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3 years ago

Ben uses a compass and a straightedge to construct ∠DEF ≅ ∠ABC, as shown below:

Mathematics

1 answer:

Len [333]3 years ago

5 0

Answer: Choice D

∠DEF ≅ ∠ABC when BH = EJ, BI = EK, and HI = JK.

======================================================

Explanation:

Effectively what Ben is doing is ensuring that

BH = EJ
BI = EK
HI = JK

are the three congruent corresponding sides. This is by construction. After those constructions, he would use SSS to prove the triangles congruent. Lastly, he can then say angle DEF is congruent to angle ABC due to CPCTC.

CPCTC = corresponding parts of congruent triangles are congruent.

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Soloha48 [4]

Given:

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To find:

The product of the polynomials.

Solution:

1. $-3 x^{2}\left(4 x^{3}-7\right)$ $=-3 x^{2}(4 x^{3}) -3 x^{2}(-7)$

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$=-12 x^{5}+21 x^{2}$

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Multiply each term of first polynomial with each term of 2nd polynomial.

Multiply the numerical coefficient and add the powers of x.

$=12 x^2+18x-10 x-15$

$=12 x^2+8x-15$

3. $(3 x-1)\left(x^{2}+5 x-2\right)=3 x(x^{2}+5 x-2)-1(x^{2}+5 x-2)$

Multiply each term of first polynomial with each term of 2nd polynomial.

Multiply the numerical coefficient and add the powers of x.

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Add or subtract like terms together.

$=3x^{3}+14 x^2-11x+2$

The answer for multiplying polynomials:

$1. -12 x^{5}+21 x^{2}$

$2. \ 12 x^2+8x-15$

$3. \ 3x^{3}+14 x^2-11x+2$

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Step-by-step explanation:

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