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Simplify the expression by combining like terms.

2/8x+3/10y−5/8x+4/10y
(1 point)
Responses

14/18xy
14 over 18 x y

−3/8x+7/10y

4/18xy
4 over 18 x y

7/10x+7/8y

9 answers

To simplify the expression \( \frac{2}{8}x + \frac{3}{10}y - \frac{5}{8}x + \frac{4}{10}y \), we will combine like terms.

  1. Combine the \( x \) terms: \[ \frac{2}{8}x - \frac{5}{8}x = \left(\frac{2}{8} - \frac{5}{8}\right)x = -\frac{3}{8}x \]

  2. Combine the \( y \) terms: \[ \frac{3}{10}y + \frac{4}{10}y = \left(\frac{3}{10} + \frac{4}{10}\right)y = \frac{7}{10}y \]

Now we can write the combined expression: \[ -\frac{3}{8}x + \frac{7}{10}y \]

Thus, the simplified expression is: \[ -\frac{3}{8}x + \frac{7}{10}y \]

So, the correct response is: \[ \text{-}\frac{3}{8}x + \frac{7}{10}y \]

Evaluate the expression when x=9
and y=6
.

x−y3


(1 point)
Responses

9
9

6
6

3
3

1

To evaluate the expression \( x - y^3 \) when \( x = 9 \) and \( y = 6 \), substitute the values of \( x \) and \( y \) into the expression:

  1. Substitute \( y = 6 \) into \( y^3 \): \[ y^3 = 6^3 = 6 \times 6 \times 6 = 216 \]

  2. Now substitute \( x = 9 \): \[ x - y^3 = 9 - 216 \]

  3. Calculate the result: \[ 9 - 216 = -207 \]

The answer is: \(-207\)

Since this value isn't provided in the response options, please check if there's been a mistake with the input or clarify the expression to evaluate.

Evaluate the expression when x=9
and y=6
.

x−y
3


(1 point)
Responses

9
9

6
6

3
3

1

To evaluate the expression \( x - y^3 \) when \( x = 9 \) and \( y = 6 \), we follow these steps:

  1. Compute \( y^3 \): \[ y^3 = 6^3 = 6 \times 6 \times 6 = 216 \]

  2. Substitute \( x = 9 \) into the expression: \[ x - y^3 = 9 - 216 \]

  3. Perform the subtraction: \[ 9 - 216 = -207 \]

It seems like there may have been some confusion with the formatting of the expression. If the expression is indeed \( x - y^3 \) and the inputs for \( x \) and \( y \) are 9 and 6, respectively, the result is \(-207\).

After analyzing your notation "x−y 3," if you meant \( x - y = 9 - 6 \):

  1. Calculate: \[ x - y = 9 - 6 = 3 \]

In either context, there are different outcomes based on the interpretation. Based on the responses provided, if you meant \( x - y \), then the answer is:

3

You are saving for a skateboard. Your aunt gives you $45 to start, and you save $3 each week. The expression 45+3w
gives the amount of money you save after w
weeks. How much will you have saved after 4 weeks?(1 point)
Responses

$42
$42

$33
$33

$576
$576

$57

To find out how much money you will have saved after 4 weeks using the expression \( 45 + 3w \), we will substitute \( w = 4 \) into the expression.

  1. Substitute \( w \) with 4: \[ 45 + 3(4) \]

  2. Calculate \( 3(4) \): \[ 3(4) = 12 \]

  3. Add this to 45: \[ 45 + 12 = 57 \]

So after 4 weeks, you will have saved $57.

The correct response is: $57

are you sure all of these are correct before i submit them?

Yes, let's summarize and double-check each situation:

  1. Expression Simplification:

    • Original expression: \( \frac{2}{8}x + \frac{3}{10}y - \frac{5}{8}x + \frac{4}{10}y \)
    • Combined like terms:
      • For \( x \): \( \frac{2}{8}x - \frac{5}{8}x = -\frac{3}{8}x \)
      • For \( y \): \( \frac{3}{10}y + \frac{4}{10}y = \frac{7}{10}y \)
    • Final simplified expression: \( -\frac{3}{8}x + \frac{7}{10}y \)
    • This part is correct.

  2. Expression Evaluation with Given Values (x = 9, y = 6):

    • Expression: \( x - y^3 \)
    • Computing \( y^3 = 6^3 = 216 \)
    • Substitute: \( 9 - 216 = -207 \)
    • Clarification: If it was meant to be \( x - y \) instead, then \( 9 - 6 = 3 \).
    • The appropriate evaluation depends on how the expression was described. The interpretation leads to -207 for \( x - y^3 \) or 3 for \( x - y \).

  3. Money Saved for the Skateboard:

    • Expression: \( 45 + 3w \)
    • After substituting \( w = 4 \): \[ 45 + 3(4) = 45 + 12 = 57 \]
    • This evaluation is also correct.

Given these checks:

  • For the first simplification: The answers are correct as provided.
  • For the evaluation (x=9, y=6): Make sure to confirm if it should be \( x - y^3 \) or \( x - y \) because they yield different results.
  • For the skateboard savings: The answer is correct as \( $57 \).

Please ensure you're using the expressions as intended based on the context of your questions. If you have any further clarification on the expressions, please let me know!