Factor the expression completely.

Question

100x+1000.


(1 point)
Responses

10(10x+100)
10 times open paren 10 x plus 100 close paren

100(x+10)
100 times open paren x plus 10 close paren

100(x+100)
100 times open paren x plus 100 close paren

1000(10x+1)

Answer 1

To factor the expression \(100x + 1000\) completely, we can look for the greatest common factor (GCF) of the two terms in the expression.

The GCF of \(100x\) and \(1000\) is \(100\).

Now we can factor \(100\) out of the expression:

\[ 100x + 1000 = 100(x + 10) \]

So the correct option is:

100(x + 10) (100 times open paren x plus 10 close paren).

Answer 2

Simplify.

3−(4x−5)+6


(1 point)
Responses

−4x+14
negative 4 x plus 14

4x+4
4 x plus 4

12x+21
12 x plus 21

−4x+4

Answer 3

Let's simplify the expression \(3 - (4x - 5) + 6\) step by step.

1. First, simplify inside the parentheses: \[ 3 - (4x - 5) + 6 = 3 - 4x + 5 + 6 \]

2. Combine the constant terms: \[ 3 + 5 + 6 = 14 \]

3. Now substitute back into the expression: \[ 14 - 4x \]

4. Finally, rearranging gives: \[ -4x + 14 \]

Thus, the simplified expression is:

−4x + 14 (negative 4 x plus 14).

Answer 4

Ella Grace bought 5 plants for her backyard for $20 each and 3 chairs for her firepit for $20 each. She used this expression to calculate the total amount she spent.

(5⋅20)+(3⋅20)


What is another expression to calculate the total amount spent?

(1 point)
Responses

5⋅(20+3)
5 times open paren 20 plus 3 close paren

20⋅(5+3)
20 times open paren 5 plus 3 close paren

(5+20)⋅(3+20)
open paren 5 plus 20 close paren times open paren 3 plus 20 close paren

5⋅20⋅3

Answer 5

To find another expression that calculates the total amount Ella Grace spent, we start with the given expression:

\[ (5 \cdot 20) + (3 \cdot 20) \]

We can factor this expression to simplify it. Notice that both terms include a factor of \(20\). We can rewrite the expression as:

\[ 20 \cdot (5 + 3) \]

This means she spent \(20\) dollars for each item, and the total number of items she purchased was \(5 + 3 = 8\). So, this gives us a different way to express the total cost.

Thus, the equivalent expression to calculate the total amount spent is:

20⋅(5+3) (20 times open paren 5 plus 3 close paren).

Answer 6

Which number sentence shows how the distributive property can be used to represent the area of the entire rectangle (both rectangles together)?

(1 point)
Responses

(9+6)⋅(9+11)
open paren 9 plus 6 close paren times open paren 9 plus 11 close paren

9⋅6⋅11
9 times 6 times 11

11(6+9)
11 times open paren 6 plus 9 close paren

(9⋅6)+(9⋅11)
open paren 9 times 6 close paren plus open paren 9 times 11 close paren

Answer 7

To represent the area of an entire rectangle (composed of smaller rectangles) using the distributive property, we want to express the area in a way that allows us to add the areas of the individual rectangles together.

In this case, if we have one rectangle that measures 9 units in height and combines two widths of 6 and 11, the total width is \(6 + 11\). Hence the expression for the area would be:

\[ 9 \cdot (6 + 11) \]

This expression represents the height multiplied by the total width. If we want to break it down using the distributive property, we can also express it as:

\[ (9 \cdot 6) + (9 \cdot 11) \]

This corresponds to finding the area of two smaller rectangles and adding them together.

So, both \(11(6 + 9)\) and \((9 \cdot 6) + (9 \cdot 11)\) show the way to express the area using the distributive property, but the closest one to how the distributive property applies in this context is:

(9⋅6)+(9⋅11)
(open paren 9 times 6 close paren plus open paren 9 times 11 close paren).

Answer 8

The image shows a simple diagram of a rectangle split into two parts labeled 6 and 11, with the total height of the rectangle labeled as 9. The image is simple and bland with a neutral atmosphere.

Answer 9

Based on your description of the diagram, the rectangle is split into two parts with widths labeled \(6\) and \(11\), and the total height of the rectangle is labeled as \(9\).

To calculate the area of the entire rectangle using the distributive property, you would represent it as follows:

1. The total width of the rectangle can be expressed as the sum of the two parts: \[ 6 + 11 \]

2. The area of the rectangle is then calculated as the height multiplied by the total width: \[ \text{Area} = \text{Height} \times \text{Total Width} = 9 \cdot (6 + 11) \]

Alternatively, using the distributive property to express the area by separating the individual areas of the two smaller rectangles gives: \[ \text{Area} = (9 \cdot 6) + (9 \cdot 11) \]

Thus, both methods clearly illustrate how the area of the entire rectangle can be represented.

Given this context and the options you provided previously, the most suitable expression representing the area of the entire rectangle using the distributive property would remain:

(9⋅6) + (9⋅11)
(open paren 9 times 6 close paren plus open paren 9 times 11 close paren).

This captures the area of each individual rectangle and combines them to give the total area of the larger rectangle.

Answer 10

Christine(C) and Ty(T) save quarters in a jar together. The jar had $28 in it, then Christine put in C quarters and Ty put in T quarters. Which expression can be used to represent the amount of money in the bank now?(1 point)
Responses

CT + 28
CT + 28

0.50(C + T) + 28
0.50(C + T) + 28

0.25C + 0.25T + 28
0.25C + 0.25T + 28

0.25FJ + 28

Answer 11

To represent the total amount of money in the jar after Christine (C) and Ty (T) add their quarters, we need to consider the initial amount in the jar along with the amount they contribute.

Initially, the jar had $28.

• Each quarter is worth $0.25, so:
  • The amount Christine contributes can be represented as \(0.25C\).
  • The amount Ty contributes can be represented as \(0.25T\).

Now, to find the total amount in the jar, we add the initial amount to the contributions from Christine and Ty:

\[ \text{Total amount} = 28 + 0.25C + 0.25T \]

This leads us to the expression:

0.25C + 0.25T + 28

So the correct answer is:

0.25C + 0.25T + 28 (0.25 times C plus 0.25 times T plus 28).