Question 1

Use a property of equality to solve the equation. Then check the result. $a + 5 = 0$ a = __________

Accepted Answer

The answer of Use a property of equality to solve...

Question 2

Solve the equation. $8.5 = - 10 c + 6$

Accepted Answer

A)  $c = 4.75$ 
B)  $c = - 0.25$ 
C)  $c = - 0.25$. 
D)  $c = 0.75$ 
E)  none of these

Question 3

Simplify the product. $- 3 x ^ { 2 } c ^ { 5 } \left( - 2 c ^ { 2 } x ^ { 5 } \right)$

Accepted Answer

A)  $6 x ^ { 7 } c ^ { 7 }$ 
B)  $- 6 x ^ { 5 } c ^ { 7 }$ 
C)  $2 x ^ { 7 } c ^ { 7 }$ 
D)  $3 x ^ { 7 } c ^ { 2 }$ 
E)  none of these

Question 4

Use a property of equality to solve the equation. Then check the result. $y + 11 = 16$ $y =$ __________

Accepted Answer

The answer of Use a property of equality to solve...

Question 5

Let x , y , and z represent three real numbers. Write an algebraic expression to denote the product of z , x , and y .

Accepted Answer

A)  $x y - z$ 
B)  $z - y$ 
C)  $x y z$ 
D)  $z - x y$ 
E)  $x + 2 z$

Question 6

Tell whether the given number is a solution of the equation. $\frac { y } { 5 } = 7$ ; $y = 41$

Accepted Answer

A)  restricted solution 
B)  not a solution 
C)  solution 
D)  conflicting solution 
E)  none of these

Question 7

Use a property of equality to solve the equation. Then check the result. $4 = m - 20$ $m =$ __________

Accepted Answer

The answer of Use a property of equality to solve...

Question 8

Solve the equation. $38 = - 4 - 17 b$

Accepted Answer

A)  $b = \frac { 42 } { 17 }$ 
B)  $b = - \frac { 42 } { 17 }$ 
C)  $b = - \frac { 34 } { 17 }$ 
D)  $b = - \frac { 17 } { 42 }$ 
E)  $b = \frac { 34 } { 17 }$

Question 9

What is the variable part of the term $- 6 b x$  ?...

Accepted Answer

A)  $b$ 
B)  $- 6$ 
C)  $b x$ 
D)  $- 6 b x$ 
E)  $X$

Question 10

Find the product. $\left( 6 t ^ { 4 } x ^ { 4 } \right) \left( 5 t ^ { 2 } x ^ { 2 } \right)$

Accepted Answer

A)  $11 t ^ { 6 } x ^ { 6 }$ 
B)  $30 t ^ { 6 } x ^ { 6 }$ 
C)  $30 t ^ { 8 } x ^ { 8 }$ 
D)  $30 t ^ { 2 } x ^ { 2 }$ 
E)  none of these

Question 11

Which of the following formulas illustrates the associative property of multiplication?

Accepted Answer

A)  $( a \cdot b ) \cdot c = a \cdot ( b \cdot c )$ 
B)  $a ( b + c ) = a b + b c$ 
C)  $a + b = b + a$ 
D)  None of these

Question 12

Select the expression that completes the formula below. $( x y ) ^ { k }$

Accepted Answer

A)  $x ^ { k } y ^ { k }$ 
B)  $x ^ { m + k }$ 
C)  $x ^ { m k }$ 
D)  $\frac { x ^ { k } } { y ^ { k } }$ 
E)  none of these

Question 13

Simplify the expression.  $\left( y ^ { 5 } y ^ { 5 } \right) ^ { 4 }$

Accepted Answer

A)  $y ^ { 45 }$ 
B)  $y ^ { 29 }$ 
C)  $y ^ { 40 }$ 
D)  $y ^ { 20 }$ 
E)  $y ^ { 14 }$

Question 14

In the expression $- 5 ^ { 11 }$ , what is the exponent?

Accepted Answer

The answer of In the expression \(- 5 ^ {...

Question 15

Use the distributive property to write the expression $x ( x + 8 )$ without parentheses. Simplify the result, if possible.

Accepted Answer

A)  $x ^ { 2 } + 8 x$ 
B)  $x + 8 x$ 
C)  $x + x + 8 x$ 
D)  $2 x + 8$ 
E)  $x ^ { 2 } + 8 x ^ { 2 } + 8 x$

Question 16

Write the addition property of zero using the variable m .

Accepted Answer

A)  $m + 0 = m$ 
B)  $m + 0 = 0$ 
C)  $m \cdot 0 = 0$ 
D)  Non of these

Question 17

Evaluate the following expression for the given value of the variable. $\frac { y - 4 } { 5 }$  for $y = 14$

Accepted Answer

A)  $- 10$ 
B)  $6$ 
C)  $10$ 
D)  $2$ 
E)  $- 2$

Question 18

The length of a rectangle is 7 times its width. If the perimeter of the rectangle is 112 inches, find its length and width.

