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soldier1979 [14.2K]
2 years ago
6

Which expression is not a polynomial? A. 3x + 5 B. 2/5x - 21 C. 5 D. x^-3 + 5x

Mathematics
1 answer:
Anettt [7]2 years ago
7 0

Answer:

C. 5

Step-by-step explanation:

"<em>Polynomial</em>" means <em>consisting of several terms</em>, or more than one term.

In A, we see that there are 2 terms (3x and 5), and so it is a polynomial, specifically a <em>binomial.</em>

In B, we also see 2 terms (2/5x and -21), and so it is also a polynomial, specifically a <em>binomial.</em>

In C, we only see one term (5), and so it is a <em>monomial</em>, or having only one term.

In D, we can see 2 terms (x^-3 and 5x), and so it is also a polynomial, specifically a <em>binomial</em>.

~

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2. Given a quadrilateral with vertices (−1, 3), (1, 5), (5, 1), and (3,−1):
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<h2>Explanation:</h2>

In every rectangle, the two diagonals have the same length. If a quadrilateral's diagonals have the same length, that doesn't mean it has to be a rectangle, but if a parallelogram's diagonals have the same length, then it's definitely a rectangle.

So first of all, let's prove this is a parallelogram. The basic definition of a parallelogram is that it is a quadrilateral where both pairs of opposite sides are parallel.

So let's name the vertices as:

A(-1,3) \\ \\ B(1,5) \\ \\ C(5,1) \\ \\ D(3,-1)

First pair of opposite sides:

<u>Slope:</u>

\text{For AB}: \\ \\ m=\frac{5-3}{1-(-1)}=1 \\ \\ \\ \text{For CD}: \\ \\ m=\frac{1-(-1)}{5-3}=1 \\ \\ \\ \text{So AB and CD are parallel}

Second pair of opposite sides:

<u>Slope:</u>

\text{For BC}: \\ \\ m=\frac{1-5}{5-1}=-1 \\ \\ \\ \text{For AD}: \\ \\ m=\frac{-1-3}{3-(-1)}=-1 \\ \\ \\ \text{So BC and AD are parallel}

So in fact this is a parallelogram. The other thing we need to prove is that the diagonals measure the same. Using distance formula:

d=\sqrt{(y_{2}-y_{1})^2+(x_{2}-x_{1})^2} \\ \\ \\ Diagonal \ BD: \\ \\ d=\sqrt{(5-(-1))^2+(1-3)^2}=2\sqrt{10} \\ \\ \\ Diagonal \ AC: \\ \\ d=\sqrt{(3-1)^2+(-5-1)^2}=2\sqrt{10} \\ \\ \\

So the diagonals measure the same, therefore this is a rectangle.

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Can someone help me. ​
marshall27 [118]

Answer:

B

Step-by-step explanation:

yeah just pick B man lol

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Hi there!

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