Question

1.) Use the distributive Property to simplify the expression .
(-1)(4 - c)
A. 4 - c
B. -4 + c
C. 4 + c
D.-4 - c

2.)Use the distributive Property to simplify the expression
4(2x - 4)
A.8x + 4
B.8x - 4
C.8x - 16
D.4x - 16

3.) Use the distributive Property to simplify the expression
(10 + 4y) 1/2
A. 5 + 2y
B. 20 + 8y
C. 5 + 4y
D. 10 +2y

4.) To which subsets of real numbers does the number - 22 belong ? Choose all that apply (2 points)

A.Whole numbers
B.Rational numbers
C. Integers
D. Irrational numbers
E. Natural numbers

5.)What is an algebraic expression for the following word phrase: "6 times the difference of b and p" ?

A. 6b - p
B. 6(b - p)
C. 6 - bp
D. 6bp

6.)What is the simplified form of the expression ?

5(14 - 2)^2
------------------
2

A. 60
B. 30
C. 72
D. 360

7.) Evaluate u + xy, if u = 18, x = 10, and y = 8

A.188
B.36
C.98
D.224

8. A square field has an area of 479 ft^2 . What is the approximate length of a side of the field ? Give your answer to the nearest foot . Explain your response .

9. Simplify the expression (7 + 5) + 4 x 13 - 2 Show work .

Answer 1

Question 1: We have to simplify the expression (-1)(4 - c) by distributive property.

Using the distributive property a(b+c) = ab+ac

Consider (-1)(4-c) = $[(-1) \times 4] +[(-1) \times (-c)]$

=  - 4 + c

So, Option B is the correct answer.

Question 2: We have to simplify the expression 4(2x - 4) by distributive property.

Using the distributive property a(b+c) = ab+ac

Consider 4(2x-4) = $[(4) \times 2x] +[(4) \times (-4)]$

=  8x - 16

So, Option C is the correct answer.

Question 3: We have to simplify the expression$(10 + 4y) \frac{1}{2}$ by distributive property.

Using the distributive property a(b+c) = ab+ac

Consider $(10 + 4y) \frac{1}{2}$

= $(10 \times \frac{1}{2}) + ( 4y \times \frac{1}{2})$

= $5 + 2y$

So, Option A is the correct answer.

Question 4:

We have to identify the subsets of real numbers to which 22 belong.

a) 22 belongs to the set of whole numbers as whole numbers are the set of numbers starting from zero to infinity.

b) 22 belongs to the set of rational numbers as rational numbers, as 22 can be written as $\frac{22}{1}$  and rational numbers are represented in the form of $\frac{p}{q}$ where p and q are integers and q is not equal to zero.

c) 22 belongs to the set of integers as integers is the set of numbers including whole numbers and negative whole numbers.

d) 22 does'not belong to the set of irrational numbers as irrational numbers are the numbers that cannot be expressed as a ratio between two integers.

e) 22 belongs to the set of natural numbers as natural numbers are the set of numbers from zero to infinity.

Question 5: We have to identify the algebraic expression for "6 times the difference of b and p"

= $6 \times (b-p)$

= 6(b-p)

Option B is the correct answer.

Question 6:

We have to determine the value of $\frac{5(14-2)^2}{2}$

= $\frac{5 \times 144}{2}$

= 360

Option D is the correct answer.

Question 7:

We have to determine the value of u + xy, if u = 18, x = 10, and y = 8

u + xy

= (18) + (10 x 8)

= 18 + 80

= 98

Option C is the correct answer.

Question 8:

Area of square = 479 square feet

$(side)^2 = 479$

$side = \sqrt 479$

side = 21.88

Side of the square is 21.9 feet.

Question 9:

We have to simplify  (7 + 5) + 4 x 13 - 2

= 12 + 52 - 2

=12 + 50

= 62

Answer 2

Answer:

Question 1: We have to simplify the expression (-1)(4 - c) by distributive property.

Using the distributive property a(b+c) = ab+ac

Consider (-1)(4-c) =  

=  - 4 + c

So, Option B is the correct answer.

Question 2: We have to simplify the expression 4(2x - 4) by distributive property.

Using the distributive property a(b+c) = ab+ac

Consider 4(2x-4) =  

=  8x - 16

So, Option C is the correct answer.

Question 3: We have to simplify the expression by distributive property.

Using the distributive property a(b+c) = ab+ac

Consider  

=  

=  

So, Option A is the correct answer.

Question 4:

We have to identify the subsets of real numbers to which 22 belong.

a) 22 belongs to the set of whole numbers as whole numbers are the set of numbers starting from zero to infinity.

b) 22 belongs to the set of rational numbers as rational numbers, as 22 can be written as   and rational numbers are represented in the form of  where p and q are integers and q is not equal to zero.

c) 22 belongs to the set of integers as integers is the set of numbers including whole numbers and negative whole numbers.

d) 22 does'not belong to the set of irrational numbers as irrational numbers are the numbers that cannot be expressed as a ratio between two integers.

e) 22 belongs to the set of natural numbers as natural numbers are the set of numbers from zero to infinity.

Question 5: We have to identify the algebraic expression for "6 times the difference of b and p"

=  

= 6(b-p)

Option B is the correct answer.

Question 6:

We have to determine the value of  

=  

= 360

Option D is the correct answer.

Question 7:

We have to determine the value of u + xy, if u = 18, x = 10, and y = 8

u + xy

= (18) + (10 x 8)

= 18 + 80

= 98

Option C is the correct answer.

Question 8:

Area of square = 479 square feet

side = 21.88

Side of the square is 21.9 feet.

Question 9:

We have to simplify  (7 + 5) + 4 x 13 - 2

= 12 + 52 - 2

=12 + 50

= 62

Step-by-step explanation: