the length of a rectangle is six inches more than width, if the preimeter of the rectangle is 24 inches find the length

Length = 9 inches

Step-by-step explanation:

The perimeter of a rectangle is:

perimeter = 2(length + width)

24 = 2(a+b)

a = b + 6

a = length

b = width

then:

24 = 2((b+6)+b)

24/2 = b+6+b

12 = 2b + 6

12-6 = 2b

6 = 2b

b = 6/2

b = 3 inches

a = b+6

a = 3+6

a = 9 inches

Check:

24 = 2(9+3)

24 = 2*12

5x + 3y = - 4

step-by-step explanation:

the equation of a line in standard form is

ax + by = c ( a is a positive integer and b, c are integers )

express the line first of all in slope- intercept form

y = mx + c ( m is the slope and c the y-intercept )

to calculate m use the gradient formula

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

with (x₁, y₁ ) = (7, - 3) and (x₂, y₂ ) = (4, - 8)

m = = -

y = - x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (4, - 8 ), then

- 8 = - + c ⇒ c = -

y = - x - ← in slope-intercept form

multiply all terms by 3 to eliminate the fractions

3y = - 5x - 4 ( add 5x to both sides )

5x + 3y = - 4 ← in standard form