Question 1

Indicate True (T) or False (F), and for each false statement find real number replacements for a, b, and c that will provide a counterexample.
-a - b = b - a

Accepted Answer

a = 1 and b = 2 provides a counterexample

Question 2

Indicate True (T) or False (F), and for each false statement find real number replacements for a, b, and c that will provide a counterexample.
-(a - b) - c = a - (b - c)

Accepted Answer

a = 3, b = 2, and c = 1 provides a counterexample

Question 3

Indicate True (T) or False (F), and for each false statement find real number replacements for a, b, and c that will provide a counterexample.
-a + b = b + a

Accepted Answer

This statement is true because addition is commutative, meaning that changing the order of the numbers being added does not change the sum.

Question 4

Indicate True (T) or False (F), and for each false statement find real number replacements for a, b, and c that will provide a counterexample.
-(a - b) - c = a - (b - c)

Accepted Answer

The associative property of addition states that the grouping of addends does not affect the sum.

Question 5

Indicate True (T) or False (F) by each statement.
-Every real number is a natural number.

Accepted Answer

Not every real number is a natural number because real numbers include all the rational and irrational numbers, which can be negative or non-integer, whereas natural numbers are positive integers starting from 1.

Question 6

Indicate True (T) or False (F) by each statement.
-An irrational number is not a real number.

Accepted Answer

Irrational numbers are a subset of real numbers, consisting of numbers that cannot be expressed as a simple fraction.

Question 7

Indicate True (T) or False (F) by each statement.
-Every natural number is an integer.

Accepted Answer

Every natural number (1, 2, 3, ...) is also an integer, as integers include all whole numbers, both positive and negative, including zero.

Question 8

Indicate True (T) or False (F) by each statement.
-An integer is a rational number.

Accepted Answer

An integer is a rational number because it can be expressed as the ratio of itself to 1, fitting the definition of a rational number as one that can be expressed as a fraction a/b where a and b are integers and b is not zero.

Question 9

Given the sets N, Z, Q, and R, indicate to which set(s) each of the following numbers belong.
(A)  
(B) e
(C) -2
(D) 8

Accepted Answer

The answer of Given the sets N, Z, Q, and...

Question 10

Find the product:
-( 3x + 12y)( 5x + 8y)
A) 
B) 
C) 
D)

Accepted Answer

The answer of Find the product:
-( 3x + 12y)( 5x...

Question 11

Find the product:
-
A) 
B) 
C) 
D)

Accepted Answer

The answer of Find the product:
-
A) 
B) 
C) 
D) ...

Question 12

Find the product:
--3( 10r + 2) + 5( 2r + 3)
A) 7r - 1
B) -36r
C) -20r + 9
D) -20r + 2

Accepted Answer

First, distribute the numbers outside the parentheses: -3 * 10r = -30r, -3 * 2 = -6, 5 * 2r = 10r, and 5 * 3 = 15. Then, combine like terms: -30r + 10r = -20r, and -6 + 15 = 9. So, the product is -20r + 9.

Question 13

Factor the GCF from the polynomial:
-
A) 
B) 
C) 
D)

Accepted Answer

The answer of Factor the GCF from the polynomial:
-
A) 
B)...

Question 14

Factor completely using grouping: -18y² + 81y - 45 A) ( 18y - 9)(y + 5) B) 9(2y + 1)(y - 5) C) 9(2y - 1)(y + 5) D) prime

Accepted Answer

The given expression can be factored by first factoring out the greatest common factor (GCF), which is 9, resulting in 9(2y^2 + 9y - 5). Then, by using the grouping method, we can factor the quadratic expression inside the parentheses to get 9(2y - 1)(y + 5).

Question 15

Factor by grouping:

Accepted Answer

The answer of Factor by grouping: ...

Question 16

Factor the expression using integer coefficients:

Accepted Answer

The answer of Factor the expression using integer coefficients: ...

Question 17

Which polynomial can be factored using integer coefficients? Find its factored form.
A)  
B)  
C)

Accepted Answer

(4x + 5)(5x - 7)

Question 18

Factor using integer coefficients:

Accepted Answer

The answer of Factor using integer coefficients: ...

Question 19

Simplify the expression:
-
A) 
B) 
C) 
D)

Accepted Answer

The answer of Simplify the expression:
-
A) 
B) 
C) 
D) ...

Question 20

Perform the indicated operation and reduce to lowest terms:

Accepted Answer

The answer of Perform the indicated operation and reduce to...

Quiz 12: Appendix A: Basic Algebra Review

Indicate True (T) or False (F), and for each false statement find real number replacements for a, b, and c that will provide a counterexample. -a - b = b - a

Indicate True (T) or False (F), and for each false statement find real number replacements for a, b, and c that will provide a counterexample. -(a - b) - c = a - (b - c)

Indicate True (T) or False (F), and for each false statement find real number replacements for a, b, and c that will provide a counterexample. -a + b = b + a

Indicate True (T) or False (F), and for each false statement find real number replacements for a, b, and c that will provide a counterexample. -(a - b) - c = a - (b - c)

Indicate True (T) or False (F) by each statement. -Every real number is a natural number.

Indicate True (T) or False (F) by each statement. -An irrational number is not a real number.

Indicate True (T) or False (F) by each statement. -Every natural number is an integer.

Indicate True (T) or False (F) by each statement. -An integer is a rational number.

Given the sets N, Z, Q, and R, indicate to which set(s) each of the following numbers belong. (A) (B) e (C) -2 (D) 8

Find the product: -( 3x + 12y) ( 5x + 8y)

Find the product: -

Find the product: --3( 10r + 2) + 5( 2r + 3)

Factor the GCF from the polynomial: -

Factor completely using grouping: -18y² + 81y - 45

Factor by grouping:

Factor the expression using integer coefficients:

Which polynomial can be factored using integer coefficients? Find its factored form.

Factor using integer coefficients:

Simplify the expression: -

Perform the indicated operation and reduce to lowest terms:

Quiz 12: Appendix A: Basic Algebra Review

Indicate True (T) or False (F), and for each false statement find real number replacements for a, b, and c that will provide a counterexample. -a - b = b - a

Indicate True (T) or False (F), and for each false statement find real number replacements for a, b, and c that will provide a counterexample. -(a - b) - c = a - (b - c)

Indicate True (T) or False (F), and for each false statement find real number replacements for a, b, and c that will provide a counterexample. -a + b = b + a

Indicate True (T) or False (F), and for each false statement find real number replacements for a, b, and c that will provide a counterexample. -(a - b) - c = a - (b - c)

Indicate True (T) or False (F) by each statement. -Every real number is a natural number.

Indicate True (T) or False (F) by each statement. -An irrational number is not a real number.

Indicate True (T) or False (F) by each statement. -Every natural number is an integer.

Indicate True (T) or False (F) by each statement. -An integer is a rational number.

Given the sets N, Z, Q, and R, indicate to which set(s) each of the following numbers belong. (A) (B) e (C) -2 (D) 8

Find the product: -( 3x + 12y) ( 5x + 8y)

Find the product: -

Find the product: --3( 10r + 2) + 5( 2r + 3)

Factor the GCF from the polynomial: -

Factor completely using grouping: -18y2 + 81y - 45

Factor by grouping:

Factor the expression using integer coefficients:

Which polynomial can be factored using integer coefficients? Find its factored form.

Factor using integer coefficients:

Simplify the expression: -

Perform the indicated operation and reduce to lowest terms:

Factor completely using grouping: -18y² + 81y - 45