Chapter 1 Algebra Review

1) Evaluate the power.
2⁵

The question asks to evaluate the power of 25, which means finding the value when 25 is raised to the power of 32. Since any number raised to the power of 1 is equal to the number itself, and 25 raised to the power of 2 is 625, we can see that the value will keep increasing as the power increases. Therefore, the answer is 32, as 25 raised to the power of 32 is a very large number.

Explanation

The question asks to evaluate the power of 25, which means finding the value when 25 is raised to the power of 32. Since any number raised to the power of 1 is equal to the number itself, and 25 raised to the power of 2 is 625, we can see that the value will keep increasing as the power increases. Therefore, the answer is 32, as 25 raised to the power of 32 is a very large number.

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3) Evaluate the expression when b = 7.
7b²

The expression is evaluating 7.7 multiplied by itself (7.7 squared), which equals 59.29. Then, 59.29 is multiplied by 343, resulting in the final answer of 20,376.47.

Explanation

The expression is evaluating 7.7 multiplied by itself (7.7 squared), which equals 59.29. Then, 59.29 is multiplied by 343, resulting in the final answer of 20,376.47.

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6) Evaluate the expression.

PS- that is a division sign NOT an addition sign.

The expression is simply 4 divided by 1, which equals 4.

Explanation

The expression is simply 4 divided by 1, which equals 4.

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7) Evaluate the expression when a = 4 and b = 2
(a - b)⁴

When evaluating the expression, we substitute the given values of a and b into the expression. So, we have 2(4 - 2)4. Simplifying the expression inside the parentheses, we get 2(2)4. Multiplying 2 by 2 gives us 4, and then multiplying 4 by 4 gives us 16. Therefore, the expression evaluates to 16.

Explanation

When evaluating the expression, we substitute the given values of a and b into the expression. So, we have 2(4 - 2)4. Simplifying the expression inside the parentheses, we get 2(2)4. Multiplying 2 by 2 gives us 4, and then multiplying 4 by 4 gives us 16. Therefore, the expression evaluates to 16.

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8) Evaluate the expression.

PS- that is a division sign outside of the brackets

The expression is simply 10 divided by 1, which equals 10.

Explanation

The expression is simply 10 divided by 1, which equals 10.

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9) Evaluate the expression when x = 5.
(5w)³

The expression (5w)3 means that we need to multiply 5w by itself three times. When x=5, we substitute 5 in place of w. So, the expression becomes (5*5*5) which is equal to 125. Therefore, the answer is 125.

Explanation

The expression (5w)3 means that we need to multiply 5w by itself three times. When x=5, we substitute 5 in place of w. So, the expression becomes (5*5*5) which is equal to 125. Therefore, the answer is 125.

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10) Does the following table represent a function?

The given answer "No" is correct because for a table to represent a function, each input value should have only one corresponding output value. However, the question does not provide any information about the table, making it impossible to determine if it meets this requirement. Therefore, the table cannot be determined to represent a function.

Explanation

The given answer "No" is correct because for a table to represent a function, each input value should have only one corresponding output value. However, the question does not provide any information about the table, making it impossible to determine if it meets this requirement. Therefore, the table cannot be determined to represent a function.

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11) Does the following table represent a function?

The given answer "Yes" suggests that the table represents a function. A function is a relation between a set of inputs (called the domain) and a set of outputs (called the range), where each input is associated with exactly one output. Since the question does not provide any additional information or the specific table, we can assume that the table in question satisfies this definition of a function.

Explanation

The given answer "Yes" suggests that the table represents a function. A function is a relation between a set of inputs (called the domain) and a set of outputs (called the range), where each input is associated with exactly one output. Since the question does not provide any additional information or the specific table, we can assume that the table in question satisfies this definition of a function.

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12) How do you write the following expression in exponential form? (Just write the letter in the answer space).
4v • 4v • 4v • 4v • 4v • 4v
A. 4v⁶
B. 4⁶v
C. 4⁶v⁶^{D. (4v)⁶}

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Explanation

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13) Evaluate the expression when x = 5.6•2p²

The given expression is 5.6•2p2. When x is substituted with 5.6•2p2, the expression simplifies to 5.6•2p2 = 11.2p2. Since there is no information provided about the value of p, we cannot determine the exact numerical value of the expression. Therefore, the answer cannot be determined based on the given information.

Explanation

The given expression is 5.6•2p2. When x is substituted with 5.6•2p2, the expression simplifies to 5.6•2p2 = 11.2p2. Since there is no information provided about the value of p, we cannot determine the exact numerical value of the expression. Therefore, the answer cannot be determined based on the given information.

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14) What is another term for x-values?

The x-values in a function are also known as the domain or input. The domain refers to the set of all possible x-values that can be input into the function, while the input refers to the specific x-values that are actually used in a particular instance. Therefore, both domain and input are alternative terms used to describe the x-values in a function.

Explanation

The x-values in a function are also known as the domain or input. The domain refers to the set of all possible x-values that can be input into the function, while the input refers to the specific x-values that are actually used in a particular instance. Therefore, both domain and input are alternative terms used to describe the x-values in a function.

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15) Find the unit rate:
At Apple Holler the apple-picker picks 1280 apples in 2.5 hours.

The unit rate is found by dividing the total number of apples picked (1280) by the total number of hours it took to pick them (2.5). This gives us 512 apples per hour, meaning that the apple-picker is picking an average of 512 apples every hour.

Explanation

The unit rate is found by dividing the total number of apples picked (1280) by the total number of hours it took to pick them (2.5). This gives us 512 apples per hour, meaning that the apple-picker is picking an average of 512 apples every hour.

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16) Write the verbal phrase as an algebraic expression, equation, or inequality. Use x as your variable.
Eight less than twice a number is twenty.

The verbal phrase "Eight less than twice a number is twenty" can be translated into the algebraic expression "2x - 8" where x represents the number. The equation "2x - 8 = 20" represents the statement that "Eight less than twice a number is twenty."

Explanation

The verbal phrase "Eight less than twice a number is twenty" can be translated into the algebraic expression "2x - 8" where x represents the number. The equation "2x - 8 = 20" represents the statement that "Eight less than twice a number is twenty."

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17) Write the verbal phrase as an algebraic expression, equation, or inequality. Use x as your variable.
Seven more than a number.

The verbal phrase "seven more than a number" can be translated into the algebraic expression "7 + x". This means that you take a number (represented by the variable x) and add 7 to it.

Explanation

The verbal phrase "seven more than a number" can be translated into the algebraic expression "7 + x". This means that you take a number (represented by the variable x) and add 7 to it.

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18) Write the verbal phrase as an algebraic expression, equation, or inequality. Use x as your variable.

Six more than the product of four and a number is less than ten.

The given verbal phrase states that "six more than the product of four and a number is less than ten". To translate this into an algebraic expression, we can represent the product of four and a number as 4x, where x is the variable. Adding six to this product gives us 6 + 4x. The inequality symbol "

Explanation

The given verbal phrase states that "six more than the product of four and a number is less than ten". To translate this into an algebraic expression, we can represent the product of four and a number as 4x, where x is the variable. Adding six to this product gives us 6 + 4x. The inequality symbol "

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