Solved on Jan 15, 2024

Find the average of $x+15$ , $7x$ , and $x$ in terms of $x$ .

STEP 1

Assumptions
1. We are given three expressions: $x+15$ , $7x$ , and $x$ .
2. We need to find the mean (average) of these three expressions.
3. The mean is calculated by adding all the expressions together and then dividing by the number of expressions.

STEP 2

First, we will add the three expressions together to find their sum.
$Sum = (x+15) + (7x) + (x)$

STEP 3

Combine like terms to simplify the sum.
$Sum = x + 15 + 7x + x$ $Sum = 9x + 15$

STEP 4

Now, we will divide the sum by the number of expressions to find the mean. There are three expressions, so we will divide by 3.
$Mean = \frac{Sum}{Number\, of\, expressions}$

STEP 5

Plug in the values for the sum and the number of expressions to calculate the mean.
$Mean = \frac{9x + 15}{3}$

STEP 6

Divide each term in the numerator by the denominator.
$Mean = \frac{9x}{3} + \frac{15}{3}$

STEP 7

Simplify each term.
$Mean = 3x + 5$
The mean of the three expressions in terms of $x$ is $3x + 5$ in its simplest form.

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Find the average of $x+15$ , $7x$ , and $x$ in terms of $x$ .

STEP 1

Assumptions
1. We are given three expressions: $x+15$ , $7x$ , and $x$ .
2. We need to find the mean (average) of these three expressions.
3. The mean is calculated by adding all the expressions together and then dividing by the number of expressions.

STEP 2

First, we will add the three expressions together to find their sum.
$Sum = (x+15) + (7x) + (x)$

STEP 3

Combine like terms to simplify the sum.
$Sum = x + 15 + 7x + x$ $Sum = 9x + 15$

STEP 4

Now, we will divide the sum by the number of expressions to find the mean. There are three expressions, so we will divide by 3.
$Mean = \frac{Sum}{Number\, of\, expressions}$

STEP 5

Plug in the values for the sum and the number of expressions to calculate the mean.
$Mean = \frac{9x + 15}{3}$

STEP 6

Divide each term in the numerator by the denominator.
$Mean = \frac{9x}{3} + \frac{15}{3}$

STEP 7

Simplify each term.
$Mean = 3x + 5$
The mean of the three expressions in terms of $x$ is $3x + 5$ in its simplest form.

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Find the average of x+15x+15x+15, 7x7x7x, and xxx in terms of xxx.

STEP 1

Assumptions1. We are given three expressions: x+15x+15x+15, 7x7x7x, and xxx.2. We need to find the mean (average) of these three expressions.3. The mean is calculated by adding all the expressions together and then dividing by the number of expressions.

STEP 2

First, we will add the three expressions together to find their sum.Sum=(x+15)+(7x)+(x)Sum = (x+15) + (7x) + (x)Sum=(x+15)+(7x)+(x)

STEP 3

Combine like terms to simplify the sum.Sum=x+15+7x+xSum = x + 15 + 7x + xSum=x+15+7x+x Sum=9x+15Sum = 9x + 15Sum=9x+15

STEP 4

Now, we will divide the sum by the number of expressions to find the mean. There are three expressions, so we will divide by 3.Mean=SumNumber of expressionsMean = \frac{Sum}{Number\, of\, expressions}Mean=NumberofexpressionsSum​

STEP 5

Plug in the values for the sum and the number of expressions to calculate the mean.Mean=9x+153Mean = \frac{9x + 15}{3}Mean=39x+15​

STEP 6

Divide each term in the numerator by the denominator.Mean=9x3+153Mean = \frac{9x}{3} + \frac{15}{3}Mean=39x​+315​

STEP 7

Simplify each term.Mean=3x+5Mean = 3x + 5Mean=3x+5The mean of the three expressions in terms of xxx is 3x+53x + 53x+5 in its simplest form.

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Find the average of $x+15$ , $7x$ , and $x$ in terms of $x$ .

Assumptions
1. We are given three expressions: $x+15$ , $7x$ , and $x$ .
2. We need to find the mean (average) of these three expressions.
3. The mean is calculated by adding all the expressions together and then dividing by the number of expressions.

First, we will add the three expressions together to find their sum.
$Sum = (x+15) + (7x) + (x)$

Combine like terms to simplify the sum.
$Sum = x + 15 + 7x + x$ $Sum = 9x + 15$

Now, we will divide the sum by the number of expressions to find the mean. There are three expressions, so we will divide by 3.
$Mean = \frac{Sum}{Number\, of\, expressions}$

Plug in the values for the sum and the number of expressions to calculate the mean.
$Mean = \frac{9x + 15}{3}$

Divide each term in the numerator by the denominator.
$Mean = \frac{9x}{3} + \frac{15}{3}$

Simplify each term.
$Mean = 3x + 5$
The mean of the three expressions in terms of $x$ is $3x + 5$ in its simplest form.