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Ksivusya [100]
3 years ago
14

Part

Mathematics
1 answer:
lesantik [10]3 years ago
3 0
<span>y = 2−x and y = 4x + 3

Let I be the point of intersection:

I belongs to the line y=2-x and at the same time I belongs to y=4x+3, then the coordinates of I are the same for y =2-x & y= 4x+2, in short if we replace the coordinates in y = 2-x & in y=4x+3 by their respective values, we will find an equality.

b) <span>2−x = 4x + 3

Replace x  in  the equation 2−x = 4x + 3  with the here below values to find if an equality exists

for x = -3 then </span> 2-(-3) = 4(-3)+3 → 5 = -9 IMPOSSIBE, it's not an equality

for x = 2 then  2-2 = 4(2)+3 →<span> 0 = 11 IMPOSSIBE, it's not an equality

</span>for x = 1 then  2-(1) = 4(1)+3 →<span> 1 = 7 IMPOSSIBE, it's not an equality

</span>for x = - 1 then  2-(-1) = 4(-1)+3 →<span> 3 = -1 IMPOSSIBE, it's not an equality

and you can replace x with all integers from - 3 to + 3 and you will find an INEQUALITY, so all these values are not a solution of thev equation

c. Solving the equation </span><span>2−x = 4x + 3 
</span><span>2−x = 4x + 3  

1st add x to both sides: 2-x + x = 4x + 3 + x </span>→2 = 5x + 3

2nd to this new equation <span>2 = 5x + 3, subtract 3 from both sides:

</span><span>2 - 3= 5x + 3 - 3 </span>→-1 = 5x

3rd in this new equation -1=5x, divide both sides by 5 → -1/5 = x
 And x = -1/5 is the solution of the system. To find the y value, you replace in any of the 2 equation  <span>y = 2−x and y = 4x + 3, x by its value (-1/5) and you will find y = 11/5</span>




</span>
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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:

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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}}

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

substitute in the formula

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

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

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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

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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)

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

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so

The triangle BDA is a right triangle

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A=b^{2}

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b=5\ units

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

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P=4b

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