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4 years ago

Solve for x. 4 | x - 7 | + 2 | x - 7 | = 12

Mathematics

1 answer:

miv72 [106K]4 years ago

7 0

Answer: x = 9, 5

Step-by-step explanation:

4 | x - 7 | + 2 | x - 7 | = 12

6 | x - 7 | = 12 added like terms

| x - 7 | = 2 divided both sides by 6

x - 7 = 2 or x - 7 = -2 removed absolute value sign

x = 9 or x = 5 added 7 to both sides of both equations

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$\mathbf{\dfrac{x^2}{49^2} +\dfrac{y^2}{37^2} =1}$

Step-by-step explanation:

Given that :

the foci of the ellipse is (±√12,0) and C0-vertices are (0,±√37)

The foci are (-C,0) and (C ,0)

the focus has x-coordinates so the focus is lie on x- axis.

The major axis also lie on x-axis

The minor axis lies on y-axis so C0-vertices are (0,±√37)

The given focus C = ae = √12

Given co-vertices ( minor axis) (0,±b) = (0,±√37)

b= √37

We can therefore express the relation between the focus and semi major axes and semi minor axes as:

$\mathbf{c^2 = a^2 - b^2 } \\ \\ \mathbf{a^2 = c^2 + b^2 } \\ \\ \mathbf{c^2 = ( \sqrt12)^2 - (\sqrt 37)^2 } \\ \\ \mathbf{c^2 = 49 } \\ \\ \mathbf{c = \sqrt{49 }}$

The equation of ellipse formula is:

$\dfrac{x^2}{a^2} +\dfrac{y^2}{b^2} =1$

and we know that $\mathbf{a=\sqrt{49} \ \ and \ \ b=\sqrt{37}}$

Thus ; the equation of the ellipse at the origin is

$\mathbf{\dfrac{x^2}{49^2} +\dfrac{y^2}{37^2} =1}$

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