A person has a tree in his backyard. The tree grows 40 centimeters each year. Since the tree started growing, Hassan has trimmed 24 centimeters off its height. The goal for the tree's height is given by 40x-24>256, where is the number of years the tree grows.
Complete the parts below.
To solve the inequality 40x - 24 > 256, we need to isolate the variable x. Here's how:
Step 1: Add 24 to both sides of the inequality:
40x - 24 + 24 > 256 + 24
40x > 280
Step 2: Divide both sides of the inequality by 40:
(40x) / 40 > 280 / 40
x > 7
Therefore, the tree's height needs to be greater than 7 years of growth in order to reach a height greater than 256 centimeters.
Now, let's calculate the number of years the tree needs to reach that height.
The inequality 40x - 24 > 256 represents the tree's height after x years of growth minus 24 (since Hassan has trimmed 24 centimeters).
To find the number of years required for the tree to reach a height greater than 256 centimeters, we can substitute the height growth per year (40 cm) into the inequality and solve for x.
40x - 24 > 256
Step 1: Add 24 to both sides of the inequality:
40x - 24 + 24 > 256 + 24
40x > 280
Step 2: Divide both sides of the inequality by 40:
(40x) / 40 > 280 / 40
x > 7
Therefore, the tree needs to grow for more than 7 years in order to exceed a height of 256 centimeters.