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3 years ago

A direct variation passes through the point (-3,9) given y varies directly as x find the value of y when x is 2

Mathematics

1 answer:

frutty [35]3 years ago

5 0

Answer:

y=-6

Step-by-step explanation:

Proportions

A direct proportion is a relation between variables where their ratio is a constant value. This means that if y and x are proportional, then:

y = kx

Where k is the constant of proportionality.

Substituting x=-3 y=9:

9 = k(-3)

$k=\frac{9}{-3}=-3$

Now the relationship is:

y = -3x

For x=2

y = -3(2) = -6

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Solve the following equations;- x - 9 /√x + 3 =1

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Answer:

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Step-by-step explanation:

A equation is given to us and we need to find out the value of x . The given equation to us is ,

$\sf\implies \dfrac{ x -9}{\sqrt{x+3}}= 1$

Cross multiply ,

$\sf\implies x - 9 =\sqrt{ x +3}$

Squaring both sides ,

$\sf\implies (x - 9)^2 = x + 3$

Simplify the whole square ,

$\sf\implies x^2+9^2-2.9.x = x +3 \\$

$\sf\implies x^2+81 - 18x = x -3$

Add 3 and subtract x on both sides ,

$\sf\implies x^2 -18x-x +81-3=0$

Simplify ,

$\sf\implies x^2 -19x +78=0$

Split the middle term of the quadratic equation,

$\sf\implies x^2-13x-6x+78=0$

Take out common ,

$\sf\implies x( x -13)-6(x-13)=0$

Take out ( x -13 ) as common ,

$\sf\implies ( x -13)(x-6)=0$

Equate both factors to 0 ,

$\sf\implies \boxed{\pink{\sf x = 13,6}}$

Hence the value of x is 13 or 6 .

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