<span>Orthocenter is at (-3,3)
The orthocenter of a triangle is the intersection of the three heights of the triangle (a line passing through a vertex of the triangle that's perpendicular to the opposite side from the vertex. Those 3 lines should intersect at the same point and that point may be either inside or outside of the triangle. So, let's calculate the 3 lines (we could get by with just 2 of them, but the 3rd line acts as a nice cross check to make certain we didn't do any mistakes.)
Slope XY = (3 - 3)/(-3 - 1) = 0/-4 = 0
Ick. XY is a completely horizontal line and it's perpendicular will be a complete vertical line with a slope of infinity. But that's enough to tell us that the orthocenter will have the same x-coordinate value as vertex Z which is -3.
Slope XZ = (3 - 0)/(-3 - (-3)) = 3/0
Another ick. This slope is completely vertical. So the perpendicular will be complete horizontal with a slope of 0 and will have the same y-coordinate value as vertex Y which is 3.
So the orthocenter is at (-3,3).</span>
Hey there!
This equation we're given is a function. This means that we will get a certain output for each input. If your input is x, the output, or y, will be 0.3 of x plus 11.8. It appears that the independent variable (our x) is the age in the table and the height of the jump is the dependent variable (our y). We can plug some of the data into our function and see if it is true! We will use the first two columns of the table to test this out.
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Column 1
Age: 22
Height of Jump in Inches: 15.4
15.4=0.3(22)+11.8
15.4=6.6+11.8
15.4=18.4
This is equation is false, so this data point does not match the given function. We can check with one more column just to make sure, but just given this we immediately know that the given equation is not a good fit for the data.
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Column 2
Age: 24
Height of Jump in Inches: 17
17= 0.3(24)+11.8
17=7.2+11.8
17=19
This is equation is also false.
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Therefore, this equation is not a good fit for the data given.
I hope that this helps! Have a wonderful day!
210, 420, 630, 840
multiples of 2*3*5*7