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love history [14]
3 years ago
11

The bus fare in a city is People who use the bus have the option of purchasing a monthly coupon book for With the coupon​ book,

the fare is reduced to​ $0.50. How many times must someone use the bus so that the total monthly cost without the coupon book is the same as the total monthly cost with the coupon​ book? Express the total monthly cost to use the bus with a coupon​ book, f, as a function of the number of times in the month the bus is​ used, x. Then express the total monthly cost to use the bus without a coupon​ book, g, as a function of the number of times in the month the bus is​ used, x.
Mathematics
1 answer:
SashulF [63]3 years ago
7 0

Answer:

26 times

Step-by-step explanation:

The question has missing details. However, the given parameters are

Given

Without Coupon

Bus Fare = $2.00

With Coupon

Coupon = $39.00

Bus Fare = $0.50

Represent the number of fares with x

Without Coupon, cost of fares is

Cost = 2x

i.e.

f(x) = 2x

With Coupon, cost of fares is

Cost = 39 + 0.5x

i.e.

g(x) = 39 + 0.5x

To calculate when both fares will be equal, we must have:

f(x) = g(x)

2x = 39 + 0.5x

Collect like terms

2x - 0.5x = 39

1.5x = 39

Solve for x

x = 39/1.5

x = 26

This implies that, for both cost to be equal, the person must go 26 times

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Hannah and Anthony are siblings who have ages that are consecutive odd integers. The sum of their
dexar [7]

Answer:

2h-2=92 and h-2=92-h.

Step-by-step explanation:

Hannah, h, is the older sibling and their ages are consecutive odd integers. This means that Anthony's age will be 2 less than Hannah's, or h-2.

The sum of these would be h+(h-2), giving us the equation h+(h-2)=92.

 

Combining like terms we would have the first correct choice, 2h-2=92.

Our first equation can be transformed, however, to have (h-2) by itself. To do this, we would subtract h from both sides, giving us h-2=92-h.

5 0
3 years ago
A rectangular lot is 115 yards long and 70 yards wide give the length and width of another rectangle lot that has the same perim
s2008m [1.1K]

Answer:165 length 20 width

3 0
3 years ago
Given r(x) = 11/ (x - 42)
julsineya [31]

For a given function f(x) we define the domain restrictions as values of x that we can not use in our function. Also, for a function f(x) we define the inverse g(x) as a function such that:

g(f(x)) = x = f(g(x))

<u>The restriction is:</u>

x ≠ 4

<u>The inverse is:</u>

y = 4 + \sqrt{\frac{11}{x} }

Here our function is:

f(x) = \frac{11}{(x - 4)^2}

We know that we can not divide by zero, so the only restriction in this function will be the one that makes the denominator equal to zero.

(x - 4)^2 = 0

x - 4 = 0

x = 4

So the only value of x that we need to remove from the domain is x = 4.

To find the inverse we try with the general form:

g(x) = a + \sqrt{\frac{b}{x} }

Evaluating this in our function we get:

g(f(x)) = a + \sqrt{\frac{b}{f(x)} }  = a + \sqrt{\frac{b*(x - 4)^2}{11 }}\\\\g(f(x)) = a + \sqrt{\frac{b}{11 }}*(x - 4)

Remember that the thing above must be equal to x, so we get:

g(f(x)) = a + \sqrt{\frac{b}{11 }}*(x - 4) = x\\\\{\frac{b}{11 }} = 1\\{\frac{b}{11 }}*4 - a = 0

From the two above equations we find:

b = 11

a = 4

Thus the inverse equation is:

y = 4 + \sqrt{\frac{11}{x} }

If you want to learn more, you can read:

brainly.com/question/10300045

3 0
2 years ago
supposea,b,and c represent three postive whole numbers. if a+b=19, b+c=28, and a+c=25 what are the values of a, b, and c? solve
777dan777 [17]
Hello can you help me Solve each system of equations by GRAPHING. Clearly identify your solution.
(4x-y=3)
(3x+y=4)


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8 0
2 years ago
Please Help! will give Brainliest!
mixer [17]

1. The x-intercepts are x = 0 and x = 6. You can find these by looking for where the line crosses the x-axis. You can see here that it does so at 0 and 6.


2. The maximum value for this function is looking for the f(x) value at the highest point. In this case, you will see that f(x) at the highest point is 120. This happens at x = 3. Once again, this can be found just by looking for the highest point on the graph.


3. Since that is the absolute highest point, it is also the point where is goes from increasing to decreasing. As a result, we know the increasing interval is x<120 and the decreasing interval is x > 120.


4. Finally, the average rate of change between 3 and 5 is -30. You can find this by determining the amount of change in f(x) and dividing it by the amount of change in x. The basic formula is below.


\frac{new f(x) - old f(x)}{new x - old x}

\frac{60 - 120}{5 - 3}

\frac{-60}{2}

-30

6 0
3 years ago
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