Left problem
This problem can be solved with a proportion.
Use x for the unknown height of the tree.
If 2 foot tall casts a shadow 5 ft long as x foot tall casts a shadow 55 ft long.
2/5 = x/55
Cross multiply:
5x = 110
x = 22
The tree is 22 ft tall.
Right problem
Look at the table. The input goes up by 1 each step. The corresponding output goes up by 3 each step. For each change of 1 in the input, the output changes 3.
Now look at the table, and fill in the output for inputs of 2, 1, and 0.
Each time the input goes down by 1, the output goes down by 3.
We have input 3 with output 10.
Then we can calculate:
input 2 with output 7
input 1 with output 4
input 0 with output 1
Since for each change of 1 in the input, the output changes 3, the slope is 3.
That means the equation is
y = 3x + b
b is the y-intercept. Since we calculated the output of 1 for an input of 0, the y-intercept is 1.
The equation is
y = 3x + 1
That means the expression for the output is 3n + 1
Answer: D. 3n + 1
