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sasho [114]
2 years ago
14

To rent a certain meeting room, a college charges a reservation fee of $49 and an additional fee of $5.40 per hour. The chemistr

y club wants to spend less than $86.80 on renting the meeting room.
Mathematics
1 answer:
elena-14-01-66 [18.8K]2 years ago
6 0

Answer:

The maximum amount of money the chemistry club can spend without going over their buget is $81.4 ... With a total of 6 hours their allowed to use the room for.

Step-by-step explanation:

$49 is our constant and will not change. 5.40 however will. Let's use variable h for the amount hours they can rent the room for. Now we can make an inequality;

49+ 5.40h < 86.80

5.40h < 86.80

5.4h< 37.8

h< 7

Now that we know h will have to be less than seven for the chemistry club to spend less than their buget we can find that 6 is the maxium amount of hours they can spend in the room while staying within their budget.

(This answer does not consider decimals or half hours)

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PLEASE HELP THANK YOU!!!
Paul [167]

Answer:

Only C is a function

Step-by-step explanation:

To test whether a graph is a function you use the vertical line test.

If you can place a vertical line anywhere on the plane (in the domain of the "function" to be tested) and it intersects the curve at more than one point, the curve is not a function.

We see with A, wherever we put the vertical line it intersects twice.

With B, it intersects infinitely many times.

C is a function because wherever we put the vertical line, it only intersects once.

D is a function because it intersects twice providing we do not put it on the "tip" of the parabola.

The mathematical reasoning behind this is that a function must be well-defined, that is it must send every x-value to one specific y-value. There can be no confusion about where the function's input is going. If you look at graph B and I ask you what is f(3)? Is it 1? 2? 3? ... Who knows, it's not well-defined and so it's not a function. However if I ask you about C, whichever input value for x I give you, you can tell me to which y-value it gets mapped/sent to.

7 0
3 years ago
If d(x) = x2 - 7x - 7, find d(x - 1).​
satela [25.4K]

Answer: x^2-9x+1

Step-by-step explanation:

x^2-7x-7 d(x-1)

(you would just replace x to (x-1)

(x-1)^2-7(x-1)-7

(solve by square rooting (x-1)(x-1) then foil)

x^2-9x+1

7 0
3 years ago
What is the answer for 16 + b = a<br>​
Nitella [24]

Answer:

16

Step-by-step explanation:

i hope this helps

3 0
2 years ago
Part A: 180 = 4m + b B = 180 + 4m 325 = 9m + b 325 - 180 = 9m - 4m 5m = 145 m = 29 b = 180 + 4(29) = 64 y = 29x + 64
slavikrds [6]
I don't know ..,..................
5 0
2 years ago
How do you do this question?
ElenaW [278]

x*y' + y = 8x

y' + y/x = 8 .... divide everything by x

dy/dx + y/x = 8

dy/dx + (1/x)*y = 8

We have something in the form

y' + P(x)*y = Q(x)

which is a first order ODE

The integrating factor is u(x) = e^{\int P(x)dx} = e^{\int (1/x) dx} = e^{\ln(x)} = x

Multiply both sides by the integrating factor (x) and we get the following:

dy/dx + (1/x)*y = 8

x*dy/dx + x*(1/x)*y = x*8

x*dy/dx + y = 8x

y + x*dy/dx = 8x

Note the left hand side is the result of using the product rule on xy. We technically didn't need the integrating factor since we already had the original equation in this format, but I wanted to use it anyway (since other ODE problems may not be as simple).

Since (xy)' turns into y + x*dy/dx, and vice versa, this means

y + x*dy/dx = 8x turns into (xy)' = 8x

Integrating both sides with respect to x leads to

xy = 4x^2 + C

y = (4x^2 + C)/x

y = (4x^2)/x + C/x

y = 4x + Cx^(-1)

where C is a constant. In this case, C = -5 leads to a solution

y = 4x - 5x^(-1)

you can check this answer by deriving both sides with respect to x

dy/dx = 4 + 5x^(-2)

Then plugging this along with y = 4x - 5x^(-1) into the ODE given, and you should find it satisfies that equation.

6 0
3 years ago
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