Enter the missing values in the area model to find 5(2t + 4)

Question

| 2t | ___
---------------
5 |____ | +20

GPT-4o mini · Answer

To solve the area model for the expression $ 5(2t + 4) $, we can break it down into parts.

First, let's recognize that the expression $ 2t + 4 $ can be split into two terms:

$ 2t $
$ 4 $

Now we can fill in the area model. The area model consists of a rectangle divided into two parts:

One part along the top is labeled $ 2t $ (the width).
The other part alongside it is labeled $ 4 $ (the width).

On the left side (the height), we have $ 5 $ for both sections since we are multiplying everything by $ 5 $.

Let's calculate the areas of both sections:

For the section corresponding to $ 2t $: \[ \text{Area} = \text{Height} \times \text{Width} = 5 \times 2t = 10t \]
For the section corresponding to $ 4 $: \[ \text{Area} = \text{Height} \times \text{Width} = 5 \times 4 = 20 \]

Thus, the completed area model will look like this:

\[ \begin{array}{|c|c|} \hline 2t & 4 \ \hline 5 & 10t & + 20 \ \hline \end{array} \]

So, the missing values are $ 10t $ in the bottom left cell and $ 4 $ in the top right cell. The full model is:

| 2t | 4 |

| 5 | 10t | +20 |

This confirms that $ 5(2t + 4) = 10t + 20 $.

UnicornSparkles · Answer

Enter the missing values in the area model to find 5(2t + 4) | 2t | ___ --------------- 5 |____ | +20 According to the model above 5(2t + 4)

GPT-4o mini · Answer

To fill out the area model for finding $ 5(2t + 4) $, we can break it into its components and represent them in the model. We start with the expression: $$ 5(2t + 4) $$ This expression can be expanded using the distributive property: $$ 5 \times 2t + 5 \times 4 = 10t + 20 $$ Now we fill in the area model: 1. The top-left cell represents $ 2t $ (one part of the expression). 2. The top-right cell is the missing value we need to find, which represents the $ 4 $ in $ 5(2t + 4) $. 3. The left side represents the height, which is $ 5 $. Now we calculate the missing values: - The area corresponding to $ 2t $ is: $$ 5 \times 2t = 10t $$ So we fill in the bottom-left cell with $ 10t $. - For the area corresponding to $ 4 $: $$ 5 \times 4 = 20 $$ Thus, we fill in the bottom-right cell with $ 20 $. Now, we can present the completed area model: | 2t | 4 | |---|---| | 5 | 10t | +20 | In summary, the completed area model reveals: - The missing value in the top-right cell is $ 4 $. - The missing value in the bottom-left cell is $ 10t $. This results in the final model: | 2t | 4 | |---|---| | 5 | 10t | +20 | So the complete expression represented in the area model confirms that $ 5(2t + 4) = 10t + 20 $.

UnicornSparkles · Answer

Enter the missing values in the area model to find 6(6m - 4) | ___ | -4 --------------- 6 |36m | ___ According to the model above 6(6m - 4)=

GPT-4o mini · Answer

To fill in the missing values in the area model for the expression $ 6(6m - 4) $, we can break it down using the distributive property.

Given the expression:

\[ 6(6m - 4) \]

We can expand this:

\[ 6 \times 6m + 6 \times (-4) = 36m - 24 \]

Now, we can fill in the area model.

The top-left cell corresponds to the term $ 6m $ (the first part of the expression). Since it’s not specified, we can denote this as $ 6m $.
The top-right cell corresponds to the term $-4$ and is already provided.
The height of the model (the leftmost value) is $ 6 $.
The bottom-left cell should represent the area of $ 6 \times 6m = 36m$ which is already provided.
The bottom-right cell is the missing value we need to calculate, which corresponds to the area for the term $ -4 $.

Calculating the bottom-right cell:

The area for $-4$ would be:

\[ 6 \times (-4) = -24 \]

Now we can fill in all the cells of the area model:

| 6m | -4 | |---|-----| | 6 | 36m | -24 |

Therefore:

According to the model above, we have:

\[ 6(6m - 4) = 36m - 24 \]

The completed model now shows the correct values.

UnicornSparkles · Answer

Enter the missing values in the area model to find 3(4v -9) | ___ | -9 --------------- 3 |12v| ___ According to the model above 3(4v - 9)=

GPT-4o mini · Answer

To fill in the missing values in the area model for the expression $ 3(4v - 9) $, we can expand it using the distributive property.

Given the expression:

\[ 3(4v - 9) \]

We can expand this:

\[ 3 \times 4v + 3 \times (-9) = 12v - 27 \]

Now, we can fill in the area model.

The top-left cell corresponds to the term $ 4v $ (the first part of the expression).
The top-right cell corresponds to the given term $ -9 $.
The height of the model (the leftmost value) is $ 3 $.
The bottom-left cell represents the value for $ 3 \times 4v = 12v $, which is already provided.
The bottom-right cell should correspond to the area for the term $ -9 $.

Calculating the bottom-right cell:

The area for $ -9 $ would be:

\[ 3 \times (-9) = -27 \]

Now we can fill in all the cells of the area model:

| 4v | -9 | |---|-----| | 3 | 12v | -27 |

Therefore:

According to the model above,

\[ 3(4v - 9) = 12v - 27 \]

So the completed model now shows all the correct values.

UnicornSparkles · Answer

Enter the missing values in the area model to find 7(7p - 7) | ___ | -7 --------------- 7 |49p| ___ According to the model above 7(7p - 7)

GPT-4o mini · Answer

To fill in the missing values in the area model for the expression $ 7(7p - 7) $, we can expand it using the distributive property.

Given the expression:

\[ 7(7p - 7) \]

We can expand this expression:

\[ 7 \times 7p + 7 \times (-7) = 49p - 49 \]

Now we can fill in the area model accordingly.

The top-left cell corresponds to the term $ 7p $ (the first part of the expression).
The top-right cell corresponds to the term $-7$ (which is already given).
The height of the model (the leftmost value) is $ 7 $.
The bottom-left cell represents the value for $ 7 \times 7p = 49p$, which is already provided.
The bottom-right cell corresponds to the area for the term $ -7 $.

Calculating the bottom-right cell:

The area for $-7$ would be:

\[ 7 \times (-7) = -49 \]

Now we can fill in all the cells of the area model:

| 7p | -7 | |---|-----| | 7 | 49p | -49 |

Therefore:

According to the model above,

\[ 7(7p - 7) = 49p - 49 \]

So the completed model now shows all the correct values.