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3 years ago

Write an equation in slope-intercept form

Mathematics

1 answer:

satela [25.4K]3 years ago

8 0

Answer:

y = mx + b

m = Slope = (Y2 -Y1) ÷ (X2 -X1)

Slope = (10 -5) ÷ (-3 -4)

Slope = 5 ÷ -7 = -5/7 =m

b = y - mx

Let's take one of the 2 given points (4, 5) and input into b = y - mx

b = 5 - (-5/7 * 4)

b = 5 + 20/7

b = 7 +(6/7)

So, the equation is :

y = -(5/7)x + 7 +(6/7)

Step-by-step explanation:

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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

Which term can be used in the blank of 36x3−22x2−__ so the greatest common factor of the resulting polynomial is 2x? Select two

maria [59]

Answer:

4xy and 12x

Step-by-step explanation:

In this question, we are to select which of the options to put into the blank space that will make the greatest common factor of the polynomial 2x. We are to select two options

Now, looking at the blank space, we should understand that , any answer we shall be choosing shall be an answer that contains x alongside the number.

This makes 24 and 44y out of the way.

Now let’s look at 4xy and 12x. Let’s insert them into the blank space;

36x^3-22x^2 - 4xy which gives : 2x(18x^2-11x-2y)

and 36x^3-22x^2-12x = 2x(18x^2-11x-6)

The reason why we will not use 44y and 24 is because 2x is not a factor of either.

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7y-3x= -5 solve for x

nika2105 [10]

7y - 3x = -5
-3x = -7y - 5
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11Alexandr11 [23.1K]

D. 13
This is the answer .

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dexar [7]

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