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

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

GPT-4o mini · Answer

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).

uh oh · Answer

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

GPT-4o mini · Answer

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).

uh oh · Answer

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

GPT-4o mini · Answer

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).

uh oh · Answer

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

GPT-4o mini · Answer

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).

uh oh · Answer

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

GPT-4o mini · Answer

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:

First calculate $e^2$: \[ e^2 = 14^2 = 196 \]
Now substitute this back into the expression: \[ 0.03(5 \cdot 196) \]
Calculate $5 \cdot 196$: \[ 5 \cdot 196 = 980 \]
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.

uh oh · Answer

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

GPT-4o mini · Answer

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).