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lorasvet [3.4K]
3 years ago
12

Show that 2/4-x = 10/4+x is equivalent to 12x = 32 for all values of x not equal to 4 or -4

Mathematics
1 answer:
Anika [276]3 years ago
6 0

Answer:

See proof below

Step-by-step explanation:

Given the expression 2/4-x = 10/4+x

Cross multiply

10(4-x) = 2(4+x)

10(4) - 10x = 2(4)+ 2x

40 - 10x = 8 + 2x

-10x - 2x = 8 - 40

-12x = -32

Multiply both sides by -1

-1(-12x) = -1(-32)

12x = 32

This shows the required expression

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(x,y)=(37,31)

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Find the derivative of x^2=2 at x=0
VashaNatasha [74]
The answer is false they don’t equal each other.
3 0
3 years ago
The water works commission needs to know the mean household usage of water by the residents of a small town in gallons per day.
valina [46]

Answer:

A sample of 179 is needed.

Step-by-step explanation:

We have that to find our \alpha level, that is the subtraction of 1 by the confidence interval divided by 2. So:

\alpha = \frac{1 - 0.85}{2} = 0.075

Now, we have to find z in the Ztable as such z has a pvalue of 1 - \alpha.

That is z with a pvalue of 1 - 0.075 = 0.925, so Z = 1.44.

Now, find the margin of error M as such

M = z\frac{\sigma}{\sqrt{n}}

In which \sigma is the standard deviation of the population and n is the size of the sample.

A previous study found that for an average family the variance is 1.69 gallon?

This means that \sigma = \sqrt{1.69} = 1.3

If they are using a 85% level of confidence, how large of a sample is required to estimate the mean usage of water?

A sample of n is needed, and n is found for M = 0.14. So

M = z\frac{\sigma}{\sqrt{n}}

0.14 = 1.44\frac{1.3}{\sqrt{n}}

0.14\sqrt{n} = 1.44*1.3

\sqrt{n} = \frac{1.44*1.3}{0.14}

(\sqrt{n})^2 = (\frac{1.44*1.3}{0.14})^2

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Rounding up

A sample of 179 is needed.

7 0
3 years ago
Write an equation of the line that passes through the point(-6,-9) with slope -5
LUCKY_DIMON [66]

Answer:

  y = -5(x +6) -9

Step-by-step explanation:

The point-slope form of the equation for a line can be written as ...

  y = m(x -h) +k

for a line with slope m through point (h, k).

You have m=-5 and (h, k) = (-6, -9). Filling in these values gives ...

  y = -5(x -(-6)) -9

Simplifying a bit, you get ...

  y = -5(x +6) -9

4 0
4 years ago
HOW is it helpful to write numbers in different ways?
Alisiya [41]
It is helpful to write them in different ways
some ways to write them are
1.fractions
2.decimals
3.squareroots (if applicable)

so it would be more helpful in an equation to leave 6/7 in fractional form if  you are going to manipulate it more, because 0.857142857142... is much harder to keep track of than 6/7


and sometimes, they want a percent which is easier to convert to from decimal form than from fractinoal form so ex  0.857142857142...=85.7% vs 6/7 to percent

sometimes there will be square roots and they are easier if left like that ex
√2=1.4142135623...
it would be easier to leav it in square root

it depends on the equation you are trying to solve, because different forms have different pros and cons, some are easier to work with in a certain form but not in another, sometimes, you will need to change between multipule forms during the same problem
8 0
4 years ago
Read 2 more answers
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