Classify the number: 0.5

• Rational

• Irrational

• Integer

• Whole

Answer explanation

The number 0.5 is a rational number because it can be expressed as the fraction 1/2, where both the numerator and denominator are integers. It is not an integer or whole number.

Tags

CCSS.HSN.RN.B.3

• Rational

• Irrational

Answer explanation

The number \(\sqrt{3}\) cannot be expressed as a fraction of two integers, which defines a rational number. Since it is not possible to write \(\sqrt{3}\) in such a form, it is classified as an irrational number.

Tags

CCSS.HSN.RN.B.3

• 10

• 12

• 14

• 16

Answer explanation

To find f(4), substitute x with 4 in the function f(x) = 3x + 2. This gives f(4) = 3(4) + 2 = 12 + 2 = 14. Therefore, the correct answer is 14.

Tags

CCSS.HSF.IF.A.2

• All real numbers

• All real numbers except 0

• All positive numbers

• All negative numbers

Answer explanation

The function f(x) = 1/x is undefined at x = 0, as division by zero is not possible. Therefore, the domain includes all real numbers except 0.

Tags

CCSS.HSF.IF.B.5

Answer explanation

The relationship states that the total cost C is 5 times the number of items n. This can be expressed mathematically as C = 5n, which is the correct choice. The other options do not accurately represent this relationship.

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

Answer explanation

The expression "the sum of a number x and 7" translates to adding 7 to x, which is represented as x + 7. Therefore, the correct choice is x + 7.

Tags

CCSS.6.EE.A.2A

• 5

• 7

• 12

• 17

Answer explanation

To solve for x in the equation x + 5 = 12, subtract 5 from both sides. This gives x = 12 - 5, which simplifies to x = 7. Therefore, the correct answer is 7.

Tags

CCSS.6.EE.B.7

Explain why the sum of two rational numbers is rational.

• Because the sum is always an integer

• Because the sum can be expressed as a fraction

• Because the sum is always a whole number

• Because the sum is always irrational

Answer explanation

The sum of two rational numbers can be expressed as a fraction, since rational numbers are defined as the ratio of two integers. Therefore, their sum is also a ratio of integers, making it rational.

Tags

CCSS.HSN.RN.B.3

• 3

• 5

• 7

• 9

Answer explanation

To find g(2), substitute x with 2 in the function g(x) = 2x^2 - 3x + 1. This gives g(2) = 2(2)^2 - 3(2) + 1 = 8 - 6 + 1 = 3. Thus, the correct answer is 3.

Tags

CCSS.HSF.IF.A.2

• All real numbers

• All positive numbers

• All non-negative numbers

• All negative numbers

Answer explanation

The function f(x) = x^2 outputs values that are always greater than or equal to zero. Therefore, the range of the function is all non-negative numbers, which includes zero and all positive numbers.

Tags

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7