Question

Algebra 1 help!

Answer 1

Is my answer correct?

Answer 2

no

Answer 3

Can you help me? @dan815

Answer 4

I would suggest you find the equation of the lines representing g(x) and f(x) and then plot the desired x-value to be found.
You can also do it with the given facts.

Answer 5

f(x) = 2x + 1
g(x) = 4x + 1

Answer 6

Are those correct?

Answer 7

Not really, I would spot two points that belong to the function, let's say for instance, the root and the y-intercept of f(x): (-5/2, 0) and (0,5).
With this information, we can find the rate of change (slope) of our line:
\[m=\frac{ 5-0 }{0 -(-\frac{ 5 }{ 2 }) } \iff m=\frac{ 5 }{ \frac{ 5 }{ 2 } } \iff m=2\]
You got the rate of change correctly, but the y-intercept does not reflect the one in the diagram:
\[(y-5)=2(x-0) \iff y=2x +5 \]
Therefore:
\[f(x)=2x +5\]

Answer 8

The process is analogous for g(x) but since the rate of change is twice that of f(x) and the y-intercept is still the same, we can quickly deduce that \[g(x)=4x +5\]
Now it's just a matter of plotting "4" on the functions we found.

Answer 9

f(4) = 2(4) + 5
f(4) = 13

g(4) = 4(4) + 5
g(4) = 21

Answer 10

21 - 13 = 8

Answer 11

They're both lines, so we know: \[
f(x) = mx+b,\quad g(x)=m'x+b'
\]They also tell use that \(f\)'s slope is \(2\) and \(g\)'s slope is twice as big, and the graph tells use the intercepts are the same. This means: \[
f(x) = 2x+b,\quad g(x) = 4x+b
\]The question "How many units larger?" is basically asking for \(g(4)-f(4)\).\[
g(4)-f(4) = 4(4)+b - \bigg[2(4)+b)\bigg] = \ldots
\]

Answer 12

I think that my answer was correct? Wasn't it?

Answer 13

It is correct yes, but wio's method is quite interesting as well.

Answer 14

Thank you! Can you help me on a couple more? I just need you to check my work.

Answer 15

Sure thing.

Answer 16

Okay. Just give me a minute while I upload it.

Answer 17

I think you answered incorrectly, since we have t suppose that linearly the student will sustract 20% of the obtained money, giving us the rate of increase for the function (that starts at 500).
So, for every week, the function will increase 200 units.
For a second opinion, what does @wio think?

Answer 18

Well I made the table:

Answer 19

(0,500)
(1,600)
(2,680)
(3,744)

Answer 20

Well, yes, that is correct, but does the student continually sustract 20% as a succesion of events or does she just sustract the 20% for every week?.
I quote: "She will use the 20% of the money she earns every week as spending money".
This means that every week, she will sustract 50$ from her earnings, leaving her with 200$.
We suppose that she will linearly do this and the function f(x) will increase 200 for every x- value, these being the number of weeks.
This allows us to conclude that the function is a line and not a curve (curves involve some exponents).

Answer 21

will it be A?

Answer 22

That is correct, you see:
We aim to know the amount of weeks it will take for her to reach 1500$ so we aim to know the x-value that corresponds to that y-value.
Since her habit is linear, we have to conclude that the function will be linear (though not continous, but we skip that detail).

Answer 23

Thanks! Last problem!

Answer 24

A nonprofit organization is hosting a festival at a nearby city park. They are making a graph based on the following assumptions:
1. when the festival opens, there are no people at the park
2. the number of people that attend the festival increases during the first 3 hours after the festival opens and then begins to decrease
3. everyone must exit the park after 6 hours.
4. the maximum number of people at the park at one time is 900.

using your parabola, estimate the number of people at the park 4 hours after the festival opens.

Answer 25

not exactly accurate, but this is what i have got. i drew it better in graph paper. but my max point is (3,900)

Answer 26

Well ,then we have to begin translating the information into the function.

Answer 27

for the question of the estimate of the number of people into 4 hours, i thought it was 800 people.

Answer 28

i just need for you to check that. and i need to go right after because it's bedtime for me

Answer 29

Well, it is quite hard for me to predict just by eye, but we can use the information given to create a function that will allow us to predict formally what happens at x=4.

Answer 30

Let's take the two assumptions that there is nobody in the park at the beginning, this means that the parabola goes through the origin (0,0) and everyone has to leave after 6 hours, meaning that (6,0) is also a root for the functon we are facing.
So, putting this into the factor form of a parabola we obtain:
\[f(x)=k(x)(x-6) \iff f(x)=k(x^2-6x)\]
So far so good, but we have to know that the maximum is also a point belonging to the parabola, which is (3,900) so meaning we have to plot it on our function to know the "k" value:
\[f(3)=k(3^2-6(3)) \iff 900=k(9-18) \]
\[k=\frac{ 900 }{ (-9) }\]
\[k=-100\]
So our function will be represented by: \(f(x)=(-100)(x^2-6x) \iff f(x)=-100x^2+600x\)
And this last form will allow us to predict based on our assumptions how much people we can expect at time 4-hours, meaning f(4).
I'll leave the calculation of f(4) to you.