Mathematics, 27.08.2019 01:30 faithcalhoun

Write an equation of a line that is perpendicular to the line below and passes through the given point

Write an equation of a line that is perpendicular to the line below and passes through the given poi

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Answer from: sweetgigi5950

When you see an equation in the format:
y = mx + c.
Know that the slope = m.

y = -1/5 x + 3.

Therefore slope, m = -1/5. But for the new line to be perpendicular to this, the new line's slope would be the negative reciprocal of -1/5.

That is using the condition for perpendicularity:
m1* m2 = -1. m1 = -1/5.

Where m2 = new slope of the line.

m2 = -1 / (-1/5) = 5.

So the slope of the perpendicular line is 5.

Using the slope and one point format:

y - y1 = m(x - x1) here (x1 , y1) is the point given (2, 8), x1 = 2 , y1 = 8.

m = 5, the new gradient here.

y - 8 = 5(x - 2)
y - 8 = 5x - 10
y = 5x - 10 + 8
y = 5x -2.

So that's the equation of the perpendicular line passing through the given point.

Answer from: Quest

∠1≅∠2 by the alternate exterior angles theorem.

step-by-step explanation:

given, a ∥ b and ∠1 ≅ ∠3 .we have to prove that e ∥ f

we know that ∠1≅∠3 and that a || b because they are given. we see that by the alternate exterior angles theorem. therefore, ∠2≅∠3 by the transitive property. so, we can conclude that e || f by the converse alternate exterior angles theorem.

we have to fill the missing statement.

transitivity property states that if a = b and b = c, then a = c.

now, given ∠1≅∠3 and by transitivity property ∠2≅∠3 .

hence, to apply transitivity property one angle must be common which is not in result after applying this property which is ∠1.

the only options in which ∠1 is present are ∠1 and ∠2, ∠1 and ∠4

∠1 and ∠4 is not possible ∵ after applying transitivity we didn't get ∠4.

hence, the missing statement is ∠1≅∠2.

so, ∠1≅∠2 by the alternate exterior angles theorem.

Answer from: Quest

"it's not the heat, it's the humidity". that's a partly valid phrase you may have heard in the summer, but it's actually both. the heat index, also known as the apparent temperature, is what the temperature feels like to the human body when relative humidity is combined with the air temperature. this has important considerations for the human body's comfort. when the body gets too hot, it begins to perspire or sweat to cool itself off. if the perspiration is not able to evaporate, the body cannot regulate its temperature. evaporation is a cooling process. when perspiration is evaporated off the body, it effectively reduces the body's temperature. when the atmospheric moisture content (i.e. relative humidity) is high, the rate of perspiration from the body decreases. in other words, the human body feels warmer in humid conditions. the opposite is true when the relative humidity decreases because the rate of perspiration increases. the body actually feels cooler in arid conditions. there is direct relationship between the air temperature and relative humidity and the heat index, meaning as the air temperature and relative humidity increase (decrease), the heat index increases (decreases).

step-by-step explanation: