Question 1

Perform the indicated division and express your answer in simplest form.  4s2+3sr−r2s2r÷5s2+4sr−r2r\frac { 4 s ^ { 2 } + 3 s r - r ^ { 2 } } { s ^ { 2 } r } \div \frac { 5 s ^ { 2 } + 4 s r - r ^ { 2 } } { r }s2r4s2+3sr−r2​÷r5s2+4sr−r2​

Accepted Answer

A)    5s+rs2(4s+r) \frac { 5 s + r } { s ^ { 2 } ( 4 s + r )  }s2(4s+r) 5s+r​ 
B)    4s+rs2(5s−r) \frac { 4 s + r } { s ^ { 2 } ( 5 s - r )  }s2(5s−r) 4s+r​ 
C)    5s−rs2(4s−r) \frac { 5 s - r } { s ^ { 2 } ( 4 s - r )  }s2(4s−r) 5s−r​ 
D)    4s−rs2(5s−r) \frac { 4 s - r } { s ^ { 2 } ( 5 s - r )  }s2(5s−r) 4s−r​ 
E)    4s−rs2(5s+r) \frac { 4 s - r } { s ^ { 2 } ( 5 s + r )  }s2(5s+r) 4s−r​

Question 2

Evaluate the following expression for the given value of the variable.  x−84\frac { x - 8 } { 4 }4x−8​  for  x=28x = 28x=28

Accepted Answer

A)    −-−  20
B)  13
C)  20
D)  5
E)    −-−  5

Question 3

Evaluate:  −x−8x2−4x−12 for x=−4\frac { - x - 8 } { x ^ { 2 } - 4 x - 12 } 	ext { for } x = - 4x2−4x−12−x−8​ for x=−4

Accepted Answer

A)    −35- \frac { 3 } { 5 }−53​ 
B)    −15- \frac { 1 } { 5 }−51​ 
C)    15\frac { 1 } { 5 }51​ 
D)    −12- \frac { 1 } { 2 }−21​

Question 4

Express the sentence as a formula. Assume that  kkk  is a constant of variation. The distance  SSS  that a body falls varies directly with the square of the time  zzz  .

Accepted Answer

A)    s=kz2s = \frac { k } { z ^ { 2 } }s=z2k​ 
B)    s=k+z2s = k + z ^ { 2 }s=k+z2 
C)    s=kz2s = k z ^ { 2 }s=kz2 
D)    s=k−z2s = k - z ^ { 2 }s=k−z2 
E)    s=z2ks = \frac { z ^ { 2 } } { k }s=kz2​

Question 5

Use similar triangles to help solve the problem. An airplane ascends 160 feet as it flies a horizontal distance of 1,000 feet. How much altitude will it gain as it flies a horizontal distance of 1 mile? ( Hint: 5,280 feet = 1 mile.) Round your answer to the nearest integer.

Accepted Answer

A)  x = 870 ft
B)  x = 813 ft
C)  x = 845 ft
D)  x = 885 ft
E)  x = 833 ft

Question 6

Perform the indicated operation and simplify.  6z⋅z3\frac { 6 } { z } \cdot z ^ { 3 }z6​⋅z3

Accepted Answer

A)    z16\frac { z ^ { 1 } } { 6 }6z1​ 
B)    6z4\frac { 6 } { z ^ { 4 } }z46​ 
C)    6z26 z ^ { 2 }6z2 
D)    6z46 z ^ { 4 }6z4

Question 7

A school board has determined that there should be 3 teachers for every 50 students. How many teachers are needed for an enrollment of 2,750 students?

Accepted Answer

A)  190 teachers
B)  176 teachers
C)  165 teachers
D)  181 teachers
E)  222 teachers

Question 8

Write the ratio 27 feet to 12 yards as a fraction in simplest form. ( Hint : 3 feet = 1 yard.)

Accepted Answer

A)    34\frac { 3 } { 4 }43​ 
B)    43\frac { 4 } { 3 }34​ 
C)    444 
D)    13\frac { 1 } { 3 }31​ 
E)    333

Question 9

Perform the indicated operation and simplify.  p3r2cd⋅c−4d3\frac { p ^ { 3 } r ^ { 2 } } { c d } \cdot c ^ { - 4 } d ^ { 3 }cdp3r2​⋅c−4d3

Accepted Answer

A)    p3r2dc5\frac { p ^ { 3 } r ^ { 2 } d } { c ^ { 5 } }c5p3r2d​ 
B)    p3r2d2c5\frac { p ^ { 3 } r ^ { 2 } d ^ { 2 } } { c ^ { 5 } }c5p3r2d2​ 
C)    cr2dp5\frac { c r ^ { 2 } d } { p ^ { 5 } }p5cr2d​ 
D)    p2rd5d2\frac { p ^ { 2 } r d ^ { 5 } } { d ^ { 2 } }d2p2rd5​ 
E)    pr2d2c5\frac { p r ^ { 2 } d ^ { 2 } } { c ^ { 5 } }c5pr2d2​ B

Question 10

A model railroad engine is 2 inches long. If the scale is 168 feet to 1 foot, how long is the real engine?

Accepted Answer

A)  31
B)  29
C)  26
D)  34
E)  28

Question 11

A dealer bought some cell phones for a total of $1,066. He gave away 1 cell phone as a gift, sold the rest for $15 more then he paid for each cell phone, and earned $98. How many cell phones did he buy?

Accepted Answer

A)  14
B)  12
C)  15
D)  13
E)  11 D

Question 12

Perform the indicated operation. Simplify the answer if possible.  t+6t−3−t+103−t\frac { t + 6 } { t - 3 } - \frac { t + 10 } { 3 - t }t−3t+6​−3−tt+10​

Accepted Answer

A)    2t+16t−3\frac { 2 t + 16 } { t - 3 }t−32t+16​ 
B)    2t+16t+3\frac { 2 t + 16 } { t + 3 }t+32t+16​ 
C)    2t−16t+3\frac { 2 t - 16 } { t + 3 }t+32t−16​ 
D)    2t−16t−3\frac { 2 t - 16 } { t - 3 }t−32t−16​ 
E)  none of these

Question 13

Use similar triangles to help solve the problem. A tree casts a shadow of 24 feet at the same time as a 5-foot tall man casts a shadow of 4 feet. Find the height of the tree.

Accepted Answer

A)  h = 27 ft
B)  h = 42 ft
C)  h = 30 ft
D)  h = 35 ft
E)  h = 22 ft

Question 14

Perform the indicated operation. $$\frac { 8 a } { y } - \frac { 6 a } { y }$$

Accepted Answer

The answer of Perform the indicated operation. \[\frac { 8...

Question 15

Write the ratio as a fraction in simplest form.  333  inches to  121212  inches

Accepted Answer

A)    44\frac { 4 } { 4 }44​ 
B)    14\frac { 1 } { 4 }41​ 
C)    444 
D)    43\frac { 4 } { 3 }34​ 
E)    34\frac { 3 } { 4 }43​

Question 16

Perform the indicated operation. Simplify the answer if possible.  5a+9−2−9−a\frac { 5 } { a + 9 } - \frac { 2 } { - 9 - a }a+95​−−9−a2​

Accepted Answer

A)    7a−9\frac { 7 } { a - 9 }a−97​ 
B)    7a+9\frac { 7 } { a + 9 }a+97​ 
C)    −7a+9\frac { - 7 } { a + 9 }a+9−7​ 
D)    7aa−9\frac { 7 a } { a - 9 }a−97a​ 
E)  none of these

Question 17

Solve the formula for t : $$\frac { 5 } { y } + \frac { 2 } { t } = 7$$

Accepted Answer

The answer of Solve the formula for t : \[\frac...

Question 18

Solve  d=4cbc−bd = \frac { 4 c b } { c - b }d=c−b4cb​  for c .

Accepted Answer

A)    c=bd4b−1c = \frac { b d } { 4 b - 1 }c=4b−1bd​ 
B)    c=14c = \frac { 1 } { 4 }c=41​ 
C)    c=d(c−b) 4bc = \frac { d ( c - b )  } { 4 b }c=4bd(c−b) ​ 
D)    c=−bd4b−dc = - \frac { b d } { 4 b - d }c=−4b−dbd​ D

Question 19

Solve for the variable in the proportion.  35=x15\frac { 3 } { 5 } = \frac { x } { 15 }53​=15x​

Accepted Answer

A)    x=7x = 7x=7 
B)    x=9x = 9x=9 
C)    x=10x = 10x=10 
D)    x=12x = 12x=12 
E)    x=6x = 6x=6

Question 20

A man roller-blades at a rate 5 miles per hour faster than he jogs. In the same time it takes him to roller-blade 6 miles he can jog 3 miles. How fast does he jog?

Accepted Answer

A)  4 mph
B)  3 mph
C)  5 mph
D)  1 mph
E)  2 mph

Exam 7: Rational Expressions and Equations

Perform the indicated division and express your answer in simplest form. 4s2+3sr−r2s2r÷5s2+4sr−r2r\frac { 4 s ^ { 2 } + 3 s r - r ^ { 2 } } { s ^ { 2 } r } \div \frac { 5 s ^ { 2 } + 4 s r - r ^ { 2 } } { r }s2r4s2+3sr−r2​÷r5s2+4sr−r2​

Correct AnswerverifiedShow Answer

Evaluate the following expression for the given value of the variable. x−84\frac { x - 8 } { 4 }4x−8​ for x=28x = 28x=28

Correct AnswerverifiedShow Answer

Evaluate: −x−8x2−4x−12 for x=−4\frac { - x - 8 } { x ^ { 2 } - 4 x - 12 } \text { for } x = - 4x2−4x−12−x−8​ for x=−4

Correct AnswerverifiedShow Answer

Express the sentence as a formula. Assume that kkk is a constant of variation. The distance SSS that a body falls varies directly with the square of the time zzz .

