Question

Add the linear expressions: 7(n−2)+5(n+4)+3(n+1) .(1 point)
Responses

15n
15 n

3n+3
3 n plus 3

15n+9
15 n plus 9

15n+3

Answer 1

Subtract: (j+2)−2(3−9j) .(1 point)
Responses

19j−4
19 j minus 4

19j+4
19 j plus 4

−17j−4
negative 17 j minus 4

−8j−4

Answer 2

Subtract: (2u−7y)−(7u+2y) .(1 point)
Responses

5u−5y
5 u minus 5 y

−5u−9y
negative 5 u minus 9 y

−5u−5y
negative 5 u minus 5 y

5u−9y

Answer 3

Simplify 9+3(4a−7)−5a+6 (1 point)
Responses

43a−78
43 a minus 78

43a+78
43 a plus 78

7a+6
7 a plus 6

7a−6

Answer 4

Paulita is going to build a storage cube. Each edge is 14 inches. The wood costs $0.03 per square inch. Use 0.03(5e2) , where e is the edge length, to evaluate for e = 14 . (1 point)
Responses

$147.00
$147.00

$4.41
$4.41

$4.20
$4.20

$29.40

Answer 5

Simplify 2x + 11y − 1 + 5x − 3y +7 .(1 point)
Responses

13xy + 2xy − 6
13 x y plus 2 x y minus 6

7x +8y − 6
7 x plus 8 y minus 6

7x +8y +6
7 x plus 8 y plus 6

13xy + 2xy + 6

Answer 6

To add the linear expressions \( 7(n - 2) + 5(n + 4) + 3(n + 1) \), we first distribute each term:

1. Distributing \( 7(n - 2) \):
\[
7n - 14
\]

2. Distributing \( 5(n + 4) \):
\[
5n + 20
\]

3. Distributing \( 3(n + 1) \):
\[
3n + 3
\]

Next, we combine all the terms:

\[
(7n - 14) + (5n + 20) + (3n + 3)
\]

Now, combine the \( n \) terms and the constant terms:

- Combining \( n \) terms:
\[
7n + 5n + 3n = 15n
\]

- Combining constant terms:
\[
-14 + 20 + 3 = 9
\]

Putting it all together, we have:

\[
15n + 9
\]

Thus, the final result is \( 15n + 9 \).

The correct response is:

**15n + 9** (15 n plus 9).

Answer 7

To simplify the expression \((j + 2) - 2(3 - 9j)\), let's first distribute the \(-2\) across the terms inside the parentheses:

1. Distributing \(-2\):
\[
-2(3) + -2(-9j) = -6 + 18j
\]

Now substituting this back into the expression:

\[
(j + 2) - (6 - 18j)
\]

This can be rewritten as:

\[
j + 2 - 6 + 18j
\]

Now, combine the like terms:

- The \(j\) terms:
\[
j + 18j = 19j
\]

- The constant terms:
\[
2 - 6 = -4
\]

Bringing it all together, we get:

\[
19j - 4
\]

Thus, the final result is \(19j - 4\).

The correct response is:

**19j - 4** (19 j minus 4).

Answer 8

To simplify the expression \((2u - 7y) - (7u + 2y)\), we will first distribute the negative sign across the second set of parentheses:

\[
(2u - 7y) - (7u + 2y) = 2u - 7y - 7u - 2y
\]

Now, combine the like terms:

1. For the \(u\) terms:
\[
2u - 7u = -5u
\]

2. For the \(y\) terms:
\[
-7y - 2y = -9y
\]

Putting it all together, we have:

\[
-5u - 9y
\]

Thus, the final result is \(-5u - 9y\).

The correct response is:

**−5u−9y** (negative 5 u minus 9 y).

Answer 9

To simplify the expression \(9 + 3(4a - 7) - 5a + 6\), we will follow these steps:

1. First, distribute the \(3\) in \(3(4a - 7)\):
\[
3(4a) - 3(7) = 12a - 21
\]

2. Substitute this back into the expression:
\[
9 + (12a - 21) - 5a + 6
\]

3. Combine like terms:
- Start with the constant terms:
\[
9 - 21 + 6 = -12 + 6 = -6
\]
- Then combine the \(a\) terms:
\[
12a - 5a = 7a
\]

So, putting it all together, we have:
\[
7a - 6
\]

Thus, the final simplified expression is \(7a - 6\).

The correct response is:

**7a - 6** (7 a minus 6).

Answer 10

To find the cost of the wood needed for Paulita's storage cube, we can use the expression \(0.03(5e^2)\) where \(e\) is the edge length of the cube.

Given that \(e = 14\) inches, we can substitute this value into the expression:

1. First calculate \(e^2\):
\[
e^2 = 14^2 = 196
\]

2. Now substitute this back into the expression:
\[
0.03(5 \cdot 196)
\]

3. Calculate \(5 \cdot 196\):
\[
5 \cdot 196 = 980
\]

4. Now multiply this result by \(0.03\):
\[
0.03 \cdot 980 = 29.40
\]

Thus, the total cost of the wood is \($29.40\).

The correct response is:

**$29.40**.

Answer 11

To simplify the expression \(2x + 11y - 1 + 5x - 3y + 7\), we can follow these steps:

1. Start by grouping the like terms together:
- \(x\) terms: \(2x + 5x\)
- \(y\) terms: \(11y - 3y\)
- Constant terms: \(-1 + 7\)

2. Now simplify each group:
- For the \(x\) terms:
\[
2x + 5x = 7x
\]
- For the \(y\) terms:
\[
11y - 3y = 8y
\]
- For the constant terms:
\[
-1 + 7 = 6
\]

3. Combine all the results:
\[
7x + 8y + 6
\]

Thus, the simplified expression is \(7x + 8y + 6\).

The correct response is:

**7x + 8y + 6** (7 x plus 8 y plus 6).