Answer:
c
Step-by-step explanation:
Let 1/x = a &
1/y = b
So, now the equation:
2a +3b = 13 --------------------(i)
5a - 4b = -2 --------------------(ii)
To eliminate a, Multiply equation (i) by 5 and multiply (ii) by (-2)
(i)*5 10a + 15b = 65
(ii)*(-2) <u> - 10a + 8b = 4</u> ( Now add, a will be eliminated}
23b = 69
b= 69/23
b = 3
Plug in the value of b in equation (i)
2a + 3*3 = 13
2a + 9 = 13
2a = 13 - 9
2a = 4
a= 4/2
a = 2
Now a = 1/x ------>x = 1/a = 1/2
b = 1/y ----------->y = 1/b = 1/3
Answers:
A triangle is possible.
The triangle is <u>acute</u> and <u>scalene</u>
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Explanation:
We use the triangle inequality theorem to see if a triangle is possible with these side lengths.
Consider the side lengths a, b, and c. A triangle is possible if and only if the following 3 conditions hold true
Basically pick any two sides. If the sum is larger than the third side, then a triangle is possible.
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In this case we have: a = 8, b = 14, c = 16. The order of the a,b,c values doesn't really matter.
Then:
All three inequalities mentioned are true; therefore, <u>a triangle is possible</u> with these side lengths.
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We'll use those a,b,c values in the converse of the pythagorean theorem to determine what kind of triangle this is. So far we know it's <u>scalene</u> because all three side lengths are different. It would be isosceles if it had exactly two equal sides, and equilateral if all 3 sides were the same length.
The last equation is false, which tells us this triangle is not a right triangle. It's either acute or obtuse.
Since is the case here, we can conclude the triangle is <u>acute</u>
If was the case, then the triangle would be obtuse.
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Summary: