Equations and Graphs of Rational Functions Precalculus 12

A car can travel 450 km in the same time it takes a train to travel 350 km. The car's average speed is 20 km/h faster than the average speed of the train. What is the average speed of the car? Give your answer to two decimal places.

I would just like help with figuring out the right equation for this word problem, because I cannot figure this out.

Answer:

The function rule in slope-intercept form is:

[tex]y = \frac{1}{2}x-\frac{7}{2}[/tex]

Step-by-step explanation:

The slope-intercept form of a function is given as:

[tex]y = mx+b[/tex]

Here

m is the rate of change of function and b is the y-intercept

The rate of change is calculated as:

[tex]m = \frac{difference\ in\ y}{difference\ in\ x}[/tex]

For this, any two pairs of input and output can be taken.

So using the pairs (1,-3) and (2,-1)

[tex]m=\frac{2-1}{-1+3}\\=\frac{1}{2}[/tex]

Putting the value of slope in slope-intercept form

[tex]y = \frac{1}{2}x+b[/tex]

Putting (1,-3) in the equation

[tex]-3 = \frac{1}{2}(1)+b\\-3 = \frac{1}{2}+b\\b = -3-\frac{1}{2}\\b = \frac{-6-1}{2}\\b= \frac{-7}{2}[/tex]

Putting the value of b

[tex]y = \frac{1}{2}x-\frac{7}{2}[/tex]

Hence,

The function rule in slope-intercept form is:

[tex]y = \frac{1}{2}x-\frac{7}{2}[/tex]

Answer:

(a) >, decreasing

(b) 0, horizontal

Step-by-step explanation:

(a) dy/dt = eᵗ (y − 1)²

eᵗ is always positive, and (y − 1)² is always positive.  So dy/dt is always positive.  Meaning the graph of the solution can never be decreasing.

(b) When y = 1, dy/dt = e¹ (1 − 1)² = 0.  However, this graph does not have a horizontal tangent line at y=1, so this is not the solution of the differential equation.

Answer:

I think it’s A,C, and E

Step-by-step explanation:

I’m not for sure but if you plot those points in the shaded region for graph C, those should be correct .

Answer:

1

Step-by-step explanation:

Answer:

(2/5,0)

Step-by-step explanation:

The equation to find a line is mx+b=y. In this case m is 5, and b is -2.

5x+-2=y

Since we want to find the x-intercept, y has to be 0.

So: 5x+-2=0

5x=2

x=2/5

Answer:

what figures? pls share the picture of the figures

Step-by-step explanation:

Answer:

7398

Step-by-step explanation:

Answer:

7398

I mean, this is the answer. You COULD just use a calculator, but here.

Glad I can help. :)

9514 1404 393

Answer:

  4^0

Step-by-step explanation:

The rules of exponents are ...

  (a^b)(a^c) = a^(b+c)

  (a^b)/(a^c) = a^(b-c)

So, your expression simplifies to ...

  [tex]4^5\times4^{-7}\div4^{-2}=4^{5-7-(-2)}=\boxed{4^0}[/tex]

Answer:

all except e

Step-by-step explanation:

Answer:

all of them acept number 1

Step-by-step explanation:

i just want points

Answer:

i think the answer is 10x^3-12^2-198x-40

Answer:

slope is 0

Step-by-step explanation:

Answer:

slope is 0

Step-by-step explanation:

I used another app to find the awnser for you

Answer:

y=4x+1

Step-by-step explanation:

First you need to solve for slope using the equation:

y2-y1/x2-x1

It doesn't matter what point is 1 or what point is 2. Lets just say that (-2,-7) is point 1, and (-1,-3) is point 2.

(-3)-(-7)/(-1)-(-2)=-4/-1=4

Next you find the y-intercept. To do this you can plug in plug in everything we know into the equation: y=mx+b, and solve for b.

(Lets use point one)

-7=4(-2)+b

-7=--8+b

1=b

Last we can put it all together.

y=4x+1

Answer:

7^12=13,841,287,201

Step-by-step explanation:

when you are putting a  power to a power, you just multiply the powers by each other

Answer:

7^12

Step-by-step explanation:

(7^6)^2

7^12

Answer:

35

Step-by-step explanation:

5*1+3*10

5+30 = 35

Step-by-step explanation:

[tex]{:}\longrightarrow[/tex][tex]\sf S_n={\dfrac {n}{2}}\left [2a-(a-1)d\right][/tex]

[tex]{:}\longrightarrow[/tex][tex]\sf S_101={\dfrac {101}{2}}\left [26 (12)4\right] [/tex]

[tex]{:}\longrightarrow[/tex][tex]\sf 50.5×1248 [/tex]

[tex]{:}\longrightarrow[/tex][tex]\sf S_101=63504[/tex]

[tex]{:}\longrightarrow[/tex][tex]\sf a_101=13+(101-1)-4 [/tex]

[tex]{:}\longrightarrow[/tex][tex]\sf a_101=13+100(-4)[/tex]

[tex]{:}\longrightarrow[/tex][tex]\sf 13-400 [/tex]

[tex]{:}\longrightarrow[/tex][tex]\sf a_101=-387 [/tex]

Answer:

to get a green and pink it would be 24

i cant find find the special edit sorry

Step-by-step explanation:

Answer:

60 percent

Step-by-step explanation:

Answer:

60% are roses

Step-by-step explanation:

1. Add all the numbers together to find the total

15+6+4= 25 total flowers

2. Put the total as the denominator, and the rose count as the numerator since we are trying to find what percentage are roses

15/25

3. Simplify fraction

15/25= 3/5

4. Divide numerator by denominator

300/5

5. Simplify

300/5= 60%

Answer:

$0.05

Step-by-step explanation:

<3

Answer: (1, 1), (-8, -2)

Step-by-step explanation:

Let’s start with the first solution: ( , 1)

We know that the y-coordinate for this solution is 1, so we can plug that in to find the x-coordinate.

x - 3y = -2

x - 3(1) = -2

x - 3 = -2

x = -2 + 3

x = 1

Therefore, for this solution x = 1, so our final solution is (1, 1).

