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4 years ago

the area of a rectangular pool is given by the trinomial to 2y^2+y - 3 what are the possible dimensions of a pool. use factoring

1 answer:

4 0

2y² + y - 3

(2y+3)(y-1)

2y(y-1) + 3(y-1)
2y² - 2y + 3y - 3
2y² + y - 3

2y + 3 = 0
2y = -3
y = -3/2
y = -1 1/2

y - 1 = 0
y = 1

2y² + y - 3 = 0
2(-3/2)² + (-3/2) - 3 = 0
2(9/4) - 3/2 - 3 = 0
18/4 - 3/2 - 3 = 0
18/4 - (3/2 * 2/2) - 3(4/4) = 0
18/4 - 6/4 - 12/4 = 0
(18 - 6 - 12)/4 = 0
(18 -18)/4 = 0
0/4 = 0
0 = 0

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we will select each points and find equation of line

option-A:

points are B(5,2) and C(7,-5)

x1=5,y1=2 , x2=7 , y2=-5

Firstly, we will find slope

$m=\frac{y_2-y_1}{x_2-x_1}$

we can plug values

$m=\frac{-5-2}{7-5}$

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we can use point slope form of line

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$y-2=-3.5(x-5)$

$y=\frac{-7}{2}x+\frac{39}{2}$ ...........Answer

option-B:

points are D(11,6) and E(5,9)

x1=11,y1=6 , x2=5 , y2=9

Firstly, we will find slope

$m=\frac{y_2-y_1}{x_2-x_1}$

we can plug values

$m=\frac{9-6}{5-11}$

$m=-0.5$

we can use point slope form of line

$y-y_1=m(x-x_1)$

we can plug values

$y-6=-0.5(x-11)$

$y=\frac{-1}{2}x+\frac{23}{2}$ ...........Answer

option-C:

points are F(-7,12) and G(3,-8)

x1=-7,y1=12 , x2=3 , y2=-8

Firstly, we will find slope

$m=\frac{y_2-y_1}{x_2-x_1}$

we can plug values

$m=\frac{-8-12}{3+7}$

$m=-2$

we can use point slope form of line

$y-y_1=m(x-x_1)$

we can plug values

$y-12=-2(x+7)$

$y=-2x-2$ ...........Answer

option-D:

points are H(4,4) and I(8,9)

x1=4,y1=4 , x2=8 , y2=9

Firstly, we will find slope

$m=\frac{y_2-y_1}{x_2-x_1}$

we can plug values

$m=\frac{9-4}{8-4}$

$m=1.25$

we can use point slope form of line

$y-y_1=m(x-x_1)$

we can plug values

$y-4=1.25(x-4)$

$y=\frac{5}{4}x-1$ ...........Answer

option-E:

points are J(7,2) and K(-9,8)

x1=7,y1=2 , x2=-9 , y2=8

Firstly, we will find slope

$m=\frac{y_2-y_1}{x_2-x_1}$

we can plug values

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we can use point slope form of line

$y-y_1=m(x-x_1)$

we can plug values

$y-2=\frac{3}{8}(x-7)$

$y=\frac{3}{8}x-\frac{5}{8}$ ...........Answer

option-F:

points are L(5,-7) and M(4,-12)

x1=5,y1=-7 , x2=4 , y2=-12

Firstly, we will find slope

$m=\frac{y_2-y_1}{x_2-x_1}$

we can plug values

$m=\frac{-12+7}{4-5}$

$m=5$

we can use point slope form of line

$y-y_1=m(x-x_1)$

we can plug values

$y+7=5(x-5)$

$y=5x-32$ ...........Answer

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