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1 year ago

Consider the linear equation below.

Mathematics

1 answer:

densk [106]1 year ago

8 0

4- distributive property

Reason
X(y+u)= xy+xu
Expansion is distributive property

Hope it helps

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Identify the polygon with vertices A(5,0), B(2,4), C(−2,1), and D(1,−3), and then find the perimeter and area of the polygon. HE

inn [45]

Answer:

Part 1) The polygon is a square

Part 2) The perimeter is equal to $20\ units$

Part 3) The area is equal to $25\ units^{2}$

Step-by-step explanation:

we have

$A(5,0), B(2,4), C(-2,1),D(1,-3)$

Plot the points

see the attached figure

we know that

the formula to calculate the distance between two points is equal to

$d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}$

Find the distance AB

$A(5,0),B(2,4)$

substitute in the formula

$d=\sqrt{(4-0)^{2}+(2-5)^{2}}$

$d=\sqrt{(4)^{2}+(-3)^{2}}$

$d=\sqrt{25}$

$AB=5\ units$

Find the distance BC

$B(2,4), C(-2,1)$

substitute in the formula

$d=\sqrt{(1-4)^{2}+(-2-2)^{2}}$

$d=\sqrt{(-3)^{2}+(-4)^{2}}$

$d=\sqrt{25}$

$BC=5\ units$

Find the distance CD

$C(-2,1),D(1,-3)$

substitute in the formula

$d=\sqrt{(-3-1)^{2}+(1+2)^{2}}$

$d=\sqrt{(-4)^{2}+(3)^{2}}$

$d=\sqrt{25}$

$CD=5\ units$

Find the distance AD

$A(5,0),D(1,-3)$

substitute in the formula

$d=\sqrt{(-3-0)^{2}+(1-5)^{2}}$

$d=\sqrt{(-3)^{2}+(-4)^{2}}$

$d=\sqrt{25}$

$AD=5\ units$

we have that

AB=BC=CD=AD

Find the distance BD (diagonal)

$B(2,4),D(1,-3)$

substitute in the formula

$d=\sqrt{(-3-4)^{2}+(1-2)^{2}}$

$d=\sqrt{(-7)^{2}+(-1)^{2}}$

$BD=\sqrt{50}\ units$

Verify if the polygon is a square

If the triangle BDA is a right triangle, then the polygon is a square

Applying the Pythagoras theorem

$BD^{2}=AD^{2}+AB^{2}$

substitute

$(\sqrt{50})^{2}=5^{2}+5^{2}$

$50=50$ -----> is true

The triangle BDA is a right triangle

therefore

The polygon is a square

Find the Area of the polygon

The area of a square is equal to

$A=b^{2}$

we have

$b=5\ units$

$A=5^{2}=25\ units^{2}$

Find the perimeter of the polygon

The perimeter of a square is equal to

$P=4b$

we have

$b=5\ units$

$P=4(5)=20\ units$

6 0

3 years ago

Solve for the probability that a student is selected at random from a group of 20 students will draw a 6 from a bag with the num

Mariana [72]

Depending on what the number is in for the bag

8 0

3 years ago

WRITE a Linear FUNCTION, f, with the given values: f(-4) = -5 and f(2) = -3

Crazy boy [7]

Answer:

answer to the question is A

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3 years ago

If a car travels 792 feet in 12 seconds what is the speed of the car in miles per hour?

UkoKoshka [18]

Answer:

Step-by-step explanation:

1 mile contains 5280 feet

x mile contains 792 feet Cross Multiply

5280 x = 792 Divide by 5280

x = 792 / 5280

x = 0.15 miles

1 hour = 3600 seconds

Distance travelled in 12 sec = 0.15 miles

3600 sec = x Cross Multiply

12x = 3600 * 0.15 Combine

12x = 540 Divide both sides by 12

12x/12 = 540/12

x = 45 miles / hour

6 0

3 years ago

Read 2 more answers

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iogann1982 [59]

Graph these numbers and then connect at the end.

3. y (6,-3). x (2,-4) z (5,-7)

4. U (5,4). T (5,1) S (1,0) V(-3,4)

i hope these help.

7 0

2 years ago