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3 years ago

How many solutions y=10x+2 y=8x+2x+2

Mathematics

1 answer:

Wewaii [24]3 years ago

6 0

Answer:

Infinutely many solutions

Step-by-step explanation:

y = 10x + 2 --------- (1)

y = 8x +2x +2

=> y = 10x + 2---------- (2)

(1) -> 10x -y + 2 = 0

(2) -> 10x -y + 2 = 0

a1=10 ; b1=-1 ; c1 = 2

a2=10 ; b2=-1 ; c2= 2

a1/a2 = 10/10 = 1

b1/b2 = -1/-1 = 1

c1/c2 = 2/2 = 1

therefore, a1/a2 = b1/b2 = c1/c2

Therefore the line coincides and there are infinitely many solutions.

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3 years ago

The width of a container is 5 feet less than its height. Its length is 1 foot longer than its height. The volume of the containe

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The height of container is 8 feet

Solution:

Let "w" be the width of container

Let "l" be the length of container

Let "h" be the height of container

The width of a container is 5 feet less than its height

Therefore,

width = height - 5

w = h - 5 ------ eqn 1

Its length is 1 foot longer than its height

length = 1 + height

l = 1 + h ---------- eqn 2

The volume of container is given as:

$v = length \times width \times height$

Given that volume of the container is 216 cubic feet

$216 = l \times w \times h$

Substitute eqn 1 and eqn 2 in above formula

$216 = (1 + h) \times (h-5) \times h\\\\216 = (h+h^2)(h-5)\\\\216 = h^2-5h+h^3-5h^2\\\\216 = h^3-4h^2-5h\\\\h^3-4h^2-5h-216 = 0$

Solve by factoring

$(h-8)(h^2+4h+27) = 0$

Use the zero factor principle

If ab = 0 then a = 0 or b = 0 ( or both a = 0 and b = 0)

Therefore,

$h - 8 = 0\\\\h = 8$

Also,

$h^2+4h+27 = 0$

Solve by quadratic equation formula

$\text {For a quadratic equation } a x^{2}+b x+c=0, \text { where } a \neq 0\\\\x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}$

$\mathrm{For\:} a=1,\:b=4,\:c=27:\quad h=\frac{-4\pm \sqrt{4^2-4\cdot \:1\cdot \:27}}{2\cdot \:1}$

$h = \frac{-4+\sqrt{4^2-4\cdot \:1\cdot \:27}}{2}=\frac{-4+\sqrt{92}i}{2}$

Therefore, on solving we get,

$h=-2+\sqrt{23}i,\:h=-2-\sqrt{23}i$

Thus solutions of "h" are:

h = 8

$h=-2+\sqrt{23}i,\:h=-2-\sqrt{23}i$

"h" cannot be a imaginary value

Thus the solution is h = 8

Thus the height of container is 8 feet

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3 years ago

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3 years ago

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