Question 1

Place the correct symbol (<, >, or =) between the pair of real numbers. -|2| -|-2|

Accepted Answer

The absolute value of both 2 and -2 is 2, so -|2| and -|-2| both equal -2, making them equal.

Question 2

Evaluate the expression. |7 - 8|

Accepted Answer

The absolute value of 7-8 is equal to the absolute value of -1, which is 1. Therefore, the answer is A)1.

Question 3

Evaluate the following expression. 7² · 7

Accepted Answer

The expression uses a base-7 numbering system. Converting it to base-10: 7² · 7 = 7*7^4 + 1*7^3 + 1*7^2 + 1*7^1 + 2*7^0 = 16807 + 343 + 49 + 7 + 2 = 17208. Multiplying by 7 gives 120456, which is not an option because the correct interpretation is to see the expression as a string of digits in base 7, not as an algebraic expression. The correct interpretation is 71127 (in base 7) multiplied by 7. Converting 71127 from base 7 to base 10 gives 1*7^4 + 1*7^3 + 1*7^2 + 2*7^1 + 7*7^0 = 2401 + 343 + 49 + 14 + 7 = 2814. Multiplying by 7 gives 19703, which indicates a misunderstanding in the conversion process. The correct approach is to recognize the expression as a representation in base 7, directly multiply the base 7 number by 7, and then convert if necessary. However, the multiplication should be understood in the context of the base, not directly in base 10. The correct answer, therefore, is derived from understanding the expression in its intended base and context. Given the misunderstanding in the explanation, the correct answer is actually 343 when correctly interpreting the base-7 expression and performing the multiplication within that base, or understanding the question as asking for a direct evaluation in base 10 without conversion.

Question 4

Is the interval bounded or unbounded? -6 < x < -1

Accepted Answer

The interval is bounded because there are finite values that x can take within the interval (-6 and -1).

Question 5

Use absolute value notation to describe the situation. The distance between u and -5 is no less than 9.

Accepted Answer

The absolute value notation for the distance between u and -5 being no less than 9 is |u + 5| ≥ 9.

Question 6

Identify the rules of algebra illustrated from left to right by the following statement.

Accepted Answer

The answer of Identify the rules of algebra illustrated from...

Question 7

Plot the two real numbers on the real number line.Then place the appropriate inequality symbol (< or >) between them.​ ​
​  ,  ​

Accepted Answer

The answer of Plot the two real numbers on the...

Question 8

Evaluate the expression for the given value of x. expression: -3x² + 3x - 2 value: x = -4

Accepted Answer

The expression given is -3x^12 + 3x - 2. Substituting x = -4, we get -3(-4)^12 + 3(-4) - 2 = -3(16777216) - 12 - 2 = -50331660 - 14 = -50331674. Therefore, the correct answer is -62.

Question 9

Evaluate the expression.  , x < -5

Accepted Answer

The answer of Evaluate the expression.  , x <...

Question 10

Place the correct symbol (<, >, or =) between the pair of real numbers. -(-4) -4

Accepted Answer

The expression -(-4) simplifies to 4, so the comparison is 4 > -4, making option C correct.

Question 11

Use absolute value notation to describe the situation. t is more than five units from -8.

Accepted Answer

The absolute value of t plus 8 must be greater than 5 which represents that t is more than 5 units from -8.

Question 12

List the coefficients of the variable terms in the expression:

Accepted Answer

The answer of List the coefficients of the variable terms...

Question 13

Identify the rules of algebra illustrated from left to right by the following statement. (z​ - 7) + 7 = z + (-7 + 7) = z + 0 = z

Accepted Answer

The statement illustrates the associative property of addition, followed by the additive inverse property, and finally the additive identity property.

Question 14

List the terms of the expression: 9v² + 13v + 8

Accepted Answer

The terms in the given expression are separated by the addition sign (+). Therefore, each group of numbers and variables between two addition signs is a separate term. The expression has three terms: 1. 9v² 2. 13v 3. 8 Therefore, the best choice is D, which lists all three terms.

Question 15

Use absolute value notation to describe the situation. The elevation at the bottom of a mountain is 398 feet above sea level.The elevation at the top of the mountain is 4672 feet above sea level.What is the height of the mountain?

Accepted Answer

The height of the mountain is the difference in elevation between the top and the bottom, which is |4672 - 398|.

Question 16

Use inequality notation to describe the set. s is at least -22 but less than -16

Accepted Answer

The inequality notation for "s is at least -22 but less than -16" is -22 ≤ s < -16. The correct choice is B.

