Answer:
(1, 5)
Step-by-step explanation:
The solution to the system of equations is the point of intersection of the two lines. From inspection of the graph, the point of intersection is at (1, 5).
<u>Proof</u>
The solution to a system of equations is the point at which the two lines meet.
⇒ g(x) = f(x)
⇒ 3x + 2 = |x - 4| + 2
⇒ 3x = |x - 4|
⇒ 3x = x - 4 and 3x = -(x - 4)
⇒ 3x = x - 4
⇒ 2x = -4
⇒ x = -2
Inputting x = -2 into the 2 equations:
⇒ g(-2) = 3 · -2 + 2 = -4
⇒ f(-2) = |-2 - 4| + 2 = 8
Therefore, as the y-values are different, x = -2 is NOT a solution
⇒ 3x = -(x - 4)
⇒ 3x = 4 - x
⇒ 4x = 4
⇒ x = 1
Inputting x = 1 into the 2 equations:
⇒ g(1) = 3 · 1 + 2 = 5
⇒ f(1) = |1 - 4| + 2 = 5
Therefore, as the y-values are the same, x = 1 IS a solution
and the solution is (1, 5)
Answer: The girls collected 18 more aluminum cans than the boys.
Step-by-step explanation:
boys:
16 x 12 = 192
girls:
15 x 14 = 210
210 - 192 = 18
126 1/4 = 126 3/12 = 125 15/12
- 78 2/3 = - 78 8/12 = - 78 8/12
--------------------------------------...
47 7/12
1) Find the lowest common denominator (LCD) for the fractions. In this case, 12 is the LCD.
2) Rewrite the fractions 1/4 and 2/3 using 12 as the denominator (second column). You get 3/12 and 8/12.
3) Since it's confusing to subtract 8/12 from 3/12, you need to borrow one from the 126. Doing so is the same as taking 12/12 from 126. This changes to 125, and the 12/12 adds to the 3/12 making it 15/12.
4) Subtract 8/12 from 15/12 to get 7/12.
5) Subtract 78 from 125 to get 47.
6) The answer is 47 7/12.
