Question

Factor the expression: 9x + 21(1 point)
Responses

9 (x + 3)
9 (x + 3)

3(3x + 6)
3(3x + 6)

3(3x + 18)
3(3x + 18)

3(3x + 7)

Answer 1

Factor the expression: 35x + 20(2 points)
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
5( Response area x + Response area)

Answer 2

Add the expressions.

(2.5x + 3) + (5x - 1.2)

(1 point)
Responses

7.5x + 1.8
7.5x + 1.8

2.5x + 1.2
2.5x + 1.2

2.5x + 4.2
2.5x + 4.2

7.5x + 3

Answer 3

Subtract the expressions.

(8y + 6) - (3y + 4)

(1 point)
Responses

11y + 10
11y + 10

5y + 10
5y + 10

5y - 4
5y - 4

5y + 2

Answer 4

Simplify the expression by using the Distributive Property and combining like terms.

5(3x + 4) - 7x - 3

(1 point)
Responses

15x + 20
15x + 20

8x + 17
8x + 17

22x + 23
22x + 23

8x + 1

Answer 5

Part 1: At the State Fair it costs $2.75 for a piece of pizza and $3.50 for a funnel cake. How much would it cost to order "p" pieces of pizza and "f" funnel cakes? Show how to set this up as an algebraic expression.(2 points)

Answer 6

To factor the expression \( 9x + 21 \), we need to identify the greatest common factor (GCF) of the terms.

The GCF of \( 9x \) and \( 21 \) is \( 3 \).

Now, we can factor out \( 3 \):

\[
9x + 21 = 3(3x) + 3(7) = 3(3x + 7)
\]

Thus, the correct factored expression from the options given is:

**3(3x + 7)**.

Answer 7

To factor the expression \( 35x + 20 \), we first find the greatest common factor (GCF) of the two terms.

The GCF of \( 35x \) and \( 20 \) is \( 5 \).

Now, we can factor out \( 5 \):

\[
35x + 20 = 5(7x) + 5(4) = 5(7x + 4)
\]

So, filling in the responses, we have:

**5( Response area x + Response area)**

- In the first response area (after "5("), you insert **7**.
- In the second response area (after "x +"), you insert **4**.

Final answer: **5(7x + 4)**.

Answer 8

To add the expressions \( (2.5x + 3) + (5x - 1.2) \), we first combine the like terms.

1. Combine the \( x \) terms:
\[
2.5x + 5x = 7.5x
\]

2. Combine the constant terms:
\[
3 - 1.2 = 1.8
\]

Putting it all together, we have:
\[
(2.5x + 3) + (5x - 1.2) = 7.5x + 1.8
\]

Thus, the correct response is:

**7.5x + 1.8**.

Answer 9

To subtract the expressions \( (8y + 6) - (3y + 4) \), we'll distribute the negative sign to the second expression and then combine like terms.

1. Rewrite the expression:
\[
(8y + 6) - (3y + 4) = 8y + 6 - 3y - 4
\]

2. Combine the \( y \) terms:
\[
8y - 3y = 5y
\]

3. Combine the constant terms:
\[
6 - 4 = 2
\]

Putting it all together, we have:
\[
(8y + 6) - (3y + 4) = 5y + 2
\]

Thus, the correct response is:

**5y + 2**.

Answer 10

To simplify the expression \( 5(3x + 4) - 7x - 3 \), we will use the Distributive Property and combine like terms.

1. **Distribute \(5\) into the parentheses:**
\[
5(3x) + 5(4) = 15x + 20
\]

So the expression becomes:
\[
15x + 20 - 7x - 3
\]

2. **Combine like terms:**
- Combine the \(x\) terms:
\[
15x - 7x = 8x
\]
- Combine the constant terms:
\[
20 - 3 = 17
\]

Putting it all together, we get:
\[
15x + 20 - 7x - 3 = 8x + 17
\]

Thus, the correct response is:

**8x + 17**.

Answer 11

To set up the cost of ordering \( p \) pieces of pizza and \( f \) funnel cakes as an algebraic expression, we can multiply the cost of each item by the number of items ordered.

1. **Cost of pizza:** Each piece of pizza costs $2.75. If you order \( p \) pieces, the total cost for the pizza is:
\[
2.75p
\]

2. **Cost of funnel cakes:** Each funnel cake costs $3.50. If you order \( f \) funnel cakes, the total cost for the funnel cakes is:
\[
3.50f
\]

3. **Total cost:** To find the total cost of ordering \( p \) pieces of pizza and \( f \) funnel cakes, we add the two costs together:
\[
\text{Total Cost} = 2.75p + 3.50f
\]

Putting it all together, the algebraic expression representing the total cost is:

\[
2.75p + 3.50f
\]