The following is an incomplete paragraph proving that the opposite angles of parallelogram ABCD are congruent:
1 answer:
For a better understanding of the answer to the question provided here kindly check the diagram that has been attached here.
The attached diagram has the complete construction details as has been asked to do in the question.
Let us now begin answering.
As can be clearly seen from the attached diagram angles PBC and BAD are congruent by the Corresponding Angles Theorem AB acts as the transversal for the lines BC and AD which are parallel.
Also, it can be clearly seen that the angles ABC and BAT are congruent by the Alternate Interior Angles Theorem as AB acts as the transversal for the lines BC and TAD which are parallel.
Thus, the only option from the given list of options which matches the answer is Option A.
Thus, Option A is the correct option and thus the final answer.
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Problem 7
<h3>Answer: Choice A) 7</h3>--------------------------------------
Work Shown:
p(x) = x^4+x^3-kx-x+6
If (x-2) is a factor of p(x), then x = 2 is a root of p(x). This is a special case of the remainder theorem.
This means p(2) = 0
Replace every x with 2 and solve for k
p(x) = x^4+x^3-kx^2-x+6
p(2) = 2^4+2^3-k(2)^2-2+6
p(2) = 16+8-4k-2+6
p(2) = 28-4k
0 = 28-4k .... replace p(2) with 0
4k = 28
k = 28/4
k = 7
The polynomial
p(x) = x^4+x^3-7x^2-x+6
has the factor (x-2)
============================================
Problem 8
<h3>Answer: D) 40</h3>--------------------------------------
Work Shown:
Check out the diagram below to see the synthetic division table. We're after the remainder which is highlighted in yellow.
An alternative is to use direct substitution
p(x) = 2x^4+4x^3-x^2-5
p(-3) = 2(-3)^4+4(-3)^3-(-3)^2-5 ... replace every x with -3
p(-3) = 2(81)+4(-27)-9-5
p(-3) = 162-108-9-5
p(-3) = 40
This helps confirm we got the right remainder and the right answer.
