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2 years ago

Which equation represents the vertical line passing through (14,-16)?.

1 answer:

6 0

The vertical line shall have its x-coordinate equal to 14 because the points (14, -16) is on this vertical line.

<u>Given the following data:</u>

Points (x, y) = (14, -16)

To find an equation of the vertical line that passes through the given points (14, -16):

The standard form of an equation of line is given by the formula;

$y=mx+b$

<u>Where:</u>

x and y are the points.

m is the slope.

b is the intercept.

For any equation of a straight line, the x-coordinate of a vertical line will always be the same irrespective of the point chosen on the vertical line. because a vertical line is perpendicular to the x-axis.

Deductively, the vertical line shall have its x-coordinate equal to 14 because the points (14, -16) is on this vertical line.

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Answer:

A. The solutions are $x=3i,\:x=-3i$ .

B. The factored form of the quadratic expression $x^2+9=(x-3i)(x+3i)$

Step-by-step explanation:

A. To find the solutions to the quadratic equation $x^2+9=0$ you must:

$\mathrm{Subtract\:}9\mathrm{\:from\:both\:sides}\\\\x^2+9-9=0-9\\\\\mathrm{Simplify}\\\\x^2=-9\\\\\mathrm{For\:}x^2=f\left(a\right)\mathrm{\:the\:solutions\:are\:}x=\sqrt{f\left(a\right)},\:\:-\sqrt{f\left(a\right)}\\\\x=\sqrt{-9},\:x=-\sqrt{-9}$

$x=\sqrt{-9} = \sqrt{-1}\sqrt{9}=\sqrt{9}i=3i\\\\x=-\sqrt{-9}=-\sqrt{-1}\sqrt{9}=-\sqrt{9}i=-3i$

The solutions are:

$x=3i,\:x=-3i$

B. Two expressions are equivalent to each other if they represent the same value no matter which values we choose for the variables.

To factor $x^2+9$ :

First, multiply the constant in the polynomial by $i^2$ where $i^2$ is equal to -1.

$x^2+9i^2$

Since both terms are perfect squares, factor using the difference of squares formula

$a^2-i^2=(a+i)(a-i)$

$x^2+9=x^2+9i^2=\left(-3i+x\right)\left(3i+x\right)$

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