Answer:
answers in bold
table 1: (2.2, 10.68), (3, 13), (0.6, 6.04), (5, 18.8)
table 2: (12, 17/2), (7, 31/6), (15, 21/2), (20, 13 5/6)
Explanation:
to solve these tables, we plug in the given values into the equation given.
TABLE 1:
rule: x2.9 + 4.3 <-- x in this equation is equal to the input
input: 2.2
(2.2)(2.9) + 4.3 <-- we multiply 2.2 x 2.9
6.38 + 4.3 = 10.68
so, the output for 2.2 is 10.68
input: 3
(3)(2.9) + 4.3 <--- multiply 3 x 2.9
8.7 + 4.3 = 13
the output for 3 is 13
input: 0.6
(0.6)(2.9) + 4.3
1.74 + 4.3 = 6.04
the output for 0.6 is 6.04
output: 18.8
to find the output, we set the equation equal to the output and solve for x
x2.9 + 4.3 = 18.8 < we want the variable alone, so subtract 4.3 from both sides
-4.3 -4.3
x2.9 = 14.5 < now divide 2.9 from both sides to get x alone
x2.9/2.9 = x
14.5/2.9 = 5
x = 5
we know that the input is the variable x, so the input to the output 18.8 is 5
in an ordered pair, the table looks like the following: (2.2, 10.68), (3, 13), (0.6, 6.04), (5, 18.8)
TABLE 2:
rule: x2/3 + 1/2
input: 12
(12)(2/3) +1/2
8 + 1/2 < add the fraction & whole number by finding the LCD.
16/2 + 1/2 = 17/2
the output for 12 is 17/2
input: 7
(7)(2/3) + 1/2
14/3 + 1/2 = 31/6
the output for 7 is 31/6
input: 15
(15)(2/3) + 1/2
10 + 1/2 = 21/2
the output for 15 is 21/2
output: 13 5/6
first, i will convert 13 5/6 to an improper fraction to make it easier to work with
83/6
similar to table 1, we set the equation equal to the output and solve for x
x2/3 + 1/2 = 83/6 < subtract 1/2 from both sides
- 1/2 - 1/2
x2/3 = 40/3 < divide both sides by 2/3 to get x alone
x2/3 ÷ 2/3 = x
40/3 ÷ 2/3 = 20
x = 20
the input is the variable x, and x = 20
so the input for the output 13 5/6 is 20
in an ordered pair, it looks like this:
(12, 17/2), (7, 31/6), (15, 21/2), (20, 13 5/6)