Question

What is the value of the expression below when w = 4

3w^2 - 3w + 8

Answer 1

To find the value of the expression \( 3w^2 - 3w + 8 \) when \( w = 4 \), we will substitute \( 4 \) for \( w \) and then evaluate the expression.

1. Substitute \( w = 4 \):

\[
3(4)^2 - 3(4) + 8
\]

2. Calculate \( 4^2 \):

\[
= 3(16) - 3(4) + 8
\]

3. Multiply:

\[
= 48 - 12 + 8
\]

4. Combine the terms:

\[
= 48 - 12 = 36
\]
\[
= 36 + 8 = 44
\]

So, the value of the expression \( 3w^2 - 3w + 8 \) when \( w = 4 \) is \( \boxed{44} \).

Answer 2

What is the value of the expression below when w = 8

w – 2

Answer 3

To find the value of the expression \( w - 2 \) when \( w = 8 \), we will substitute \( 8 \) for \( w \):

\[
w - 2 = 8 - 2
\]

Now, calculate:

\[
8 - 2 = 6
\]

So, the value of the expression \( w - 2 \) when \( w = 8 \) is \( \boxed{6} \).

Answer 4

What is the value of the expression below when x = 8 and y = 7

10x – 4y

Answer 5

To find the value of the expression \( 10x - 4y \) when \( x = 8 \) and \( y = 7 \), we will substitute \( 8 \) for \( x \) and \( 7 \) for \( y \):

\[
10x - 4y = 10(8) - 4(7)
\]

Now, calculate each term:

1. Calculate \( 10(8) \):

\[
10(8) = 80
\]

2. Calculate \( 4(7) \):

\[
4(7) = 28
\]

Now, substitute these values back into the expression:

\[
80 - 28
\]

Finally, perform the subtraction:

\[
80 - 28 = 52
\]

So, the value of the expression \( 10x - 4y \) when \( x = 8 \) and \( y = 7 \) is \( \boxed{52} \).

Answer 6

What is the value of the expression below when z = 4

8z – 6

Answer 7

To find the value of the expression \( 8z - 6 \) when \( z = 4 \), we will substitute \( 4 \) for \( z \):

\[
8z - 6 = 8(4) - 6
\]

Now, calculate:

1. Calculate \( 8(4) \):

\[
8(4) = 32
\]

2. Substitute this value back into the expression:

\[
32 - 6
\]

Now, perform the subtraction:

\[
32 - 6 = 26
\]

So, the value of the expression \( 8z - 6 \) when \( z = 4 \) is \( \boxed{26} \).

Answer 8

What is the value of the expression below when x = 5

4x^2 – 3x + 4

Answer 9

To find the value of the expression \( 4x^2 - 3x + 4 \) when \( x = 5 \), we will substitute \( 5 \) for \( x \):

\[
4x^2 - 3x + 4 = 4(5)^2 - 3(5) + 4
\]

Now, calculate each term step by step:

1. Calculate \( (5)^2 \):

\[
(5)^2 = 25
\]

2. Calculate \( 4(25) \):

\[
4(25) = 100
\]

3. Calculate \( 3(5) \):

\[
3(5) = 15
\]

Now, substitute these values back into the expression:

\[
100 - 15 + 4
\]

Now, perform the operations:

1. Calculate \( 100 - 15 \):

\[
100 - 15 = 85
\]

2. Then, add \( 4 \):

\[
85 + 4 = 89
\]

So, the value of the expression \( 4x^2 - 3x + 4 \) when \( x = 5 \) is \( \boxed{89} \).

Answer 10

Enter the missing values in the area model to find 6 (6b – 1)

6 ____ 6b -6 ____


According to the model above 6 (6b - 1)

Answer 11

To fill in the missing values in the area model for the expression \( 6(6b - 1) \), we can follow the distributive property of multiplication over addition.

First, let's break down the expression:

\[
6(6b - 1) = 6 \cdot 6b - 6 \cdot 1
\]

This means that:

- The first term (missing value above) will be \( 6 \cdot 6b \)
- The second term (missing value below) will be \( -6 \cdot 1 \)

Thus, we can fill in the area model as follows:

- The left area will represent \( 6 \) (as it is the common factor).
- The right area will represent \( 6b \) for the first term and \( -1 \) for the second term.

**The filled area model looks like this:**

\[
\begin{array}{|c|c|}
\hline
6 & 6b \\
\hline
6 & -6 \\
\hline
\end{array}
\]

So, the completed area model corresponds with the factored expression \( 6(6b - 1) \).

Now, if we calculate the total area, we have:

1. The area of the first rectangle: \( 6 \cdot 6b = 36b \)
2. The area of the second rectangle: \( 6 \cdot (-1) = -6 \)

Thus, the expression expands to:

\[
36b - 6
\]

Therefore, the completed area model is:

\[
6(6b - 1) = 36b - 6
\]