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3 years ago

Point K is on line segment JL. Given KL = 2x – 2, JL = 4x + 9, and

Mathematics

1 answer:

sergeinik [125]3 years ago

7 0

Answer:

JL = 21

Step-by-step explanation:

Given that K is on line segment JL, therefore:

KL + JK = JL (according to segment addition postulate)

KL = 2x - 2

JK = 5x + 2

JL = 4x + 9

Thus:

$(2x - 2) + (5x + 2) = (4x + 9)$

Solve for x

$2x - 2 + 5x + 2 = 4x + 9$

$2x +5x - 2 + 2 = 4x + 9$

$7x = 4x + 9$

Subtract 4x from both sides

$7x - 4x = 4x + 9 - 4x$

$3x = 9$

Divide both sides by 3

$\frac{3x}{3} = \frac{9}{3}$

$x = 3$

Find the numerical length of JL

$JL = 4x + 9$

Plug in the value of x

$JL = 4(3) + 9 = 12 + 9 = 21$

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iVinArrow [24]

$\fbox{Solution by using Matrix}$

$\text{Linear Equation} = -8x-8y=0 , -8x+2y=-20$

$\text{Rewrite the linear equations above as a matrix}$

$\left[\begin{array}{ccc}8&-8&0\\-8&2&-20\\\end{array}\right]$

$\text{Apply to Row2 : Row2 + Row1}$

$\left[\begin{array}{ccc}8&-8&0\\-8&-6&-20\\\end{array}\right]$

$\text{ Simplify rows}$

$\left[\begin{array}{ccc}8&-8&0\\0&1&10/3\\\end{array}\right]$

$\text{Note: The matrix is now in echelon form.}$ $\text{The steps below are for back substitution.}$

$\text{Apply to Row1 : Row1 + 8 Row2}$

$\left[\begin{array}{ccc}8&0&80/30\\0&1&10/3\\\end{array}\right]$

$\text{ Simplify rows}$

$\left[\begin{array}{ccc}1&0&10/3\\0&1&10/3\\\end{array}\right]$

$\text{Therefore, the solution is}$

$x= \dfrac{10}{3} \ \text{and} \ \ y=\dfrac{10}{3}$

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3 years ago