Perimeter = 2L + 2W

Let x = width and let 2x = length

Perimeter = 66

2x + 2(2x) = 66

2x + 4x = 66 --> 6x = 66 --> x = 66/6 --> x = 11

The width of the rectangle is 11 cm.

6 0

3 years ago

Write the equation of each line using the given information.

Leni [432]

a) x – 2y + 6 = 0 b) x + y = 1 c) y = 1 d) y = -3x + 8

<h3>Solution:</h3>

a. The points (-4,1) and (2,4) both lie on the line

The general line equation on which (a, b) and (c, d) lies is:

$y-\mathrm{b}=\frac{d-b}{c-a}(x - a)$

Here the given points are (a, b) = (-4, 1) and (c, d) = (2, 4)

Thus the required equation is:

$y-1=\frac{4-1}{2-(-4)}(x-(-4))$

On solving we get,

$\begin{array}{l}{\rightarrow y-1=\frac{3}{2+4}(x+4)} \\\\ {\rightarrow y-1=\frac{3}{6}(x+4)} \\\\ {\rightarrow 2(y-1)=1(x+4)} \\\\ {\rightarrow 2 y-2=x+4} \\\\ {\rightarrow x-2 y+6=0}\end{array}$

b.) m= -1 and the point (2, -1) lies on the line

The equation of line in point slope form is y – b = m(x – a)

where m is slope and (a, b) is a point on it

Here m = -1 and (a, b) = (2, -1)

Thus the required equation is:

y – (-1) = -1(x - 2)

y + 1 = -x + 2

y = -x + 2 -1

y = -x + 1

c. )It has the same slope as y = 5 and passes through (1, 1)

our line has same slope with y = 5, then our equation would be y = k and it passes through (x, y) = (1, 1) so, then by substitution

1 = k

k =1

Then our equation will be y = k

y = 1

d. ) m= -3 and it has a y-intercept of (0, 8)

line equation in slope intercept form is y = mx + b where m is slope and b is y – intercept.

Then, our equation will be y = -3x + 8

We took y- intercept = 8 as it is the value of y when x = 0

6 0

3 years ago

How do you solve the problem?

sleet_krkn [62]

3x-17+x+40+2x-5=180
6x=162
x=27
(From left to right) 67,64, 49

4 0

3 years ago