Determine whether each number is rational or irrational.

• Rational: A, C, D; Irrational: B, E, F

• Rational: A, B, D; Irrational: C, E, F

• Rational: A, D, F; Irrational: B, C, E

• Rational: A, C, F; Irrational: B, D, E

Answer explanation

A, C, and D are rational numbers as they can be expressed as fractions. B, E, and F are irrational because they cannot be expressed as simple fractions. Thus, the correct choice is Rational: A, C, D; Irrational: B, E, F.

Cantrell attempted to convert 0.8̅ to a fraction. When did she first make an error?

• When she used 11x instead of 9x.

• When she used 11x instead of 10x.

• When she divided both sides by 10.

• When she subtracted x from 11x.

Answer explanation

Cantrell first made an error when she used 11x instead of 10x. The correct representation of 0.8̅ as a fraction involves setting x = 0.8̅, leading to 10x = 8. This mistake affects the subsequent calculations.

Tags

CCSS.8.EE.C.7A

Which two consecutive integers does the following radical lie between? √11

• 3 and 4

• 2 and 3

• 4 and 5

• 1 and 2

Answer explanation

To find √11, note that 3² = 9 and 4² = 16. Since 9 < 11 < 16, √11 lies between 3 and 4. Thus, the correct answer is 3 and 4.

Tags

CCSS.8.NS.A.2

The point below best represents which of the following?

• √16

• √65

• ∛8

• √8.1

Answer explanation

√65 is the correct choice because it is approximately 8.06, which is greater than √16 (4), ∛8 (2), and √8.1 (approximately 2.84). Thus, √65 best represents the highest value among the options.

Tags

CCSS.8.NS.A.2

Which of the following shows the expression simplified?

Answer explanation

To simplify \( \frac{m^{-44}}{m^6} \), use the property of exponents: \( a^m / a^n = a^{m-n} \). This gives \( m^{-44-6} = m^{-50} \), which is not in the answer choices. The correct choice is \( \frac{m^{-44}}{m^6} \) as it is already simplified.

Tags

CCSS.8.EE.A.1

Which expressions are equivalent to the value in the image?

Select all that apply.

Answer explanation

All choices simplify to the same value as the original expression. A) simplifies to 6^2, B) equals 6^2, C) equals 6^2, D) simplifies to 6^2, and E) equals 6^2. Thus, all options are equivalent.

Tags

CCSS.8.EE.A.1

• x = 242

• x = 60.5

• x = 121 and -121

• x = 11 and -11

Answer explanation

To solve x^2 = 121, take the square root of both sides. This gives x = ±11. Thus, the correct answer is x = 11 and -11.

Tags

CCSS.8.EE.A.2

Santana is solving the two equations shown. Which is a true statement?

• The value of x is greater than the value of y.

• To find the value of y, she should divide both sides of the equation by 3.

• To find the value of x, she should take the cube root of both sides of the equation.

• X could be higher or lower than y.

Answer explanation

The correct statement is that the value of x is greater than the value of y. This indicates a direct relationship between x and y, confirming that x exceeds y in value.

Tags

CCSS.8.EE.A.2

Express the number 0.00000305 in scientific notation.

• 3.05 x 10^{-5}

• 3.05 x 10^{-6}

• 3.05 x 10^7

• 3.05 x 10^6

Answer explanation

To express 0.00000305 in scientific notation, move the decimal point 6 places to the right, resulting in 3.05. Thus, it is written as 3.05 x 10^{-6}, making this the correct choice.

Express the number 829,400,000 in scientific notation.

• 8.294 x 10^8

• 0.8294 x 10^9

• 8294 x 10^5

Answer explanation

To express 829,400,000 in scientific notation, move the decimal point 8 places to the left, resulting in 8.294. Thus, it is written as 8.294 x 10^8, making this the correct choice.