Question 6

Question

A)Sarah wants to buy balloons (b) that cost $2 dollars each and cupcakes. The expression that represents her purchase is 2b+2
2
𝑏
+
2
. How much will she spend if she buys 6 balloons?(1 point)
Responses

$2.00
$2.00

$28
$28

$14.00
$14.00
Question 7
A)
Simplify

3(16+5x)
3
(
16
+
5
𝑥
)

(1 point)
Responses

48+15x
48
+
15
𝑥
48 plus 15 x

−5x+16
−
5
𝑥
+
16
negative 5 x plus 16

−5x−16
−
5
𝑥
−
16
negative 5 x minus 16

48−15x
48
−
15
𝑥
48 minus 15 x
Question 8
A)What is the definition of the math term "variable"?(1 point)
Responses

A letter that represents an unknown number
A letter that represents an unknown number

A letter that represents a given number
A letter that represents a given number
Question 9
A)
Use the substitution method to solve the following algebraic expression:

25w + 100 = ? where w = -4

(1 point)
Responses

200
200

-200
-200

100
100

0
0
Question 10
A)
Combine the following Like Terms

3a - 2b + 4 + 6b + 7a

(1 point)
Responses

4a -4b +4
4a -4b +4

10a - 4b +4
10a - 4b +4

10a +8b + 4
10a +8b + 4

10a -4b - 4

Answer 1

Here are the answers to each of your questions:

Question 6

Sarah's expression for her purchase of balloons and cupcakes is given as \(2b + 2\).

• If she buys 6 balloons, we substitute \(b\) with 6:

  \[ 2(6) + 2 = 12 + 2 = 14 \]

So, she will spend $14.00.

Response: $14.00

---

Question 7

We need to simplify the expression \(3(16 + 5x)\).

• Distributing the 3, we have:

  \[ 3(16) + 3(5x) = 48 + 15x \]

So, the simplified expression is 48 + 15x.

Response: 48 + 15x

---

Question 8

The definition of the math term "variable" is:

• A letter that represents an unknown number.

Response: A letter that represents an unknown number

---

Question 9

To solve the expression \(25w + 100\) where \(w = -4\):

• Substitute -4 for \(w\):

  \[ 25(-4) + 100 = -100 + 100 = 0 \]

So, the answer is 0.

Response: 0

---

Question 10

We need to combine the like terms in \(3a - 2b + 4 + 6b + 7a\).

• Combine \(3a + 7a\) and \(-2b + 6b\):

  \[ (3a + 7a) + (-2b + 6b) + 4 = 10a + 4b + 4 \]

Thus, the combined result is 10a + 4b + 4.

No response matches exactly, so the likely intent is: 10a + 4b + 4 (though it seems there's an error in the given options).

If we take a closer look at the options provided, none of them directly matches what you would expect from combining the terms correctly. Please review the options to ensure correctness.

---

Let me know if you have any further questions!

Answer 2

Give me all the answers in order.

Answer 3

Sure! Here are the answers in order:

Question 6

$14.00

Question 7

48 + 15x

Question 8

A letter that represents an unknown number

Question 9

0

Question 10

10a + 4b + 4

Let me know if you need any more assistance!

Answer 4

No return is wrong.

Answer 5

I apologize for any confusion. Let's carefully revisit each question, recalculate, and ensure we provide the correct answers.

Question 6

Sarah's purchase expression is \(2b + 2\). If \(b = 6\):

\[ 2(6) + 2 = 12 + 2 = 14 \] Answer: $14.00

---

Question 7

We simplify \(3(16 + 5x)\):

\[ 3 \times 16 + 3 \times 5x = 48 + 15x \] Answer: 48 + 15x

---

Question 8

The definition of "variable" is:

Answer: A letter that represents an unknown number

---

Question 9

For the expression \(25w + 100\) where \(w = -4\):

\[ 25(-4) + 100 = -100 + 100 = 0 \] Answer: 0

---

Question 10

Combining like terms in \(3a - 2b + 4 + 6b + 7a\):

\[ (3a + 7a) + (-2b + 6b) + 4 = 10a + 4b + 4 \]

If we look closely at the provided options, the correct combination of like terms should ideally present with \(10a + 4b + 4\), and it seems my initial summary did not correctly reflect the standard options given.

Answer: 10a + 4b + 4 (Though it appears this option is not listed in the choices.)

---

So, summarizing again, here are the answers:

1. $14.00
2. 48 + 15x
3. A letter that represents an unknown number
4. 0
5. 10a + 4b + 4 (Please double-check if this option was included.)

I appreciate your patience, and I hope this clears up any discrepancies! Let me know if you have any further questions.

Answer 6

Question 10
A)
Combine the following Like Terms

3a - 2b + 4 + 6b + 7a

(1 point)
Responses

4a -4b +4
4a -4b +4

10a - 4b +4
10a - 4b +4

10a +8b + 4
10a +8b + 4

10a -4b - 4
10a -4b - 4

Answer 7

Let’s carefully combine the like terms in the expression \(3a - 2b + 4 + 6b + 7a\).

1. Combine the \(a\) terms:

   • \(3a + 7a = 10a\)

2. Combine the \(b\) terms:

   • \(-2b + 6b = 4b\)

3. The constant term remains unchanged:

   • \(4\)

Putting it all together, we get:

\[ 10a + 4b + 4 \]

Now, checking against the provided options:

• 4a - 4b + 4
• 10a - 4b + 4
• 10a + 8b + 4
• 10a - 4b - 4

None of the provided options exactly match \(10a + 4b + 4\). It seems like there might be an error in the options listed.

The closest answer, but incorrect, is 10a - 4b + 4, since the correct version has \(4b\) not \(-4b\).

Given the options, the answer should be:

Answer: None match exactly, but the correct combination is 10a + 4b + 4.

If we were to select among your choices despite them being incorrect, you could clarify or ask for possible errors in the answer choices.