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3 years ago

Which of the following is the equation of the line that is parallel to y=35x+8 y = 3 5 x + 8 and goes through point (-10,4)?

Mathematics

1 answer:

xeze [42]3 years ago

4 0

Slope-intercept form of a line is y=mx+b.

Where m= slope and b= y-intercept.

First step is to compare the given equation y=35x+8 with the above equation to get the value of m.

After comparing the two equations we will get m=35.

Slope of paralle lines always equal which means slope of a line which is parallel to the above line will also be 35.

Now the line is passing through (-10,4).

Point slope form of a line is :

$y-y_{1} =m(x-x_{1} )$

Next step is to plug in m=35, x1=-10 and y1=4 in the above equation. So,

y-4=35(x-(-10)

y-4=35(x+10)

y-4=35x+350

y=35x+350+4

y=35x+354.

So, the equation of the line is y=35x+354.

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2 years ago

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Step-by-step explanation:

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2 years ago

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If 180° < α < 270°, cos⁡ α = −817, 270° < β < 360°, and sin⁡ β = −45, what is cos⁡ (α + β)?

eduard

Answer:

$cos(\alpha+\beta)=-\frac{84}{85}$

Step-by-step explanation:

we know that

$cos(\alpha+\beta)=cos(\alpha)*cos(\beta)-sin(\alpha)*sin(\beta)$

Remember the identity

$cos^{2} (x)+sin^2(x)=1$

step 1

Find the value of $sin(\alpha)$

we have that

The angle alpha lie on the III Quadrant

The values of sine and cosine are negative

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Find the value of sine

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substitute

$(-\frac{8}{17})^{2}+sin^2(\alpha)=1$

$sin^2(\alpha)=1-\frac{64}{289}$

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$sin(\alpha)=-\frac{15}{17}$

step 2

Find the value of $cos(\beta)$

we have that

The angle beta lie on the IV Quadrant

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step 3

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we have

$cos(\alpha)=-\frac{8}{17}$

$sin(\alpha)=-\frac{15}{17}$

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$cos(\beta)=\frac{3}{5}$

substitute

$cos(\alpha+\beta)=-\frac{8}{17}*\frac{3}{5}-(-\frac{15}{17})*(-\frac{4}{5})$

$cos(\alpha+\beta)=-\frac{24}{85}-\frac{60}{85}$

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Step-by-step explanation:

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Answer:

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