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ozzi
3 years ago
8

Which equation represents the line passing through the points (3, 2) and (–9, 6)?

Mathematics
1 answer:
prisoha [69]3 years ago
4 0
(3,2),(-9,6)
slope = (6 - 2) / (-9 - 3) = -4/12 = -1/3

y = mx + b
slope(m) = -1/3
use either of ur points...(3,2)....x = 3 and y = 2
now we sub into the formula and find b, the y int
2 = -1/3(3) + b
2 = -1 + b
2 + 1 = b
3 = b
so ur equation is : y = -1/3x + 3 <==
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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
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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        

<em>Verify if the polygon is a square</em>

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

so

The triangle BDA is a right triangle

therefore

The polygon is a square

<em>Find the Area of the polygon</em>

The area of a square is equal to

A=b^{2}

we have

b=5\ units

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

<em>Find the perimeter of the polygon</em>

The perimeter of a square is equal to

P=4b

we have

b=5\ units

P=4(5)=20\ units

6 0
2 years ago
1.13 Thank you! (Sorry it’s so blurry)
VikaD [51]
\sqrt[8]{48^4}  can be rewritten as 48^4 to the \frac{1}{8}  power:

(48^4)^ \frac{1}{8}

Now, applying exponent rules (multiply exponent inside parentheses by the one outside parentheses), we get:

(48^ \frac{1}{2})

This is equivalent to \sqrt{48}, so now, we just simplify:

\sqrt{48}=  \sqrt{16*3}= \sqrt{16}* \sqrt{3}=4 \sqrt{3}

So:

\sqrt[8]{48^4} =4 \sqrt{3} 


4 0
3 years ago
Can someone please answer?
gtnhenbr [62]

Answer:

The answer is 24

Step-by-step explanation:

6 0
2 years ago
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Which system of equations can be used to find the roots of the equation 4x^2=x^3+2x?
irina [24]
Next time, please share the answer choices.
Starting from scratch, it's possible to find the roots:

<span>4x^2=x^3+2x should be rearranged in descending order by powers of x:

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Clearly, one root is 0.  We must now find the roots of (x^2 - 4x + 2):

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5 0
2 years ago
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The surface area of a tabletop is 5760 square inches. What expression shows this number in scientific notation?
aniked [119]
The answer is C

5.76 x 10 ^3 means you move the decimal 3 times:

57.6> 576.0> 5760
8 0
3 years ago
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