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3 years ago

A number is more than 9 units from 3.

Mathematics

2 answers:

coldgirl [10]3 years ago

6 0

Answer: It's either -6 or 12. I'm assuming it's 12 because it says "more than."

Step-by-step explanation:

DedPeter [7]3 years ago

6 0

You must account for both the number being more than 9 units smaller than 3 and being more than 9 units larger than 3. To do that, you set the absolute value of the difference between the number and 3 greater than 9.

Let x be the number

|x - 3| > 9

Now solve for x.

Suppose x - 3 is positive. Then

x - 3 > 9 ⇒ x > 12

Suppose x - 3 is negative. Then |x - 3| = -(x - 3) = 3 - x

Then

3 - x > 9 ⇒ x < -6

These are the 2 possibilities.

Hope this helps

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Step-by-step explanation:

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2 years ago

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2 years ago

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goblinko [34]

Answer:

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Step-by-step explanation:

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-----------------------

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3 years ago

How do you find the equation of a triangles altitude using point slope formula?

forsale [732]

1. An altitude of a triangle is a line segment from a vertex perpendicular to the opposite side. Find the equations of the altitudes of the triangle with vertices (4, 5),(-4, 1) and (2, -5). Do this by solving a system of two of two of the altitude equations and showing that the intersection point also belongs to the third line. 
(Scroll Down for Answer!)Answer by jim_thompson5910(34047) (Show Source):You can put this solution on YOUR website!
If we plot the points and connect them, we get this triangle:

Let point
A=(xA,yA)
B=(xB,yB)
C=(xC,yC)

-------------------------------
Let's find the equation of the segment AB

Start with the general formula

Plug in the given points

Simplify and combine like terms

So the equation of the line through AB is

-------------------------------
Let's find the equation of the segment BC

Start with the general formula

Plug in the given points

Simplify and combine like terms

So the equation of the line through BC is

-------------------------------
Let's find the equation of the segment CA

Start with the general formula

Plug in the given points

Simplify and combine like terms

So the equation of the line through CA is

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Now plug the slope and the point (2,-5) into

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So the altitude for vertex C is

Now to find the equation of the line that is perpendicular to that goes through the point A(4,5), simply negate and invert the slope to get

Now plug the slope and the point (2,-5) into

Solve for y and simplify

So the altitude for vertex A is

Now to find the equation of the line that is perpendicular to that goes through the point B(-4,1), simply negate and invert the slope to get

Now plug the slope and the point (-4,1) into

Solve for y and simplify

So the altitude for vertex B is

------------------------------------------------------------
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Plug in into the first equation

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Divide both sides by 3 to isolate x

Now plug this into

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