Correct AnswerverifiedShow Answer

Use similar triangles to help solve the problem. An airplane ascends 160 feet as it flies a horizontal distance of 1,000 feet. How much altitude will it gain as it flies a horizontal distance of 1 mile? ( Hint: 5,280 feet = 1 mile.) Round your answer to the nearest integer.

Correct AnswerverifiedShow Answer

Perform the indicated operation and simplify. 6z⋅z3\frac { 6 } { z } \cdot z ^ { 3 }z6​⋅z3

Correct AnswerverifiedShow Answer

A school board has determined that there should be 3 teachers for every 50 students. How many teachers are needed for an enrollment of 2,750 students?

Correct AnswerverifiedShow Answer

Write the ratio 27 feet to 12 yards as a fraction in simplest form. ( Hint : 3 feet = 1 yard.)

Correct AnswerverifiedShow Answer

Perform the indicated operation and simplify. p3r2cd⋅c−4d3\frac { p ^ { 3 } r ^ { 2 } } { c d } \cdot c ^ { - 4 } d ^ { 3 }cdp3r2​⋅c−4d3

Correct AnswerverifiedB

A model railroad engine is 2 inches long. If the scale is 168 feet to 1 foot, how long is the real engine?

Correct AnswerverifiedShow Answer

A dealer bought some cell phones for a total of $1,066. He gave away 1 cell phone as a gift, sold the rest for $15 more then he paid for each cell phone, and earned $98. How many cell phones did he buy?

Correct AnswerverifiedD

Perform the indicated operation. Simplify the answer if possible. t+6t−3−t+103−t\frac { t + 6 } { t - 3 } - \frac { t + 10 } { 3 - t }t−3t+6​−3−tt+10​

Correct AnswerverifiedShow Answer

Use similar triangles to help solve the problem. A tree casts a shadow of 24 feet at the same time as a 5-foot tall man casts a shadow of 4 feet. Find the height of the tree.

Correct AnswerverifiedShow Answer

Perform the indicated operation. 8ay−6ay\frac { 8 a } { y } - \frac { 6 a } { y }y8a​−y6a​

Correct AnswerverifiedShow Answer

Write the ratio as a fraction in simplest form. 333 inches to 121212 inches

Correct AnswerverifiedShow Answer

Perform the indicated operation. Simplify the answer if possible. 5a+9−2−9−a\frac { 5 } { a + 9 } - \frac { 2 } { - 9 - a }a+95​−−9−a2​

Correct AnswerverifiedShow Answer

Solve the formula for t : 5y+2t=7\frac { 5 } { y } + \frac { 2 } { t } = 7y5​+t2​=7

Correct AnswerverifiedShow Answer

Solve d=4cbc−bd = \frac { 4 c b } { c - b }d=c−b4cb​ for c .

Correct AnswerverifiedD

Solve for the variable in the proportion. 35=x15\frac { 3 } { 5 } = \frac { x } { 15 }53​=15x​

Correct AnswerverifiedShow Answer

A man roller-blades at a rate 5 miles per hour faster than he jogs. In the same time it takes him to roller-blade 6 miles he can jog 3 miles. How fast does he jog?

Correct AnswerverifiedShow Answer

Perform the indicated division and express your answer in simplest form. $\frac { 4 s ^ { 2 } + 3 s r - r ^ { 2 } } { s ^ { 2 } r } \div \frac { 5 s ^ { 2 } + 4 s r - r ^ { 2 } } { r }$

Correct Answer
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Evaluate the following expression for the given value of the variable. $\frac { x - 8 } { 4 }$ for $x = 28$

Correct Answer
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Evaluate: $\frac { - x - 8 } { x ^ { 2 } - 4 x - 12 } \text { for } x = - 4$

Correct Answer
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Express the sentence as a formula. Assume that $k$ is a constant of variation. The distance $S$ that a body falls varies directly with the square of the time $z$ .

Correct Answer
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Correct Answer
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Perform the indicated operation and simplify. $\frac { 6 } { z } \cdot z ^ { 3 }$

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Perform the indicated operation and simplify. $\frac { p ^ { 3 } r ^ { 2 } } { c d } \cdot c ^ { - 4 } d ^ { 3 }$

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B

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D

Perform the indicated operation. Simplify the answer if possible. $\frac { t + 6 } { t - 3 } - \frac { t + 10 } { 3 - t }$

Correct Answer
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Correct Answer
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Perform the indicated operation. $\frac { 8 a } { y } - \frac { 6 a } { y }$

Correct Answer
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Write the ratio as a fraction in simplest form. $3$ inches to $12$ inches

Correct Answer
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Perform the indicated operation. Simplify the answer if possible. $\frac { 5 } { a + 9 } - \frac { 2 } { - 9 - a }$

Correct Answer
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Solve the formula for t : $\frac { 5 } { y } + \frac { 2 } { t } = 7$

Correct Answer
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Solve $d = \frac { 4 c b } { c - b }$ for c .

Correct Answer
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D

Solve for the variable in the proportion. $\frac { 3 } { 5 } = \frac { x } { 15 }$

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Correct Answer
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