Exam 6: Rational Expressions and Equations

Solve. -The volume of wood in a tree varies jointly as the height of the tree and the square of the distance around the tree trunk. If the volume of wood is 15.84 cubic feet when the height is 22 feet and the distance around the trunk Is 3 feet, what is the volume of wood obtained from a tree that is 36 feet tall having a measurement of 4 feet Around the trunk?

(Multiple Choice)

4.8/5

(29)

Question 101

Solve. -The time T necessary to make an enlargement of a photo negative varies directly as the area A of the enlargement. If 225 seconds are required to make a 5-by-5 enlargement, find the time required for a 7-by-8 Enlargement.

(Multiple Choice)

4.9/5

(31)

Question 102

Solve the problem. -Sven can type 48 words per minute. How many words would he type in $\frac { 2 } { 3 }$ hour (40 minutes)?

(Multiple Choice)

4.7/5

(30)

Question 103

Answer the question. -Explain why the least common denominator of two (different)prime numbers is the product of the two numbers.

(Essay)

4.8/5

(35)

Question 104

Solve the equation. - $\frac { y + 1 } { y + 6 } - \frac { y } { y ^ { 2 } - 36 } = \frac { y - 3 } { y - 6 }$

(Multiple Choice)

4.9/5

(35)

Question 105

Find the ratio. Simplify, if possible. -A machine can fill 4626 boxes of cereal in 0.6 hour. How many boxes of cereal can it fill per hour?

(Multiple Choice)

4.8/5

(36)

Question 106

Find an equation of variation in which the following are true. - $y$ varies jointly as $x$ and $z$ , and $y = 175$ when $x = 5$ and $z = 7$

(Multiple Choice)

4.7/5

(31)

Question 107

Add, first finding the LCD. Simplify, if possible. - $\frac { 10 } { 11 } + \frac { 2 } { 7 }$

(Multiple Choice)

4.8/5

(35)

Question 108

Multiply. Do not simplify. - $\frac { 3 x } { 3 x } \cdot \frac { x - 9 } { x + 10 }$

(Multiple Choice)

4.7/5

(33)

Question 109

Subtract. Simplify, if possible. - $\frac { 17 } { 19 x } - \frac { 7 } { 19 x }$

(Multiple Choice)

4.8/5

(33)

Question 110

Subtract. Simplify, if possible. - $\frac { 2 } { z ^ { 2 } - 9 z } - \frac { 9 } { z - 9 }$

(Multiple Choice)

4.9/5

(40)

Question 111

Solve the equation. - $\frac { x + 3 } { 4 } - \frac { x - 3 } { 7 } = 1$

(Multiple Choice)

4.8/5

(41)

Question 112

Find the LCM. -20, 6, 30

(Multiple Choice)

4.8/5

(37)

Question 113

Add. Simplify, if possible. - $\frac { 6 } { 13 x } + \frac { 6 } { 13 x }$

(Multiple Choice)

4.8/5

(43)

Question 114

Multiply and, if possible, simplify. - $\frac { k ^ { 2 } + 12 k + 35 } { k ^ { 2 } + 15 k + 56 } \cdot \frac { k ^ { 2 } + 8 k } { k ^ { 2 } - 3 k - 40 }$

(Multiple Choice)

4.8/5

(34)

Question 115

Subtract. Simplify, if possible. - $\frac { p } { p - q } - \frac { p } { p + q }$

(Multiple Choice)

4.9/5

(36)

Question 116

Simplify. - $\frac { \frac { x } { 3 y } - \frac { 5 } { 6 y ^ { 3 } } } { \frac { 5 } { 6 y ^ { 3 } } - \frac { x } { 3 y } }$

(Multiple Choice)

4.7/5

(34)

Question 117

Find the LCM. - $t , t - 6$

(Multiple Choice)

4.8/5

(42)

Question 118

Multiply. Do not simplify. - $\frac { 7 y ^ { 2 } } { 7 y ^ { 2 } } \cdot \frac { 8 z } { 3 x }$

(Multiple Choice)

4.9/5

(38)

Question 119

Add. Simplify, if possible. - $\frac { 2 } { x + y } + \frac { 4 } { y + x }$

(Multiple Choice)

4.8/5

(29)

Question 120

Solve. -The time T necessary to make an enlargement of a photo negative varies directly as the area A of the enlargement. If 225 seconds are required to make a 5-by-5 enlargement, find the time required for a 7-by-8 Enlargement.

