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Readme [11.4K]
2 years ago
8

9. Which lines are parallel if mZ4=mZ5? Justify your answer.

Mathematics
1 answer:
Natali5045456 [20]2 years ago
8 0

Answer:

r || s

Step-by-step explanation:

m∠4 = m∠5  Given.

These angles are called alternate interior angles and because you are given that they are = then there are two parallel lines. The converse of the theorem stated.  If alternate interior angles are cut by a transverse and two lines and the alternate interior angles are equal, then you have a pair of parallel lines.

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What is the value of the exponital expression below 36 1/2
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Find the slope of a line that passes through (-2,1) and (4,9)
melamori03 [73]

Answer:

m = 4/3

Step-by-step explanation:

To find the slope of a line use the formula, where "m" means slope:

m=\frac{y_{2}-y_{1} }{x_{2}-x_{1} }

*You don't need to show this part on paper*

Choose which point you want to be point 1 and point 2. Remember the points are written (x, y).

Point 1: (-2, 1)       x₁ = -2  y₁ = 1

Point 2: (4, 9)      x₂ = 4   y₂ = 9

Substitute the coordinates into the formula:

*Show this part on paper*

m=\frac{y_{2}-y_{1} }{x_{2}-x_{1} }

m=\frac{9-1 }{4-(-2) }         Simplify

m=\frac{8 }{6 }                Reduce by dividing by 2

m=\frac{4 }{3 }               Slope

The slope of the line is 4/3

8 0
3 years ago
Determine whether the integral is convergent or divergent. ∫[infinity] 2 e^−1/x / x^2 dx : O Convergent O divergent If it is con
monitta

Let f(x)=e^{-1/x}. Then f'(x)=\frac1{x^2}e^{-1/x}>0 for all x\ge2, so f is strictly increasing. As x\to\infty, e^{-1/x}\to e^0=1, so f is bounded above by 1. This is to say,

e^{-1/x}

and the integral of \frac1{x^2} converges over the same domain, so this integral must also converge by comparison.

We have, by setting y=-\frac1x,

\displaystyle\int_2^\infty\frac{e^{-1/x}}{x^2}\,\mathrm dx=\int_{-1/2}^0e^y\,\mathrm dy=e^0-e^{-1/2}=1-\frac1{\sqrt e}

8 0
3 years ago
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