ILEARN review

David is building a ramp for his skateboard. The ramp forms a right triangle with the ground, with one leg of the triangle being 3 cm and the other leg being 4 cm. What is the length of the hypotenuse of the ramp?

• 5 cm

• 6 cm

• 7 cm

• 8 cm

Answer explanation

To find the hypotenuse of a right triangle, use the Pythagorean theorem: a² + b² = c². Here, 3² + 4² = 9 + 16 = 25. Thus, c = √25 = 5 cm. Therefore, the hypotenuse is 5 cm.

Tags

CCSS.8.G.B.7

Rohan is trying to measure the diagonal of a square field using a rope. He knows the side of the square is 1 unit. Which of the following numbers represents the length of the diagonal of the square field?

• 0.75

• 1.333...

Answer explanation

The number \( \sqrt{2} \) is irrational because it cannot be expressed as a fraction of two integers. In contrast, \( \frac{1}{2} \), 0.75, and 1.333... are all rational numbers.

Tags

CCSS.8.NS.A.2

Liam has a ribbon that is 0.666... meters long. Convert the length of the ribbon into a fraction.

Answer explanation

To convert 0.666... to a fraction, let x = 0.666... . Then, 10x = 6.666... . Subtracting these gives 9x = 6, so x = 6/9, which simplifies to 2/3. Thus, the correct answer is \frac{2}{3}.

Tags

CCSS.7.NS.A.2D

CCSS.8.NS.A.1

Answer explanation

The volume of a cylinder is calculated using the formula V = πr²h. Here, r = 3 cm and h = 5 cm. Thus, V = π(3²)(5) = π(9)(5) = 45π cm³. Therefore, the correct answer is 45π cm³.

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

Grace is measuring the thickness of a thin sheet of paper. She finds that the thickness is 0.00045 meters. What is the scientific notation for this thickness?

Answer explanation

To convert 0.00045 to scientific notation, move the decimal point 5 places to the right, giving 4.5. This corresponds to multiplying by 10 raised to the power of -5, so the correct answer is 4.5 × 10^{-5}.

Tags

CCSS.8.EE.A.3

Daniel is tracking his daily exercise time and the calories he burns. A scatter plot shows a positive linear association between the time he exercises and the calories burned. Which of the following best describes this pattern?

• As Daniel exercises more, he burns fewer calories.

• As Daniel exercises more, he burns more calories.

• There is no relationship between exercise time and calories burned.

• The calories burned are inversely proportional to exercise time.

Answer explanation

A positive linear association means that as one variable increases, the other also increases. This is best described by the choice: 'As one variable increases, the other increases.' The other options describe different relationships.

Tags

CCSS.HSF-LE.A.1B

Aria is building a ramp for her skateboard. The ramp forms a right triangle with the ground. The hypotenuse of the ramp is 10 cm long, and one leg of the triangle is 6 cm long. What is the length of the other leg of the ramp?

• 8 cm

• 7 cm

• 9 cm

• 5 cm

Answer explanation

Using the Pythagorean theorem, a² + b² = c², where c is the hypotenuse. Here, 6² + b² = 10². This simplifies to 36 + b² = 100. Thus, b² = 64, and b = 8 cm. Therefore, the length of the other leg is 8 cm.

Tags

CCSS.8.G.B.7

Which of the following is a rational number?

• 0.25

Answer explanation

A rational number can be expressed as a fraction of two integers. 0.25 is equivalent to 1/4, making it a rational number. In contrast, π, √3, and e are all irrational numbers.

Olivia is trying to convert the repeating decimal 0.8181... into a fraction for her math homework. Can you help her find the correct fraction?

Answer explanation

Let x = 0.8181... . Then, 100x = 81.8181... . Subtracting gives 99x = 81, so x = \frac{81}{99}. This fraction simplifies to \frac{9}{11}, but the correct answer in the context is \frac{81}{99}.

Tags

CCSS.7.NS.A.2D

CCSS.8.NS.A.1

Answer explanation

The volume of a cone is calculated using the formula \( V = \frac{1}{3} \pi r^2 h \). Substituting \( r = 4 \) cm and \( h = 9 \) cm gives \( V = \frac{1}{3} \pi (4^2)(9) = \frac{1}{3} \pi (16)(9) = 48\pi \, \text{cm}^3 \). Thus, the correct answer is \( 48\pi \, \text{cm}^3 \).

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3