Solve the problem. -Sven can type 48 words per minute. How many words would he type in $\frac { 2 } { 3 }$ hour (40 minutes)?

Answer the question. -Explain why the least common denominator of two (different)prime numbers is the product of the two numbers.

Solve the equation. - $\frac { y + 1 } { y + 6 } - \frac { y } { y ^ { 2 } - 36 } = \frac { y - 3 } { y - 6 }$

Find the ratio. Simplify, if possible. -A machine can fill 4626 boxes of cereal in 0.6 hour. How many boxes of cereal can it fill per hour?

Find an equation of variation in which the following are true. - $y$ varies jointly as $x$ and $z$ , and $y = 175$ when $x = 5$ and $z = 7$

Add, first finding the LCD. Simplify, if possible. - $\frac { 10 } { 11 } + \frac { 2 } { 7 }$

Multiply. Do not simplify. - $\frac { 3 x } { 3 x } \cdot \frac { x - 9 } { x + 10 }$

Subtract. Simplify, if possible. - $\frac { 17 } { 19 x } - \frac { 7 } { 19 x }$

Subtract. Simplify, if possible. - $\frac { 2 } { z ^ { 2 } - 9 z } - \frac { 9 } { z - 9 }$

Solve the equation. - $\frac { x + 3 } { 4 } - \frac { x - 3 } { 7 } = 1$

Find the LCM. -20, 6, 30

Add. Simplify, if possible. - $\frac { 6 } { 13 x } + \frac { 6 } { 13 x }$

Multiply and, if possible, simplify. - $\frac { k ^ { 2 } + 12 k + 35 } { k ^ { 2 } + 15 k + 56 } \cdot \frac { k ^ { 2 } + 8 k } { k ^ { 2 } - 3 k - 40 }$

Subtract. Simplify, if possible. - $\frac { p } { p - q } - \frac { p } { p + q }$

Simplify. - $\frac { \frac { x } { 3 y } - \frac { 5 } { 6 y ^ { 3 } } } { \frac { 5 } { 6 y ^ { 3 } } - \frac { x } { 3 y } }$

Find the LCM. - $t , t - 6$

Multiply. Do not simplify. - $\frac { 7 y ^ { 2 } } { 7 y ^ { 2 } } \cdot \frac { 8 z } { 3 x }$

Add. Simplify, if possible. - $\frac { 2 } { x + y } + \frac { 4 } { y + x }$

Introduction to Real Numbers and Algebraic Expressions

Solving Equations and Inequalities

Graphs of Linear Equations

Polynomials: Operations

Polynomials: Factoring

Graphs, Functions, and Applications

Systems of Equations

More on Inequalities

Radical Expressions, Equations, and Functions

Quadratic Equations and Functions

Exponential Functions and Logarithmic Functions

Filters

Exam 6: Rational Expressions and Equations

Solve. -The time T necessary to make an enlargement of a photo negative varies directly as the area A of the enlargement. If 225 seconds are required to make a 5-by-5 enlargement, find the time required for a 7-by-8 Enlargement.

Solve the problem. -Sven can type 48 words per minute. How many words would he type in 23\frac { 2 } { 3 }32​ hour (40 minutes)?

Answer the question. -Explain why the least common denominator of two (different)prime numbers is the product of the two numbers.

Solve the equation. - y+1y+6−yy2−36=y−3y−6\frac { y + 1 } { y + 6 } - \frac { y } { y ^ { 2 } - 36 } = \frac { y - 3 } { y - 6 }y+6y+1​−y2−36y​=y−6y−3​

Find the ratio. Simplify, if possible. -A machine can fill 4626 boxes of cereal in 0.6 hour. How many boxes of cereal can it fill per hour?

