Answer:
g(x) = (1/2)x + 3
f(x) = g(x) at (-1/2 , 13/4)
Step-by-step explanation:
g(x) and f(x) will have exactly one solution when they are not parallel (same slope) and when they are not equivalent functions (like doubling or halving all terms).
f(x) = (-5/2)x - 3
g(x) = (1/2)x + 3 <= choose an easy equation.
To find the solution, equate the two functions:
f(x) = g(x)
(-5/2)x - 3 = (1/2)x + 3
(-5/2)x - (1/2)x = 3 + 3 <= move variables to one side, constants to other
(-6/2)x = 6 <= simplify
x = 6 / (-6/2) <=isolate x
x = -6/12
x = -1/2
Substitute x = -1/2 into any equation to find y
g(x) = (1/2)x + 3
g(1/2) = (1/2)(1/2) + 3
g(1/2) = (1/4) + 3
g(1/2) = (1/4) + (12/4) <= find common denominator to add
y = (13/4) <= the function symbol can be replaced by y
The coordinates are (-1/2 , 13/4).
Let the price of a student ticket be t. That makes the price of an adult ticket t + 3, as adult tickets are three more dollars than student tickets. Now we have:
student ticket = t
adult ticket = t + 3
To model the scenario that Mr. Williams bought 7 student tickets and 6 adult tickets, set the sum of the products of those numbers and the ticket costs equal to 83 (the cost of all tickets combined) and solve algebraically for t.
83 = 7t + 6(t + 3)
83 = 7t + 6t + 18
83 = 13t + 18
65 = 13t
5 = t
Remember, t represents the cost of one student ticket, thus one student ticket costs 5 dollars, and one adult ticket costs 5 + 3 dollars or 8 dollars.
Answer:
The price of one adult ticket is $8.
You could have found the answer in less time than it took you to post the question.
-- Jessica's hourly rate is $7.50 per hour for the first 40 hours,
-- It's (1.5 x $7.50) for each hour over 40 hours.
-- Jessica earned (40 x $7.50) for the first 40 hours.
-- She earned (1.5 x $7.50) for each of the next 8 hours.
First multiplyum, then addum up.
No it is not greater because the whole number is bigger
