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

3w^2 - 3w + 8

11 answers

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 \( w = 4 \):

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

  1. Calculate \( 4^2 \):

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

  1. Multiply:

\[ = 48 - 12 + 8 \]

  1. Combine the terms:

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

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

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

w – 2

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 \( \boxed{6} \).

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

10x – 4y

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 \( 10(8) \):

\[ 10(8) = 80 \]

  1. 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 \( \boxed{52} \).

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

8z – 6

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 \( 8(4) \):

\[ 8(4) = 32 \]

  1. 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 \( \boxed{26} \).

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

4x^2 – 3x + 4

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 \( (5)^2 \):

\[ (5)^2 = 25 \]

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

\[ 4(25) = 100 \]

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

\[ 3(5) = 15 \]

Now, substitute these values back into the expression:

\[ 100 - 15 + 4 \]

Now, perform the operations:

  1. Calculate \( 100 - 15 \):

\[ 100 - 15 = 85 \]

  1. Then, add \( 4 \):

\[ 85 + 4 = 89 \]

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

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

6 ____ 6b -6 ____

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

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:

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