Agardener is planting two types of trees take a is 4 feet tall and grows at a rate of 22 inches per year tybee is 6 feet tall and grows at a rate of 18 inches per year algebraically determine exactly how many years you will take for these trees could be the same height

After 6 years both the trees will be of same height

Solution:

Let "x" be the number of years that both the trees take to be the same height

Type A is 4 feet tall and grows at a rate of 22 inches per year

We know that,

1 feet = 12 inches

4 feet = 4 x 12 inches = 48 inches

Therefore height of type A after x years is given as:

⇒ initial height + 22 inches per year

⇒ 48 + 22(x)

⇒ 48 + 22x eqn 1

Type B is 6 feet tall and grows at a rate of 18 inches per year

We know that,

1 feet = 12 inches

6 feet = 12 x 6 inches = 72 inches

Therefore height of type B after x years is given as:

⇒ initial height + 18 inches per year

⇒ 72 + 18(x)

⇒ 72 + 18x eqn 2

For height Type A to equal height Type B:

Height Type A = Height Type B

eqn 1 = eqn 2

48 + 22x = 72 + 18x

22x - 18x = 72 - 48

4x = 24

x = 6

Therefore after 6 years both the trees will be of same height

5.6%

step-by-step explanation:

step-by-step explanation:

we are given a graph for system of inequalities.

in order to write the system of inequalities for the given graph, we need to find the inequality for each of the line separately.

let us find the slope of dotted line first.

taking two coordinates on the graph.

let us say (0,0) and (3,1).

let us find the slope of the line now.

slope of the dotted line would be =.

y-intercept of dotted line is y=0 only.

plugging slope m= and b=0 in slope-intercept form y=mx+b, we get

.

the line is shaded up of that dotted line.

therefore, for shading up we would take greater than inequality symbol > .

and because it's a dotted line we would take only > symbol in place of = sign in above equation of line.

therefore, inequality for dotted line would be

let us take two points (3,1) and (0,4) on the solid line.

slope of the solid line would be =.

for the solid line we have y-intercept b= 4.

plugging slope m= -1 and b=4 in slope-intercept form y=mx+b, we get

y = -1x + 4.

the line is shaded down of that solid line.

therefore, for shading down we would take less than inequality symbol < .

and because it's a solid line we would take ≤ symbol in place of = sign in above equation of line.

therefore, inequality for solid line would be