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2 years ago

The length of a rectangle is 2 km less than 3 times the width. If the perimeter is 68 km,What is the length of the rectangle

Mathematics

1 answer:

11111nata11111 [884]2 years ago

6 0

Answer:

The length of the rectangle is 25 km

Step-by-step explanation:

Let

x ----> the length of rectangle

y ----> the width of rectangle

we know that

The perimeter of rectangle is

$P=2(x+y)$

we have

$P=68\ km$

$68=2(x+y)$

simplify

$34=(x+y)$ ---- > equation A

$x=3y-2$ ---> equation B

substitute equation B in equation A and solve for y

$34=(3y-2)+y$

$34=4y-2$

$4y=34+2$

$4y=36$

$y=9\ km$

Find the value of x

$x=3(9)-2=25\ km$

therefore

The length of the rectangle is 25 km

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Write the slope-intercept form of the equation that passes through the given points. (separate equations for each of them)

guajiro [1.7K]

Answer:

Part 1) $y=-\frac{1}{5}x-1$

Part 2) $y=3x-16$

Part 3) $y=4$

Step-by-step explanation:

we know that

The equation of the line into slope intercept form is equal to

$y=mx+b$

where

m is the slope

b is the y-intercept

Part 1) we have

(10,-3) (5,-2)

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The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

substitute

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$m=\frac{1}{-5}$

$m=-\frac{1}{5}$

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$m=-\frac{1}{5}$

$point (10,-3)$

substitute in the equation $y=mx+b$ and solve for b

$-3=-\frac{1}{5}(10)+b$

$-3=-2+b$

$b=-3+2=-1$

substitute

$y=-\frac{1}{5}x-1$

Part 2) we have

(6,2) (7,5)

Find the slope

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

substitute

$m=\frac{5-2}{7-6}$

$m=\frac{3}{1}$

$m=3$

Find the value of b

we have

$m=3$

$point (6,2)$

substitute in the equation $y=mx+b$ and solve for b

$2=3(6)+b$

$2=18+b$

$b=2-18=-16$

substitute

$y=3x-16$

Part 3) we have

(4,4) (-7,4)

Find the slope

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

substitute

$m=\frac{4-4}{-7-4}$

$m=\frac{0}{-11}$

$m=0$

This is a horizontal line (parallel to the x-axis)

The y-intercept b is equal to the y-coordinate

therefore

The equation of the line is

$y=4$

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