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3 years ago

Choose two angles that are each separately alternate exterior angles with 412.

Mathematics

1 answer:

Alborosie3 years ago

6 0

Answer:

∠2 and ∠5

Step-by-step explanation:

we know that

Alternate Exterior Angles are a pair of angles on the outer side of each of those two lines but on opposite sides of the transversal

In this problem

∠12 and ∠2 are alternate exterior angles

∠12 and ∠5 are alternate exterior angles

therefore

∠2 and ∠5 are each separately alternate exterior angles with ∠12

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The length of each side of a regular pentagon is increased by 8 inches, so the perimeter is now 65 inches. What is the original

evablogger [386]

Here as the Pentagon is regular so it's all sides will be of equal length . And if we assume It's each side be s , then it's perimeter is going to be (s+s+s+s+s) = 5s.And as here , each side is increased by 8 inches and then it's perimeter is 65 inches , so we got that it's side after increament is (s+8) inches and original length is s inches . And if it's each side is (s+8) inches , so it's perimeter will be 5(s+8) and as it's equal to 65 inches . So , 5(s+8) = 65

${:\implies \quad \sf 5(s+8)=65}$

${:\implies \quad \sf 5s+5\times 8=65}$

${:\implies \quad \sf 5s+40=65}$

${:\implies \quad \sf 5s=65-40}$

${:\implies \quad \sf 5s=25}$

${:\implies \quad \sf s=\dfrac{25}{5}=5}$

${:\implies \quad \bf \therefore \quad \underline{\underline{s=5\:\: Inches}}}$

As we assumed the original side to be s .

Hence, the original side's length 5 inches 

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2 years ago

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Answer:

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Step-by-step explanation:

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2 years ago

Given cosθ=√3/3 and sinθ<0. What is the value of sinθ?

KATRIN_1 [288]

$\sin^{2} \theta+\cos^{2} \theta=1 \\ \\ \sin^{2} \theta+\left(\frac{\sqrt{3}}{3} \right)^{2}=1 \\ \\ \sin^{2} \theta+\frac{1}{3}=1 \\ \\ \sin^{2} \theta=\frac{2}{3} \\ \\ \theta=-\frac{\sqrt{2}}{\sqrt{3}}=\boxed{-\frac{\sqrt{6}}{3}}$

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1 year ago

Y(x) = e^x+rx+sx^2 satisfies y'' − y' = 5x if r=? and s=?

motikmotik

Answer:

Step-by-step explanation:

3 0

3 years ago

Line l1 passes through (-2, 5), and (-1, -10)

zalisa [80]

The equations of the lines l1 with points (-2, 5), and (-1, -10) and the line l2 with points (5, 15), and (3, 8), gives the coordinate of the intersection between the lines as the point; (-45/37, -250/37)

<h3>Which method can be used to describe the lines to find the intersection point?</h3>

The slope, m1, of line 1 l1 is found as follows;

m1 = (5 - (-10))/(-2- (-1)) = -15

The equation of line l1 in point and slope form is therefore;

y1 - 5 = -15•(x - (-2))

Which gives;

y1 = -15•(x - (-2)) + 5 = -15•x - 25

y1 = -15•x - 25

The slope, m2, of line 2 l2 is found as follows;

m2 = (15 - 8)/(5 - 3) = 3.5

Equation of line l2 is therefore;

y2 - 15 = 3.5•(x - 5)

Which gives;

y2 = 3.5•(x - 5) + 15 = 3.5•x - 2.5

y2 = 3.5•x - 2.5

At the intersection point, we have;

y1 = y2

Therefore;

-15•x - 25 = 3.5•x - 2.5

18.5•x = -22.5

x = -22.5/18.5 = -45/37

y2 = 3.5•x - 2.5

At the intersection point, we have;

y = y2 = 3.5×(-22.5/18.5) - 2.5 = -250/37

y = -250/37

The coordinates of the intersection between the lines is therefore;

(-45/37, -250/37)

Learn more about the equation of a straight line here:

brainly.com/question/13763238

#SPJ1

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1 year ago