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3 years ago

12

PLEASE HELP ILL GIVE BRAINLIEST! IGNORE WHERE IT SAYS 6 POINTS, THATS HOW MUCH ITS WORTH IN THE GRADEBOOK!

2 answers:

kakasveta [241]3 years ago

3 0

Answer: x = 13

Step-by-step explanation:

They are equal so set them equal and solve for x.

(4x+1) = 53

4x = 52

x = 13

MatroZZZ [7]3 years ago

3 0

Answer:

Since the lines l and m are parallel,

angle (4x + 1) and angle 53 are both corresponding angles

We know that corresponding angles are equal, so:

4x + 1 = 53

4x = 52

x = 13

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4 years ago

A quadrilateral has vertices at A(–5, 5), B(1, 8), C(4, 2), D(–2, –2). Use slope to determine if the quadrilateral is a rectangl

lianna [129]

With the properties of rectangle in mind we must perform two verification. Verify to see if opposite sides are parallel and adjacent sides are perpendicular.

We need to determine the slope of each side, using the formula,

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

<u>Slope of AB</u>

$m_{AB}=\frac{8-5}{1--5}$

$\Rightarrow m_{AB}=\frac{8-5}{1+5}$

$\Rightarrow m_{AB}=\frac{3}{6}$

$\Rightarrow m_{AB}=\frac{1}{2}$

<u>Slope of BC</u>

$m_{BC}=\frac{2-8}{4-1}$

$\Rightarrow m_{BC}=\frac{-6}{3}$

$\Rightarrow m_{BC}=-2$

<u>Slope of CD</u>

$m_{CD}=\frac{-2-2}{-2-4}$

$\Rightarrow m_{CD}=\frac{-2-2}{-2-4}$

$\Rightarrow m_{CD}=\frac{-4}{-6}$

$\Rightarrow m_{CD}=\frac{2}{3}$

<u>Slope of AD</u>

$m_{AD}=\frac{-2-5}{-2--5}$

$\Rightarrow m_{AD}=\frac{-2-5}{-2+5}$

$\Rightarrow m_{AD}=\frac{-7}{3}$

<u>Verify Parallel sides</u>

If the quadrilateral is a rectangle, then opposite sides should have the same slope. But

$m_{AD} = \frac{-7}{3} \neq m_{BC}=-2$

$m_{AB}=\frac{1}{2} \neq m_{CD}=\frac{2}{3}$

<u>Verify Perpendicularity</u>

And also the product of slopes of all sides with a common vertex should be -1. But

$m_{AB} \times m_{BC}=\frac{1}{2} \times -2=-1$

$m_{AB} \times m_{AD}=\frac{1}{2} \times -\frac{7}{3} \neq -1$

$\Rightarrow m_{CD} \times m_{AD}=\frac{2}{3} \times -\frac{7}{3} \neq -1$

$\Rightarrow m_{CD} \times m_{BC}=\frac{2}{3} \times -2 \neq -1$

Since the quadrilateral fails to satisfy all these conditions, the quadrilateral is not a rectangle

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