Answer: No, we don't have a right triangle
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Explanation:
If a triangle with sides a,b,c makes the equation a^2+b^2 = c^2 true, where c is the longest side, then this triangle is a right triangle. This is the converse of the pythagorean theorem.
Here we have a = 2, b = 5 and c = 7.
So...
a^2+b^2 = c^2
2^2+5^2 = 7^2
4+25 = 49
29 = 49
The last equation is false, so the first equation is false for those a,b,c values. Therefore, we do <u>not</u> have a right triangle.
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In contrast, consider the classic 3-4-5 right triangle
a = 3, b = 4 and c = 5 would make a^2+b^2 = c^2 true because 3^2+4^2 = 5^2 is a true equation (both sides lead to 25).
9514 1404 393
Answer:
The slope of f(x) is greater than the slope of g(x). The y-intercept of f(x) is equal to the y-intercept of g(x).
Step-by-step explanation:
The y-intercept is the function value when x=0. The table shows f(0) = 1. The equation shows g(0) = 1, so the y-intercepts are equal.
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The value of f(x) changes by (11 -1) = 10 when the value of x changes by (2 -0) = 2. That means the slope of f(x) is 10/2 = 5.
The slope of g(x) is the x-coefficient, 4. We note that 5 > 4, so the slope of f(x) is greater than for g(x).
The slope of f(x) is greater than the slope of g(x). The y-intercept of f(x) is equal to the y-intercept of g(x).
Answer:
No, it is not a square
Step-by-step explanation:
If one wall is 19", that would mean the wall perpendicular to this wall is also 19" (in fact all of the walls would be 19"!) If this was a square, then the diagonal we draw at 20.62" would serve as the hypotenuse of a right triangle. One wall would serve as a leg, and another wall as another leg. If this is a square, then the Pythagorean's Theorem would be satisfied when we plug in the 2 wall measures for a and b, and the diagonal for c:
We need to see if this is a true statement. If the left side equals the right side, then the 2 legs of the right triangle are the same length, and the room, then is a square.
361 + 361 = 425.1844
Is this true? Does 722 = 425.1844? Definitely not. That means that the room is not a square.
MKL = 83, JKL = 127, JKM = 9x - 10 <em>given</em>
JKL + MKL = JKM <em>angle addition postulate</em>
127 + 83 = 9x - 10 <em>substitution</em>
210 = 9x - 10 <em>simplify (add like terms)</em>
220 = 9x <em>addition property of equality</em>
= x
