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2 years ago

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what is the equation of the line that is parallel to the given line and passes through the point (2, 3) ? a. x + 2y = 4 b. x + 2

y = 8 c. 2x + y =4 d. 2x + y = 8

1 answer:

aleksandr82 [10.1K]2 years ago

3 0

Answer:

see explanations

Step-by-step explanation:

The given blue line has a slope of m = -1/2.

The line parallel to the given line passing through point (x0,y0)=(2,3) is given by the point-slope form:

(y-y0)=m(x-x0)

substitute values

(y-3) = (-1/2)(x-2)

Expand and transpose

y = (-1/2)x + 1 + 3

y = (-1/2)x + 4 ....................(1)

We choose the second equation b. x+2y=8 and convert to slope-intercept form:

2y=-x+8

y = (-1/2)x + 4, which is exactly equation (1)

So

b. x+2y=8 is the correct answer.

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2 years ago

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Free_Kalibri [48]

QUESTION 1

We want to solve,

$\frac{1}{(x-4)}+\frac{x}{(x-2)}=\frac{2}{x^{2}-6x+8}$

We factor the denominator of the fraction on the right hand side to get,

$\frac{1}{(x-4)}+\frac{x}{(x-2)}=\frac{2}{x^{2}-4x - 2x+8}.$

This implies
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We multiply through by LCM of
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We group like terms and equate everything to zero,

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We split the middle term,

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We factor to get,

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We add x to both sides,

$\sqrt{x+11} =x-1$

We square both sides,

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We expand to get,

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We solve this quadratic equation by factorization,

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