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romanna [79]
3 years ago
7

Triangle DEF is similar to triangle FGH. Both are right triangles.

Mathematics
1 answer:
ser-zykov [4K]3 years ago
8 0
<span>Congruent triangles are triangles with the same sides and the same measure of angles. You are given triangle DEF which is similar to triangle FGH. From the figure, side FH is larger than side DF. So the statement of them being congruent cancels out. Triangle DEF is smaller in size than triangle FGH. So they are not congruent. The slope is defined as the rise over run. Side DF has the same slope as side FH. Sides DE and FE are proportional to sides FG and HG. Only C and D is correct.

</span>
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Given P(x) = 2x3 - 11x2 + 18x - 15 is divided by x – 3. Use synthetic division to find the quotient and the remainder.
katrin [286]
You can find the remainder right away by simply plugging in x=3. The polynomial remainder theorem guarantees that the value of p(3) is the remainder upon dividing p(x) by x-3, but I digress...

Synthetic division yields

3   |   2   -11   18   -15
.    |           6   -15     9
- - - - - - - - - - - - - - - - -
.    |   2     -5     3     -6

which translates to

\dfrac{2x^3-11x^2+18x-15}{x-3}=2x^2-5x+3-\dfrac6{x-3}

(and note that p(3)=2(3)^3-11(3)^2+18(3)-15=-6, as expected)
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Answer:

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