$54000 as ratio 1:3:8

1 answer:

8 0

Find the fraction of $54000 corresponding to 1, 3 and 8 in 1:3:8:

First, sum up 1, 3 and 8: 1+3+8 = 12.
Next, divide 1, 3 and 8 by this sum (12): (1/12), (3/12) and (8/12).
Next, mult. $54000 by each of these 3 fractions:

(1/12)($54000), (3/12)($54000), AND (8/12)($54000), or

$4500, $13500, $36000

Check: Do these amounts sum up to the original $54000?

$ 4500
+13500
+36000
------------
$54000 YES. How would you show that these 3 amounts are in the ratio 1:3:8?

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5. Find the value(s) of x so that the line containing the points (2x + 3, x + 2) and (0, 2) is

Dvinal [7]

Answer:

x = -2 or -9

Step-by-step explanation:

You want the values of x such that the line defined by the two points (2x+3, x+2) and (0, 2) is perpendicular to the line defined by the two points (x+2, -3-3x) and (8, -1).

<h3>Slope</h3>

The slope of a line is given by the slope formula:

m = (y2 -y1)/(x2 -x1)

Using the formula, the slopes of the two lines are ...

m1 = (2 -(x+2))/(0 -(2x+3)) = (-x)/(-2x-3) = x/(2x +3)

and

m2 = (-1 -(-3-3x))/(8 -(x+2)) = (2+3x)/(6 -x)

<h3>Perpendicular lines</h3>

The slopes of perpendicular lines have product of -1:

$\dfrac{x}{2x+3}\cdot\dfrac{2+3x}{6-x}=-1\\\\x(3x+2)=(2x+3)(x-6)\qquad\text{multiply by $(2x+3)(6-x)$}\\\\3x^2+2x=2x^2-9x-18\qquad\text{eliminate parentheses}\\\\x^2+11x+18=0\qquad\text{put in standard form}\\\\(x+2)(x+9)=0\qquad\text{factor}$