<h3>
Answer: Choice D. 8m, 9m, 10m</h3>
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Explanation:
If a = 8 and b = 9 are the two legs of a triangle and c = 10 is the hypotenuse, then
a^2 + b^2 = c^2
8^2 + 9^2 = 10^2
64 + 81 = 100
145 = 100
We get a false equation as 145 and 100 are two different values. So the original equation is false when (a,b,c) = (8,9,10)
By the converse of the pythagorean theorem, we have proven that this particular triangle is not a right triangle
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Contrast this with something like choice A where we have a = 3, b = 4, c = 5 leading to
a^2 + b^2 = c^2
3^2 + 4^2 = 5^2
9 + 16 = 25
25 = 25
we get a true equation so a triangle with sides 3,4,5 is a right triangle. Choices B and C follow a similar path.
Slope of the line passing through two points <span><span>P=<span>(<span><span>x1</span>,<span>y1</span></span>) </span></span></span>and <span><span>Q=<span>(<span><span>x2</span>,<span>y2</span></span>)</span></span></span> is given by <span><span>m=<span><span><span>y2</span>−<span>y1/</span></span><span><span>x2</span>−<span>x1</span></span></span></span></span>.
We have that <span><span><span>x1</span>=−8</span></span>, <span><span><span>y1</span>=−3</span></span>, <span><span><span>x2</span>=−3</span></span>, <span><span><span>y2</span>=4</span></span>.
Plug given values into formula for slope: <span><span>m=<span><span><span>(4)</span>−<span>(<span>−3</span>)/</span></span><span><span>(<span>−3</span>)</span>−<span>(<span>−8</span>)</span></span></span>=<span>7/5</span></span></span>.
Now y-intercept is <span><span>b=<span>y1</span>−m⋅<span>x1</span></span></span> .
<span><span>b=−3−<span>(<span>7/5</span>)</span>⋅<span>(<span>−8</span>)</span>=<span>41/5.</span></span></span>
Finally, equation of the line can be written in the form <span><span>y=mx+b</span></span>.
<span><span>y=<span>7/5</span>x+<span>41/5</span></span></span>
Red line slope=3/4
Blue line slope=2/3
If we divide the area we have to cover by the area of a piece, we will get the number of pieces needed:
