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arsen [322]
3 years ago
15

Simplify the expression: 2/3 divided by - {1/6 - 8/6}

Mathematics
1 answer:
solmaris [256]3 years ago
4 0

Answer:

4/7

Step-by-step explanation:

1/6-8/6=-7/6

-[1/6-8/6]=7/6

---------------------

(2/3)/(7/6)=(2/3)(6/7)=12/21=4/7

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The average heights of x number of girls and 15 boys is 123. if the average heights of boys is 125 and that of girls is 120.find
mamaluj [8]

Answer:

x = 10. In other words, there number of girls is 10.

Step-by-step explanation:

The average of a number of measurements is equal to the sum of these measurements over the number of measurements.

\displaystyle \text{Average} = \frac{\text{Sum of measurements}}{\text{Number of measurements}}.

Rewrite to obtain:

\begin{aligned}& \text{Sum of measurements}= (\text{Number of measurements}) \times (\text{Average}) \end{aligned}.

For this question:

\begin{aligned}& \text{Sum of heights of boys} \\ &= (\text{Number of boys}) \times (\text{Average height of boys}) \\ &= 15 \times 125 = 1875\end{aligned}.

\begin{aligned}& \text{Sum of heights of girls} \\ &= (\text{Number of girls}) \times (\text{Average height of girls}) \\ &= x \times 120 = 120\, x\end{aligned}.

Therefore:

\begin{aligned}& \text{Sum of boys and girls} \\ &= \text{Sum of heights of boys} + \text{Sum of heights of girls}\\ &= 1875 + 120\, x\end{aligned}.

On the other hand, there are (15 + x) boys and girls in total. Using the formula for average:

\begin{aligned}& \text{Average height of boys and girls} \\ &= \frac{\text{Sum of heights of boys and girls}}{\text{Number of boys and girls}} \\ &= \frac{1875 + 120\, x}{15 + x}\end{aligned}.

From the question, this average should be equal to 123. In other words:

\displaystyle \frac{1875 + 120\, x}{15 + x} = 123.

Solve this equation for x to obtain:

1875 + 120\, x= 123\, (15 + x).

(123 - 120)\, x = 1875 - 123 \times 15.

x = 10.

In other words, the number of girls here is 10.

5 0
3 years ago
Express the following linear equations in the form ax+by+c= 0 and indicate the values of a, b and c in each case: (1) y = x/5​
EleoNora [17]

Answer:

Did the question get cut off?

a = -(1/5)

b = 1

c = 0

Step-by-step explanation:

y = x/5 may be rewritten as y = (1/5)x

y = (1/5)x

y - (1/5)x = 0

- (1/5)x + y + 0 = 0

   ax  +   by   + c = 0

a = -(1/5)

b = 1

c = 0

8 0
2 years ago
An angle measures 12 degrees less than three times its supplement. Find the measure of the angle.
lianna [129]

Ok, so you knnow that for angles to be supplement, they need to equal 180 degrees. So you can create an equation as follows:

(3 times X minus 12) degrees plus (x)degrees equals 180 degrees

(3x-12) + (x)=180

4x-12=180

4x=192

x=48

So now you plug in "x=48" into this equation (3x-12) to find the measure of the angle.

And if I did the math correctly, the answer should be "132" degrees.

6 0
3 years ago
Read 2 more answers
What is the slope of the line on the graph?
TiliK225 [7]

Answer:The slope is defined as the ratio of the vertical change between two points, the rise, to the horizontal change between the same two points, the run. The slope of a line is usually represented by the letter m. (x1, y1) represents the first point whereas (x2, y2) represents the second point.

3 0
3 years ago
What set of transformations are applied to parallelogram ABCD to create A'B'C'D'?
allochka39001 [22]

Answer:

  Reflection across the x-axis

Step-by-step explanation:

The only apparent transformation is negation of the y-coordinate, corresponding to reflection across the x-axis.

3 0
3 years ago
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