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3 years ago

9

Please help quick im offering 10pts and brainliest answer

1 answer:

iogann1982 [59]3 years ago

6 0

Answer: The value of x is 30

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Angle PJK and Angle DJB are vertical angles. They are formed when you cross PD and KB. They are opposite one another. Vertical angles are congruent, so,

(angle PJK) = (angle DJB)
3x-40 = 2x-10
3x-40-2x = 2x-10-2x ... subtract 2x from both sides
x-40 = -10
x-40+40 = -10+40 .... add 40 to both sides
x = 30

Side Note:
if x = 30, then angle PJK is...
angle PJK = 3x-40
angle PJK = 3*x-40
angle PJK = 3*30-40
angle PJK = 90-40
angle PJK = 50 degrees
which is also the measure of angle DJB

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Nowe we can find the means for x and y like this:

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So the line would be given by:

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Step-by-step explanation:

The data given is:

x: 5,5,510,10,10, 15,15,15, 20,20,20

y: 1.6,2.2,1.4, 1.9, 2.4,2.6, 2.3,2.7, 2.8,2.6, 2.9, 3.1

For this case we need to calculate the slope with the following formula:

$m=\frac{S_{xy}}{S_{xx}}$

Where:

$S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}{n}$

$S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}$

So we can find the sums like this:

$\sum_{i=1}^n x_i = 150$

$\sum_{i=1}^n y_i =28.5$

$\sum_{i=1}^n x^2_i =2250$

$\sum_{i=1}^n y^2_i =70.69$

$\sum_{i=1}^n x_i y_i =384$

With these we can find the sums:

$S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}=2250-\frac{150^2}{12}=375$

$S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}{n}=384-\frac{150*28.5}{12}=27.75$

And the slope would be:

$m=\frac{27.75}{375}=0.074$

Nowe we can find the means for x and y like this:

$\bar x= \frac{\sum x_i}{n}=\frac{150}{12}=12.5$

$\bar y= \frac{\sum y_i}{n}=\frac{28.5}{12}=2.375$

And we can find the intercept using this:

$b=\bar y -m \bar x=2.375-(0.074*12.5)=1.45$

So the line would be given by:

$y=0.074 x +1.45$

C. = 1.45 + 0.074x

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Step-by-step explanation:

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