Answer:
a) T= 3.125h
b) $75
Step-by-step explanation:
Given: We know Tania raised $50 for staying awake 16 hours. We also know the amount of money raised varies directly with the time.
We can divide $50 into 16 hours.
50/16 = 25/8
25/8 = 3.125
3.125 = 3 1/8 (You can use a fraction or decimal, whichever is preferred)
That's how much money she earns per hour. It may not make sense because you have 1/8 of a dollar, so it's okay if you're a little confused on that.
Now let's answer the first question: Write an equation relating the money Tania raised and the amount of time, in hours, she stayed awake.
We know Tania earns $3.125 per hour, so we can make it this equation
T= 3.125h
T can represent Tania's earnings, and 3.125 is how much she earns h, hourly.
Now onto the second question: How much would she have raised by staying awake for 24 h?
We need to multiply 3.125, or 3 1/8, 24 times. Your answer should be $75.
(I apologize in advance if I misread something or made a mistake)
Answer:
Step-by-step explanation:
Domain is the set of all possible inputs (x) for the function f(x)
The range is the set of all possible values for that domain
This function is 4x + y = 3 which can be re-written as y = 3-4x
Plug in each of the domain values and you will get the range
For -2 : y = 3-4(-2) = 3 + 8 = 11
For 1: y = 3-4(1) = -1
For 5: y = 3-4(5) = -17
So range is {-17, -1, 11}
The equation of the line that passes through the points (2,1) and (5,-8) is
y = -3x + 7
<h3>
Answer: -10 and -40</h3>
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Explanation:
a = 200 = first term
d = -30 = common difference
Tn = nth term
Tn = a + d(n-1)
Tn = 200 + (-30)(n-1)
Tn = 200 - 30n + 30
Tn = -30n + 230
Set Tn less than 0 and isolate n
Tn < 0
-30n + 230 < 0
230 < 30n
30n > 230
n > 230/30
n > 7.667 approximately
Rounding up to the nearest whole number gets us 
So Tn starts to turn negative when n = 8
We can see that,
Tn = -30n + 230
T7 = -30*7 + 230
T7 = 20
and
Tn = -30n + 230
T8 = -30*8 + 230
T8 = -10 is the 8th term
and lastly
Tn = -30n + 230
T9 = -30*9 + 230
T9 = -40 is the ninth term
Or once you determine that T7 = 20, you subtract 30 from it to get 20-30 = -10 which is the value of T8. Then T9 = -40 because -10-30 = -40.
