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3 years ago

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Mathematics

1 answer:

viva [34]3 years ago

4 0

<h2>Answer:</h2>

Part A

<u>The area is 20x5+16x4−26x3+22x2+32x−24 sqaure units</u>

Part B

<u>Yes the answer is polynomial</u>

Part C

<u>The degree is 5</u>

<h2>Step-by-step explanation:</h2><h3>Part A</h3>

The solution is given in the attached figure

In mathematics, a polynomial is an expression consisting of variables and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables. So the answer is a polynomial in our case.

The degree of a polynomial is the highest degree of its individual terms with non-zero coefficients. The degree of an expression is the sum of the exponents of the variables that appear in the polynomial, and thus is a non-negative integer. In our case the degree of the polynomial is 5.

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Answer:

The fourth point of the parallelogram is one point among (-2,2), (2,10) and (8,-12).

Step-by-step explanation:

Given information: The first three vertices of parallelogram are (0,6), (5, -1) and (3,-5).

Let fourth point of the parallelogram is (a,b).

Diagonals of a parallelogram bisect each other. It means midpoint of both diagonals are same.

Midpoint formula:

$Midpoint=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$

Case 1: If the point (0,6), (5, -1) and (3,-5) are consecutive, then pairs of opposite vertices are (0,6) and (3,-5), (5,-1) and (a,b).

$(\frac{0+3}{2},\frac{6-5}{2})=(\frac{5+a}{2},\frac{-1+b}{2})$

$(\frac{3}{2},\frac{1}{2})=(\frac{5+a}{2},\frac{-1+b}{2})$

On comparing both sides, we get

$\frac{3}{2}=\frac{5+a}{2}$

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$\frac{1}{2}=\frac{-1+b}{2}$

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It means the fourth point of the parallelogram is (-2,2).

Case 2: If the point (0,6), (5, -1) and (3,-5) are not consecutive, then pairs of opposite vertices are (0,6) and (5,-1), (3,-5) and (a,b).

$(\frac{0+5}{2},\frac{6-1}{2})=(\frac{3+a}{2},\frac{-5+b}{2})$

$(\frac{5}{2},\frac{5}{2})=(\frac{3+a}{2},\frac{-5+b}{2})$

On comparing both sides, we get

$\frac{5}{2}=\frac{3+a}{2}$

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$\frac{5}{2}=\frac{-5+b}{2}$

$5=-5+b$

$b=10$

It means the fourth point of the parallelogram is (2,10).

Case 3: If the point (0,6), (5, -1) and (3,-5) are not consecutive, then pairs of opposite vertices are (5,-1) and (3,-5), (0,6) and (a,b).

$(\frac{5+3}{2},\frac{-1-5}{2})=(\frac{0+a}{2},\frac{6+b}{2})$

$(\frac{8}{2},\frac{-6}{2})=(\frac{a}{2},\frac{6+b}{2})$

On comparing both sides, we get

$\frac{8}{2}=\frac{a}{2}$

$8=a$

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$-6=6+b$

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It means the fourth point of the parallelogram is (8,-12).

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Alternate means they are on opposite sides of the transversal...
Same side means they are on the same side of the transversal..
interior mean they are inside the parallel lines
exterior means they are on the outside of parallel lines.

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FEG and CBE are indeed supplementary but they don't have a relationship
CBE and DEB are same side interior angles because they are on the same side of the transversal and inside the parallel lines
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