4:00 P.M. The table shows the linear relationship between the number of tickets remaining and the number of hours since 4:00 P.M. Ticket Sales Hours Number of Tickets Since 4 P.M. Remaining 1 12,000 2 9,000 3 6,000 4 3,000 5 0 Which function can be used to find y, the number of tickets remaining x hours since 4:00 P.M.?$ Open full-size question

A.
$Answer A: y = 3,000 x + 12,000$
B.
$Answer B: y = 3,000 x + 15,000$
C.
$Answer C: y = −− 3,000 x + 12,000$
D.
$Answer D: y = −− 3,000 x + 15,000$