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iris [78.8K]
2 years ago
13

WORTH 20 POINTS HELP

Mathematics
1 answer:
vfiekz [6]2 years ago
6 0

Below represents the proof that the quadrilateral QRST is a parallelogram

<h3>How to prove that QRST is a parallelogram?</h3>

The coordinates are given as:

Q = (-1,-1)

R = (2,9)

S = (-4,5)

T = (-7,-5)

Calculate the length of each side using:

d = \sqrt{(x_2 -x_1)^2 + (y_2 -y_1)^2}

So, we have:

QR = \sqrt{(-1 - 2)^2 + (-1 -9)^2} = \sqrt{109}

RS = \sqrt{(-4 - 2)^2 + (5 - 9)^2} = \sqrt{52}

ST = \sqrt{(-7 + 4)^2 + (-5 - 5)^2} = \sqrt{109}

TQ = \sqrt{(-7 + 1)^2 + (-5 + 1)^2} = \sqrt{52}

The above computations show that opposite sides are equal.

Next, we determine the slope of each side using:

m = \frac{y_2 -y_1}{x_2 -x_1}

So, we have:

QR = \frac{9 + 1}{2 + 3} = \frac{10}3

RS = \frac{5-9}{-4 - 2} = \frac{2}3

ST = \frac{5+5}{-4 + 7} = \frac{10}3

TQ = \frac{-5+1}{-7 + 1} = \frac{2}3

The above computations show that opposite sides are parallel, because they have equal slope

Hence, the quadrilateral QRST is a parallelogram

Read more about parallelograms at:

brainly.com/question/3050890

#SPJ1

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7 0
3 years ago
Points and Brainliest Giveaway!<br><br> What is the simplified form?<br> (2x^2 + 3x) + (4x^2 -7)
nika2105 [10]

Answer:

Explanation:

We can factor the numerator and denominator as;

(

x

−

2

)

(

x

−

1

)

2

x

(

x

−

1

)

We can now cancel common term in the numerator and denominator:

(

x

−

2

)

(

x

−

1

)

2

x

(

x

−

1

)

⇒

x

−

2

2

x

However, we cannot divide by

0

so we must exclude:

2

x

=

0

⇒

x

=

0

and

x

−

1

=

0

⇒

x

1

x

2

−

3

x

+

2

2

x

2

−

2

x

=

x

−

2

2

x

Where:

x

≠

0

and

x

≠

1

Or

x

2

−

3

x

+

2

2

x

2

−

2

x

=

x

2

x

−

2

2

x

=

1

2

−

1

x

Where:

x

≠

0

and

x

≠

1

Step-by-step explanation:

3 0
3 years ago
Read 2 more answers
Can someone please give me the (Answers) to this? ... please ...
harkovskaia [24]

Answer:please correct me if I’m wrong but I believe Part A for the slopes are…

1.3/1 or 3

2.-3

3.9/5

4.4/3

Step-by-step explanation:

It’s going up 3 and “running” 1 and it’s positive since the line is going up.

Y2-y1. -16-2

————= ————=-18/6=-3

X2-x1. 8-2

You’re just finding the slope

Solve for it. If further explanation is needed please tell me.

5 0
3 years ago
Read 2 more answers
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