Answer:
Two or more independent functions (say f(x) and g(x)) can be combined to generate a new function (say g(x)) using any of the following approach.
h(x) = f(x) + g(x)h(x)=f(x)+g(x) h(x) = f(x) - g(x)h(x)=f(x)−g(x)
h(x) = \frac{f(x)}{g(x)}h(x)=
g(x)
f(x)
h(x) = f(g(x))h(x)=f(g(x))
And many more.
The approach or formula to use depends on the question.
In this case, the combined function is:
f(x) = 75+ 10xf(x)=75+10x
The savings function is given as
s(x) = 85s(x)=85
The allowance function is given as:
a(x) = 10(x - 1)a(x)=10(x−1)
The new function that combined his savings and his allowances is calculated as:
f(x) = s(x) + a(x)f(x)=s(x)+a(x)
Substitute values for s(x) and a(x)
f(x) = 85 + 10(x - 1)f(x)=85+10(x−1)
Open bracket
f(x) = 85 + 10x - 10f(x)=85+10x−10
Collect like terms
mark as brainiest
f(x) = 85 - 10+ 10xf(x)=85−10+10x
f(x) = 75+ 10xf(x)=75+10x
Try breaking these into sections.
Twice: 2 times
The sum of: add
A number: choose a variable, like x
---Thus "the sum of a number and 4" becomes "add x and 4" which, mathematically, is "x+4"
-----Continuing to put it all together, "Twice the sum of a number and four" becomes "2 times (x+4)" which, mathematically, is "2(x+4)"
Is: equals
-------"Twice the sum of a number and four is" becomes "2(x+4)="
23 less than: subtract 23. This one tends to trick people; "23 less than" will become "__ - 23", NOT "23 - __"
three times the number: 3 times x
---"23 less than three times the number" becomes "subtract 23 from 3 times x" which, mathematically, is "3x-23"
-------So the final phrase: 2(x+4)=3x-23"
By solving a linear equation, we will see that the total cost for renting the bus is $90.
<h3>What was the total cost of renting the bus, in dollars?</h3>
Let's say that the total cost is C.
When there are 20 students, each student should pay:
p = C/20
When the other 10 students are added (for a total of 30) each student pays:
p' = C/30.
We know that the cost for each of the original 20 students decreased by $1.50, so:
p' = p - $1.50
Then we have 3 equations to work with:
p = C/20
p' = C/30.
p' = p - $1.50
Now we can replace the first and second equations into the third one:
C/30 = C/20 - $1.50
Now we can solve this linear equation for C:
C/20 - C/30 = $1.50
C*( 1/20 - 1/30) = $1.50
C*(30/600 - 20/600) = $1.50
C*(10/600) = $1.50
C*(1/60) = $1.50
C = 60*$1.50 = $90
So the total cost for renting the bus is $90.
If you want to learn more about linear equations:
brainly.com/question/1884491
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Answer:
Step-by-step explanation:
( 
, 
)
( 
, 
)
rate of change or slope m = 
= 
y = mx + b
"b" is y-intercept
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