Agardener is planting two types of trees: type a is 5 feet tall and grows at a rate of 18 inches per year. type b is 8 feet tall and grows at a rate of 14 inches per year. algebraically determine exactly how many years it will take for these trees to be the same height.

9 years

Step-by-step explanation:

The first thing that you need to do is convert 5 feet and 8 feet into inches.

5 x 12 = 60

8 x 12 = 96

The equation to solve this problem when the number of years equals x is:

60 + 18x = 96 + 14x

First, subtract 60 from each side:

18x = 36 + 14x

Next, subract 14x from each side:

4x = 36

Divide both sides by 4:

X = 9 years

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