What are the solutions to questions 4, 5, and 6?

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4. Express 72 as a product of its prime factors using a factor tree. (3 marks)

Start with 72 and find two factors.
$72 = 2 \times 36$
Continue factoring until all branches end in prime numbers.
$36 = 2 \times 18$ $18 = 2 \times 9$ $9 = 3 \times 3$
Collect all the prime factors.
$72 = 2 \times 2 \times 2 \times 3 \times 3$ $72 = 2^3 \times 3^2$
The prime factors of 72 are $2 \times 2 \times 2 \times 3 \times 3$ .
The product of its prime factors is $\boxed{2^3 \times 3^2}$ .

5. The cube below was used to hold milk. What is the volume of the cube? (3 marks)
Identify the side length of the cube from the image.
The side length of the cube is $20 \text{ cm}$ .
Use the formula for the volume of a cube.
The volume $V$ of a cube with side length $s$ is $V = s^3$ .
Substitute the side length into the formula and calculate.
$V = (20 \text{ cm})^3$ $V = 20 \text{ cm} \times 20 \text{ cm} \times 20 \text{ cm}$ $V = 8000 \text{ cm}^3$
The volume of the cube is $\boxed{8000 \text{ cm}^3}$ .

6. Salome had 6 oranges, Moraa had 18 of them while Jeremy had 12 oranges. What is the L.C.M of the numbers? (3 marks)
List the numbers given.
The numbers are 6, 18, and 12.
Find the prime factorization of each number.
$6 = 2 \times 3$ $18 = 2 \times 3 \times 3 = 2 \times 3^2$ $12 = 2 \times 2 \times 3 = 2^2 \times 3$
To find the L.C.M, take the highest power of each prime factor present in any of the numbers.
The prime factors are 2 and 3.
The highest power of 2 is $2^2$ (from 12).
The highest power of 3 is $3^2$ (from 18).
Multiply these highest powers together.
$\text{L.C.M} = 2^2 \times 3^2$ $\text{L.C.M} = 4 \times 9$ $\text{L.C.M} = 36$
The L.C.M of 6, 18, and 12 is $\boxed{36}$ .

10. Simplify the expression $5x + 20 + 8x + 10$ .
Group like terms together.
$5x + 8x + 20 + 10$
Combine the $x$ terms.
$5x + 8x = 13x$
Combine the constant terms.
$20 + 10 = 30$
Write the simplified expression.
$13x + 30$
The simplified expression is $\boxed{13x + 30}$ .

What are the solutions to questions 4, 5, and 6?

Step-by-step solution

Start with 72 and find two factors.

Continue factoring until all branches end in prime numbers.

Collect all the prime factors.

Identify the side length of the cube from the image.

Use the formula for the volume of a cube.

Substitute the side length into the formula and calculate.

List the numbers given.

Find the prime factorization of each number.

To find the L.C.M, take the highest power of each prime factor present in any of the numbers.

Multiply these highest powers together.

Group like terms together.

Combine the $x$ terms.

Combine the constant terms.

Write the simplified expression.

Still stuck on this one?

More Mathematics Questions

What are the solutions to questions 4, 5, and 6?

Step-by-step solution

Start with 72 and find two factors.

Continue factoring until all branches end in prime numbers.

Collect all the prime factors.

Identify the side length of the cube from the image.

Use the formula for the volume of a cube.

Substitute the side length into the formula and calculate.

List the numbers given.

Find the prime factorization of each number.

To find the L.C.M, take the highest power of each prime factor present in any of the numbers.

Multiply these highest powers together.

Group like terms together.

Combine the xxx terms.

Combine the constant terms.

Write the simplified expression.

Still stuck on this one?

More Mathematics Questions

Combine the $x$ terms.