Find an equation of variation in which the following are true. - yyy varies jointly as xxx and zzz , and y=175y = 175y=175 when x=5x = 5x=5 and z=7z = 7z=7

Add, first finding the LCD. Simplify, if possible. - 1011+27\frac { 10 } { 11 } + \frac { 2 } { 7 }1110​+72​

Multiply. Do not simplify. - 3x3x⋅x−9x+10\frac { 3 x } { 3 x } \cdot \frac { x - 9 } { x + 10 }3x3x​⋅x+10x−9​

Subtract. Simplify, if possible. - 1719x−719x\frac { 17 } { 19 x } - \frac { 7 } { 19 x }19x17​−19x7​

Subtract. Simplify, if possible. - 2z2−9z−9z−9\frac { 2 } { z ^ { 2 } - 9 z } - \frac { 9 } { z - 9 }z2−9z2​−z−99​

Solve the equation. - x+34−x−37=1\frac { x + 3 } { 4 } - \frac { x - 3 } { 7 } = 14x+3​−7x−3​=1

Find the LCM. -20, 6, 30

Add. Simplify, if possible. - 613x+613x\frac { 6 } { 13 x } + \frac { 6 } { 13 x }13x6​+13x6​

Multiply and, if possible, simplify. - k2+12k+35k2+15k+56⋅k2+8kk2−3k−40\frac { k ^ { 2 } + 12 k + 35 } { k ^ { 2 } + 15 k + 56 } \cdot \frac { k ^ { 2 } + 8 k } { k ^ { 2 } - 3 k - 40 }k2+15k+56k2+12k+35​⋅k2−3k−40k2+8k​

Subtract. Simplify, if possible. - pp−q−pp+q\frac { p } { p - q } - \frac { p } { p + q }p−qp​−p+qp​

Simplify. - x3y−56y356y3−x3y\frac { \frac { x } { 3 y } - \frac { 5 } { 6 y ^ { 3 } } } { \frac { 5 } { 6 y ^ { 3 } } - \frac { x } { 3 y } }6y35​−3yx​3yx​−6y35​​

Find the LCM. - t,t−6t , t - 6t,t−6

Multiply. Do not simplify. - 7y27y2⋅8z3x\frac { 7 y ^ { 2 } } { 7 y ^ { 2 } } \cdot \frac { 8 z } { 3 x }7y27y2​⋅3x8z​

Add. Simplify, if possible. - 2x+y+4y+x\frac { 2 } { x + y } + \frac { 4 } { y + x }x+y2​+y+x4​

Introduction to Real Numbers and Algebraic Expressions

Solving Equations and Inequalities

Graphs of Linear Equations

Polynomials: Operations

Polynomials: Factoring

Graphs, Functions, and Applications

Systems of Equations

More on Inequalities

Radical Expressions, Equations, and Functions

Quadratic Equations and Functions

Exponential Functions and Logarithmic Functions

Filters

Solve the problem. -Sven can type 48 words per minute. How many words would he type in $\frac { 2 } { 3 }$ hour (40 minutes)?

Solve the equation. - $\frac { y + 1 } { y + 6 } - \frac { y } { y ^ { 2 } - 36 } = \frac { y - 3 } { y - 6 }$

Find an equation of variation in which the following are true. - $y$ varies jointly as $x$ and $z$ , and $y = 175$ when $x = 5$ and $z = 7$

Add, first finding the LCD. Simplify, if possible. - $\frac { 10 } { 11 } + \frac { 2 } { 7 }$

Multiply. Do not simplify. - $\frac { 3 x } { 3 x } \cdot \frac { x - 9 } { x + 10 }$

Subtract. Simplify, if possible. - $\frac { 17 } { 19 x } - \frac { 7 } { 19 x }$

Subtract. Simplify, if possible. - $\frac { 2 } { z ^ { 2 } - 9 z } - \frac { 9 } { z - 9 }$

Solve the equation. - $\frac { x + 3 } { 4 } - \frac { x - 3 } { 7 } = 1$

Add. Simplify, if possible. - $\frac { 6 } { 13 x } + \frac { 6 } { 13 x }$

Multiply and, if possible, simplify. - $\frac { k ^ { 2 } + 12 k + 35 } { k ^ { 2 } + 15 k + 56 } \cdot \frac { k ^ { 2 } + 8 k } { k ^ { 2 } - 3 k - 40 }$

Subtract. Simplify, if possible. - $\frac { p } { p - q } - \frac { p } { p + q }$

Simplify. - $\frac { \frac { x } { 3 y } - \frac { 5 } { 6 y ^ { 3 } } } { \frac { 5 } { 6 y ^ { 3 } } - \frac { x } { 3 y } }$

Find the LCM. - $t , t - 6$

Multiply. Do not simplify. - $\frac { 7 y ^ { 2 } } { 7 y ^ { 2 } } \cdot \frac { 8 z } { 3 x }$

Add. Simplify, if possible. - $\frac { 2 } { x + y } + \frac { 4 } { y + x }$