Question 17

Identify the rule of algebra illustrated by the statement. 5p + 4p = (5 + 4)p

Accepted Answer

The statement illustrates the distributive property, which allows you to multiply a single term by each term inside a parenthesis and then add the results.

Question 18

Evaluate the expression for the given value of x. expression:  value: x = -9

Accepted Answer

When x is substituted with -9, the expression becomes 0 as e^(-9) equals 1/e^9, which is a very small value close to 0. Therefore, the answer is C.

Question 19

Plot the two real numbers on the real number line.Then place the appropriate inequality symbol (< or >) between them. -2, -3

Accepted Answer

The symbol ">" means "greater than", so -2 is to the right of -3 on the number line, indicating that -2 is greater than -3.

Question 20

Use inequality notation to describe the set. r is positive

Accepted Answer

The inequality r > 0 correctly describes the set where r is positive, meaning r is greater than zero.

Quiz 7: Prerequisites

Place the correct symbol (<, >, or =) between the pair of real numbers. -|2| -|-2|

Evaluate the expression. |7 - 8|

Evaluate the following expression. 7² · 7

Is the interval bounded or unbounded? -6 < x < -1

Use absolute value notation to describe the situation. The distance between u and -5 is no less than 9.

Identify the rules of algebra illustrated from left to right by the following statement.

Plot the two real numbers on the real number line.Then place the appropriate inequality symbol (< or >) between them. ,

Evaluate the expression for the given value of x. expression: -3x² + 3x - 2 value: x = -4

Evaluate the expression. , x < -5

Place the correct symbol (<, >, or =) between the pair of real numbers. -(-4) -4

Use absolute value notation to describe the situation. t is more than five units from -8.

List the coefficients of the variable terms in the expression:

Identify the rules of algebra illustrated from left to right by the following statement. (z - 7) + 7 = z + (-7 + 7) = z + 0 = z

List the terms of the expression: 9v² + 13v + 8

Use absolute value notation to describe the situation. The elevation at the bottom of a mountain is 398 feet above sea level.The elevation at the top of the mountain is 4672 feet above sea level.What is the height of the mountain?

Use inequality notation to describe the set. s is at least -22 but less than -16

Identify the rule of algebra illustrated by the statement. 5p + 4p = (5 + 4) p

Evaluate the expression for the given value of x. expression: value: x = -9

Plot the two real numbers on the real number line.Then place the appropriate inequality symbol (< or >) between them. -2, -3

Use inequality notation to describe the set. r is positive

Quiz 7: Prerequisites

Place the correct symbol (<, >, or =) between the pair of real numbers. -|2| -|-2|

Evaluate the expression. |7 - 8|

Evaluate the following expression. ​ 72 · 7 ​

Is the interval bounded or unbounded? -6 < x < -1

Use absolute value notation to describe the situation. The distance between u and -5 is no less than 9.

Identify the rules of algebra illustrated from left to right by the following statement.

Plot the two real numbers on the real number line.Then place the appropriate inequality symbol (< or >) between them.​ ​ ​ , ​

Evaluate the expression for the given value of x. expression: -3x2 + 3x - 2 value: x = -4

Evaluate the expression. , x < -5

Place the correct symbol (<, >, or =) between the pair of real numbers. -(-4) -4

Use absolute value notation to describe the situation. t is more than five units from -8.

List the coefficients of the variable terms in the expression:

Identify the rules of algebra illustrated from left to right by the following statement. (z​ - 7) + 7 = z + (-7 + 7) = z + 0 = z

​List the terms of the expression: ​ ​9v2 + 13v + 8

Use absolute value notation to describe the situation. The elevation at the bottom of a mountain is 398 feet above sea level.The elevation at the top of the mountain is 4672 feet above sea level.What is the height of the mountain?

Use inequality notation to describe the set. s is at least -22 but less than -16

Identify the rule of algebra illustrated by the statement. 5p + 4p = (5 + 4) p

Evaluate the expression for the given value of x. expression: value: x = -9

Plot the two real numbers on the real number line.Then place the appropriate inequality symbol (< or >) between them. -2, -3

Use inequality notation to describe the set. r is positive

Evaluate the following expression. 7² · 7

Plot the two real numbers on the real number line.Then place the appropriate inequality symbol (< or >) between them. ,

Evaluate the expression for the given value of x. expression: -3x² + 3x - 2 value: x = -4

Identify the rules of algebra illustrated from left to right by the following statement. (z - 7) + 7 = z + (-7 + 7) = z + 0 = z

List the terms of the expression: 9v² + 13v + 8