Theorem:
The measure of an exterior angle of a triangle is equal to the sum of the measures of its remote interior angles.
Angle 4 is an exterior angle of the triangle.
Angles 1 and 2 are the remote interior angles of angle 4.
m<4 = m<1 + m<2
m<4 = 30 deg + 110 deg
m<4 = 140 deg
<span>B. ∠1 and ∠9</span>
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Here's an example...
So, in our last example...
In the point ( -2, -1 ), x1 = -2 and y1 = -1 ... and, in the point ( 4, 3 ), x2 = 3 and y2 = 3
m = ( y2 - y1 ) / ( x2 - x1 ) = ( 3 - ( -1 ) ) / ( 4 - ( -2 ) ) = 4 / 6 = 2 / 3
But, notice something cool...
The order of the points doesn't matter! Let's switch them and see what we get:
In the point ( 4, 3 ), x1 = 4 and y1 = 3 ... and, in the point ( -2, -1 ), x2 = -2 and y2 = -1
m = ( y2 - y1 ) / ( x2 - x1 ) = ( -1 - 3 ) / ( -2 - 4 ) = -4 / -6 = 2 / 3 ... Same thing!
Let's try our new formula with the second example in the last lesson:
It was a line passing through
( -1, 4 ) and ( 2, -2 )
m = ( y2 - y1 ) / ( x2 - x1 ) = ( -2 - 4 ) / ( 2 - ( -1 ) ) = -6 / 3 = -2
4 and five eights is equal to 4 + 5/8.
You know that the decimal representation of 5/8 is 0.625, so the decimal representations of 4 and five eights will be 4.625.
Short answer: 100
I assume you want to find x.
We want an equation that says that x is equal to 105cm, minus that 5 percent, because that is his height before the 5% was added. That looks like:
x + 0.05x = 105
(0.05 is 5% in decimal form, which is necessary in equations like this).
x + 0.05x = 1.05x
1.05x = 105.
Isolate x by dividing both sides by 1.05
1.05x / 1.05 = x, 105 / 1.05 = 100
x = 100, so he was 100cm tall before summer
My original answer was 99.75. This is wrong because I used the 5% of 105, which is wrong because in the question it says his original height (which is x) had 5% added to it. So its 5% of x, not 5% of 105. This changes the whole equation.
