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Roman55 [17]
3 years ago
13

What is 2/3(3x+9)=−2(2x+6)

Mathematics
1 answer:
lubasha [3.4K]3 years ago
5 0
Your answer is x= -3
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3 years ago
On your paper, construct a rectangle on a coordinate plane that satisfies these criteria.
german

Answer:

A = (5,3)

B = (-5,3)

C = (-5,-8)

D = (5,-8)

Step-by-step explanation:

Required

Perimeter = 42

Construct a rectangle whose perimeter is 42 units and satisfies the given conditions.

First, name the rectangle ABCD.

Such that:

A = (x_1,y_1)

B = (x_2,y_2)

C = (x_3,y_3)

D = (x_4,y_4)

For the rectangle to be either horizontal or vertical, then:

y_1 = y_2 and y_3 = y_4

We have that:

Perimeter = 42

Replace perimeter with its formula

2(AB + BC) = 42

Divide both sides by 2

AB + BC = 21

This implies that, the distance between adjacent sides (through the edges) must be equal to 21

Having said that: a set of coordinates that satisfy the given conditions are:

A = (5,3) -- First quadrant

B = (-5,3) -- Second quadrant

C = (-5,-8) -- Third quadrant

D = (5,-8) -- Fourth quadrant

The above quadrants satisfy the condition:

y_1 = y_2 and y_3 = y_4

<u>HOW TO KNOW THE PERIMETER IS 42</u>

To do this, we simply calculate the distance between the edges and add them up

<u>Distance is calculated as:</u>

<u></u>D = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2<u></u>

<u></u>

<u>For AB</u>

A = (5,3)

B = (-5,3)

D_1 = \sqrt{(5 - (-5))^2 + (3 - 3)^2}= \sqrt{(10)^2 + (0)^2} = \sqrt{100} = 10

<u>For BC</u>

B = (-5,3)

C = (-5,-8)

D_2 = \sqrt{(-5 - (-5))^2 + (3 - (-8))^2}= \sqrt{(0)^2 + (11)^2} = \sqrt{121} = 11

<u>For CD</u>

C = (-5,-8)

D = (5,-8)

D_3 = \sqrt{(-5 -5)^2 + (-8 - (-8))^2}= \sqrt{(-10)^2 + (0)^2} = \sqrt{100} = 10

<u>For DA</u>

D = (5,-8)

A = (5,3)

D_4 = \sqrt{(5 -5)^2 + (-8 -3)^2}= \sqrt{(0)^2 + (11)^2} = \sqrt{121} = 11

So, the perimeter is:

P = D_1 + D_2 + D_3 + D_4

P = 10 + 11 + 10 +11

P = 42

See attachment for rectangle

8 0
2 years ago
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