Solve -2(x + 4) + 9 < -11 then graph.

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

AysviL [449]

Answer:

The quadrilateral is not a rectangle

Step-by-step explanation:

we know that

If a quadrilateral ABCD is a rectangle

then

Opposite sides are congruent and parallel and adjacent sides are perpendicular

Remember that

If two lines are parallel, then their slopes are the same

If two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes is equal to -1)

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

we have

A(-5,5), B(1,8), C(4,2), and D(-2,-2)

Plot the figure to better understand the problem

see the attached figure

Find the slope of the four sides and then compare

step 1

Find slope AB

A(-5,5), B(1,8)

substitute in the formula

$m=\frac{8-5}{1+5}$

$m=\frac{3}{6}$

$m_A_B=\frac{1}{2}$

step 2

Find slope BC

B(1,8), C(4,2)

substitute in the formula

$m=\frac{2-8}{4-1}$

$m=\frac{-6}{3}$

$m_B_C=-2$

step 3

Find slope CD

C(4,2), and D(-2,-2)

substitute in the formula

$m=\frac{-2-2}{-2-4}$

$m=\frac{-4}{-6}$

$m_C_D=\frac{2}{3}$

step 4

Find slope AD

A(-5,5), D(-2,-2)

substitute in the formula

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

$m=\frac{-7}{3}$

$m_A_D=-\frac{7}{3}$

step 5

Verify if the opposites are parallel

Remember that

If two lines are parallel, then their slopes are the same

The opposite sides are

AB and CD

BC and AD

we have

$m_A_B=\frac{1}{2}$

$m_C_D=\frac{2}{3}$

so

$m_A_B \neq m_C_D$

It is not necessary to continue verifying, because two of the opposite sides are not parallel

therefore

The quadrilateral is not a rectangle

4 0

3 years ago

Math homework please help new subject dont know it. (trolls = report)

Natasha2012 [34]

Find area on triangle:
A=(1/2)bh
A=(1/2)(8 units)(6 units)
A=(1/2)(48 units^2)
A=24 units^2
Just do the same for the rest of this page following the equation for the area of a triangle A=(1/2)(base)(height)

Find the error:
A=(1/2)bh
100m^2=(1/2)b(20m)
100m^2=(10m)b
10m=b
He forgot to multiply bh by 1/2

Area of parallelogram:
A=bh
A=(3 units)(3 units)
A= 9 units^2
The red line is the height and the bottom of the parallelogram is the base, just count the squares. Imagine cutting the parallelogram at the red line and moving that triangle piece to the other side, it’ll make a rectangle, that’s why the equation is the same.

6 0

3 years ago

Read 2 more answers

Paige has to make invitation cards for a party. If she can make 18 cards in 2 days, how many cards can she make in 30 days

LenaWriter [7]

Answer:

270

Step-by-step explanation:

3 0

3 years ago

Find the value of x. Round to the nearest tenth. The diagram is not drawn to scale.

likoan [24]

Answer:

Cosine 24 = adjacent / hypotenuse (x)

0.91355 = 11 / hypotenuse

hypotenuse = 11 / 0.91355

hypotenuse (x) = 12.0409391933

or x = 12.04 (rounded)

Step-by-step explanation:

4 0

3 years ago

Mala ran 30 laps in week one and will increase the number of laps she runs by 2 each week. Coby runs 16 laps in week one and wil

Alex_Xolod [135]

Answer:

5 weeks

Step-by-step explanation:

32

21

week 1 over ^

34

26

week 2 over^

36

31

week 3 over ^

38

36

week 4 over ^

40

41

week 5 over ^

8 0

3 years ago