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3 years ago

14

Which equation represents a line which is parallel to the line 7y - 4x = -14?

1 answer:

iVinArrow [24]3 years ago

4 0

Answer: Any line with a slope of 4/7 and a y-intercept that is NOT -2

You should first turn the equation into y intercept form:
7y - 4x = -14; Add 4x from both sides
7y = 4x - 14; divide 7 from both sides
y = 4/7x - 2

Since you did not include choices, the answer will be the line with the slope 4/7 and without the y-intercept -2, because lines that are parallel will always have the same slope.

Example Answers: y = 4/7x + 2, y= 4/7x - 4
y = 4/7x + 10

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Set A of six numbers has a standard deviation of 3 and set B of four numbers has a standard deviation of 5. Both sets of numbers

Alenkinab [10]

Given:

$\sigma_A=3$

$n_A=6$

$\sigma_B=5$

$n_B=4$

$\overline{x}_A=\overline{x}_B$

To find:

The variance. of combined set.

Solution:

Formula for variance is

$\sigma^2=\dfrac{\sum (x_i-\overline{x})^2}{n}$ ...(i)

Using (i), we get

$\sigma_A^2=\dfrac{\sum (x_i-\overline{x}_A)^2}{n_A}$

$(3)^2=\dfrac{\sum (x_i-\overline{x}_A)^2}{6}$

$9=\dfrac{\sum (x_i-\overline{x}_A)^2}{6}$

$54=\sum (x_i-\overline{x}_A)^2$

Similarly,

$\sigma_B^2=\dfrac{\sum (x_i-\overline{x}_B)^2}{n_B}$

$(5)^2=\dfrac{\sum (x_i-\overline{x}_B)^2}{4}$

$25=\dfrac{\sum (x_i-\overline{x}_B)^2}{4}$

$100=\sum (x_i-\overline{x}_B)^2$

Now, after combining both sets, we get

$\sigma^2=\dfrac{\sum (x_i-\overline{x}_A)^2+\sum (x_i-\overline{x}_B)^2}{n_A+n_B}$

$\sigma^2=\dfrac{54+100}{6+4}$

$\sigma^2=\dfrac{154}{10}$

$\sigma^2=15.4$

Therefore, the variance of combined set is 15.4.

7 0

3 years ago

How do I show my work for -3(5-2x)-3x=3

devlian [24]

Answer: x=6

Step-by-step explanation:

3(5-2x)-3x=3

-15+6x-3x=3

-15+3x=3

3x=3+15

3x= 18

x=6

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Answer:

44 feet

If it takes the horse 44 feet per second, and it takes the cheetah 88 feet, the difference is 44.

So, the horse must be 44 feet ahead to be safe. Hope it helps!

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