Accepted Answer

A)  the length is 980 inches and the width is 49 inches 
B)  the length is 49 inches and the width is 7 inches 
C)  the length is 70 inches and the width is 14 inches 
D)  the length is 343 inches and the width is 49 inches 
E)  the length is 343 inches and the width is 7 inches

Question 19

Use the distributive property to write the expression $8 x ( d - x )$  without parentheses. Simplify the result, if possible.

Accepted Answer

A)  $8 d x - 8 d ^ { 2 }$ 
B)  $d x + d - 8 x ^ { 2 }$ 
C)  $8 x + d - x$ 
D)  $8 d x - 8 x ^ { 2 }$ 
E)  $d x - 8 x ^ { 2 }$

Question 20

The width of a rectangle is 17 inches less than $\frac { 1 } { 2 }$  of its length. If the perimeter of the rectangle 98 inches, find the area of the rectangle. ( Hint: Find the width and the length first. )

Accepted Answer

A)  $550 \mathrm { in } ^ { 2 }$ 
B)  $5 \mathrm { in } ^ { 2 }$ 
C)  $44 \mathrm { in } ^ { 2 }$ 
D)  $220 \mathrm { in } ^ { 2 }$ 
E)  $110 \mathrm { in } ^ { 2 }$

Exam 8: An Introduction to Algebra

Use a property of equality to solve the equation. Then check the result. a+5=0a + 5 = 0a+5=0 a = __________

Solve the equation. 8.5=−10c+68.5 = - 10 c + 68.5=−10c+6

Simplify the product. −3x2c5(−2c2x5) - 3 x ^ { 2 } c ^ { 5 } \left( - 2 c ^ { 2 } x ^ { 5 } \right) −3x2c5(−2c2x5)

Use a property of equality to solve the equation. Then check the result. y+11=16y + 11 = 16y+11=16 y=y =y= __________

Let x , y , and z represent three real numbers. Write an algebraic expression to denote the product of z , x , and y .

Tell whether the given number is a solution of the equation. y5=7\frac { y } { 5 } = 75y​=7 ; y=41y = 41y=41

Use a property of equality to solve the equation. Then check the result. 4=m−204 = m - 204=m−20 m=m =m= __________

Solve the equation. 38=−4−17b38 = - 4 - 17 b38=−4−17b

What is the variable part of the term −6bx- 6 b x−6bx ?...

Find the product. (6t4x4) (5t2x2) \left( 6 t ^ { 4 } x ^ { 4 } \right) \left( 5 t ^ { 2 } x ^ { 2 } \right) (6t4x4) (5t2x2)

Which of the following formulas illustrates the associative property of multiplication?

Select the expression that completes the formula below. (xy) k( x y ) ^ { k }(xy) k

Simplify the expression. (y5y5) 4\left( y ^ { 5 } y ^ { 5 } \right) ^ { 4 }(y5y5) 4

In the expression −511- 5 ^ { 11 }−511 , what is the exponent?

Use the distributive property to write the expression x(x+8) x ( x + 8 ) x(x+8) without parentheses. Simplify the result, if possible.

Write the addition property of zero using the variable m .

Evaluate the following expression for the given value of the variable. y−45\frac { y - 4 } { 5 }5y−4​ for y=14y = 14y=14

The length of a rectangle is 7 times its width. If the perimeter of the rectangle is 112 inches, find its length and width.

Use the distributive property to write the expression 8x(d−x) 8 x ( d - x ) 8x(d−x) without parentheses. Simplify the result, if possible.

The width of a rectangle is 17 inches less than 12\frac { 1 } { 2 }21​ of its length. If the perimeter of the rectangle 98 inches, find the area of the rectangle. ( Hint: Find the width and the length first. )

Use a property of equality to solve the equation. Then check the result. $a + 5 = 0$ a = __________

Solve the equation. $8.5 = - 10 c + 6$

Simplify the product. $- 3 x ^ { 2 } c ^ { 5 } \left( - 2 c ^ { 2 } x ^ { 5 } \right)$

Use a property of equality to solve the equation. Then check the result. $y + 11 = 16$ $y =$ __________

Tell whether the given number is a solution of the equation. $\frac { y } { 5 } = 7$ ; $y = 41$

Use a property of equality to solve the equation. Then check the result. $4 = m - 20$ $m =$ __________

Solve the equation. $38 = - 4 - 17 b$

What is the variable part of the term $- 6 b x$ ?...

Find the product. $\left( 6 t ^ { 4 } x ^ { 4 } \right) \left( 5 t ^ { 2 } x ^ { 2 } \right)$

Select the expression that completes the formula below. $( x y ) ^ { k }$

Simplify the expression. $\left( y ^ { 5 } y ^ { 5 } \right) ^ { 4 }$

In the expression $- 5 ^ { 11 }$ , what is the exponent?

Use the distributive property to write the expression $x ( x + 8 )$ without parentheses. Simplify the result, if possible.

Evaluate the following expression for the given value of the variable. $\frac { y - 4 } { 5 }$ for $y = 14$

Use the distributive property to write the expression $8 x ( d - x )$ without parentheses. Simplify the result, if possible.

The width of a rectangle is 17 inches less than $\frac { 1 } { 2 }$ of its length. If the perimeter of the rectangle 98 inches, find the area of the rectangle. ( Hint: Find the width and the length first. )