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Komok [63]
3 years ago
10

WILL GIVE 5 STARS

Mathematics
1 answer:
k0ka [10]3 years ago
3 0

Answer:

Step-by-step explanation:

to know:

-to be paralel the lines have to have the same slope

-to be perpendicular the slope has to be negative invers of thhe other

-to be neither has to be none of the above two

equation to compare to is

y=mx+b where m is the slope

if your equation does not have this form make it have this form

2y=3x+1 so divide by 2

y=\frac{3}{2} x+1 so here the slope is \frac{3}{2}

4x+6y=14 so subtract 4x and then divide by 6 to isolate y

6y= -4x+14

y=\frac{-4}{6}  x + \frac{14}{6}  symplify

y=\frac{-2}{3} x + \frac{7}{3}  so the slope here is \frac{-2}{3}

So if you compare the slopes you can see that are negative reciprocal of eachother so the lines are perpendicular

and so on...

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Which expressions are equivalent to 2 (three-fourths x + 7) minus 3 (one-half x minus 5)? Check all that apply.
Mariulka [41]

Answer:

2(\frac{3}{4}x+7)+(-3)(\frac{1}{2}x+(-5))

2(\frac{3}{4}x)+2(7)+(-3)(\frac{1}{2}x)+(-3)(-5)

Step-by-step explanation:

The original expression given in the text is

2(\frac{3}{4}x+7)-3(\frac{1}{2}x-5)  (1)

And we want to check to what other expressions is equivalent. First of all, we solve it by writing explicitely each term:

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Let's verify each of the other expressions separately. For the first one:

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We see that this is equivalent to expression (1), since the first half is identical, while in the second one, the combination "+-" can be simply written as "-", so we get

2(\frac{3}{4}x+7)-3(\frac{1}{2}x-5)

Which is equivalent to (1).

For the 2nd one:

2(\frac{3}{4}x)+2(7)+3(\frac{1}{2}x)+3(-5)

This is not equivalent. In fact, here we have applied the distributive property to each term: however, the 3rd and 4th term are not correct, because the (3) must be negative (-3), as in the original expression.

If we write it explicitely in fact, we get

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Which is different from (2).

For the 3rd one:

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This one is equivalent. In fact, here we have applied the distributive property correctly. By solvign each term we get:

\frac{3}{2}x+14-\frac{3}{2}x+15

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Step-by-step explanation:

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Step-by-step explanation:

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<h3>What is meant by normal distribution?</h3>

A normal distribution is a type of continuous probability distribution for a real-valued random variable in statistics.

The normal distribution, also known as the Gaussian distribution, is a symmetric probability distribution about the mean, indicating that data near the mean occur more frequently than data far from the mean.

The confidence interval will be valid regardless of the shape of the population distribution as long as the sample is large enough to satisfy the central limit theorem.

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A sample is considered large when n ≥ 30.

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