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2 years ago

A ______ rate is a rate expressed as a fraction with a denominator of 1.

Mathematics

1 answer:

frez [133]2 years ago

3 0

Answer:

<u>Unit</u> rate is the answer

Step-by-step explanation:

Hope this helped you!

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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

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

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

$m_A_B \neq m_C_D$

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

Quadrilateral ABCD is rotated 90° about the origin. What are the coordinates

Ilya [14]

Answer:

The Answer Would Be C. A'(-5, -5), B'(-5, -1). C'(-2,-1).

D(5, -1)

Quick math. ;)

6 0

4 years ago

-1/6(2x + 12) = 1/3x + 12

Hitman42 [59]

Hope this helps
X=-21

7 0

3 years ago

0.4 of 1 minute.<br> Help please

bearhunter [10]

Answer:

24 seconds

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers

Does the point (2, 6) lie on the line that connects (1, 4) and (0, 3)? Explain.

Mkey [24]

Answer:

The point does not lie on the line

Step-by-step explanation:

Find the slope of the equation with rise/run

This gets you -1/-1 = 1

The equation will be y = x + 3, given the y intercept at (0, 3)

Plug in the point (2, 6) to see if it works in the equation

6 = 2 +3

6 $\neq$ 5

The point does not lie on the line

8 0

3 years ago