Now let’s work on the second solution: (-8, ).

We know that the x-coordinate for this solution is -8, so we can plug that in.

x - 3y = -2

-8 - 3y = -2

-3y = -2 + 8

-3y = 6

y = -2

Therefore, for this solution y = -2, so our final solution (-8, -2).

Answer:

The answer is A.

Step-by-step explanation:

The ratio is 1 second/2 centimeters, but since they're asking for a unit ratio, you need to divide the top and bottom by 2 which gives you a unit ratio of ½ second/1 centimeter.

Answer:

Perhaps, B or A

Step-by-step explanation:

Answer:81%

Step-by-step explanation:

Answer:

60% tiger trout

Step-by-step explanation:

First, do 22+18=  40

Then, when doing % its always out of 100. So, 100 - 40= 60%

Which means, there were 60% Tiger trout.                                                                                                                                                            

Answer:

1.5

Step-by-step explanation:

Answer:

$348

Step-by-step explanation:

40 + 8 = 48 x 7.25 = 348

Answer:

Screen record as your parent puts the password in or wipe off your screen and give the parent your phone to put the password in then look at the fingerprint circles and that where each number is, then try all the possible combinations

Step-by-step explanation:

Answer:

The answer is "Pretty confident our candidate will win".

Step-by-step explanation:

All the following theories:  

[tex]H_o[/tex]: The loss of our candidate  

[tex]H_a[/tex]: Our candidate  

P values of 0.058, 0.026 and 0.045 are defined.  

All values are below 0.10, but 2 of them will be below 0.05, which indicates very good proof of Ha.  Therefore, the right reply is that our candidate will win very comfortably.

Answer:

The equation is C(t) = 1.50t + 4.00 and the data table is below.

Step-by-step explanation:

We are given that a cafe charges $1.50 for every minute that someone uses the internet. The cafe also charges an initial $4 fee to use the internet.

We need to find a function, in terms of t, that will find these values.

We can treat this as a linear equation. If we initially pay $4, this is acquired before we pay the fee every minute. Therefore, this would be our y-intercept at x = 0. Our first coordinate is (0, 4).

Secondly, if we are charged every minute, this would be a recurring payment and therefore we would spend $1.50 after each minute elapses. This gives us our slope: 1.50 or [tex]\frac{3}{2}[/tex].

Therefore, we can set up our function.

C is the total cost and t is the time, in minutes, that internet is used at the cafe. Our equation can be set up as [tex]C(t) = 1.50t + 4.00[/tex].

Now, we can create a table of values for t = 0 to t = 5 to determine what C(t) is at each of these prime intervals.

[tex]\begin{array}{|c|c|} \cline{1-2} \textbf{C} & \textbf{t} \\ \cline{1-2} a & 0 \\ \cline{1-2} b & 1 \\ \cline{1-2} c & 2 \\ \cline{1-2} d & 3 \\ \cline{1-2} e & 4 \\ \cline{1-2} f & 5 \\ \cline{1-2} \end{array}[/tex]

This is what our table looks like, but we need to fill the C column. Therefore, we can use substitution of our t-values into the equation and solve for C.

[tex]\bullet \ \text{For t = 0,}[/tex]

[tex]C(0) = 1.50(0) + 4\\\\C(0) = 0 + 4\\\\C(0) = 4.00[/tex]

[tex]\bullet \ \text{For t = 1,}[/tex]

[tex]C(1) = 1.50(1) +4\\\\C(1) = 1.50 + 4\\\\C(1) = 5.50[/tex]

[tex]\bullet \ \text{For t = 2,}[/tex]

[tex]C(2) = 1.50(2) + 4\\\\C(2) = 3.00 + 4\\\\C(2) = 7.00[/tex]

[tex]\bullet \ \text{For t = 3,}[/tex]

[tex]C(3) = 1.50(3) + 4\\\\C(3) = 4.50 + 4\\\\C(3) = 8.50[/tex]

[tex]\bullet \ \text{For t = 4,}[/tex]

[tex]C(4) = 1.50(4) + 4\\\\C(4) = 6.00 + 4\\\\C(4) = 10.00[/tex]

[tex]\bullet \ \text{For t = 5,}[/tex]

[tex]C(5) = 1.50(5) + 4\\\\C(5) = 7.50 + 4\\\\C(5) = 11.50[/tex]

Now, we can insert these values into our table.

[tex]\begin{array}{|c|c|} \cline{1-2} \textbf{C} & \textbf{t} \\ \cline{1-2} 4.00 & 0 \\ \cline{1-2} 5.50 & 1 \\ \cline{1-2} 7.00 & 2 \\ \cline{1-2} 8.50 & 3 \\ \cline{1-2} 10.00 & 4 \\ \cline{1-2} 11.50 & 5 \\ \cline{1-2} \end{array}[/tex]

Therefore, our equation is C(t) = 1.50t + 4.00 and our data table is above.

Answer:

By combining like terms, we have 16x + 18

Step-by-step explanation:

Here, we want to combine like terms

we simply bring terms that are similar together in this case

Thus, we have

7x + 9x + 3 + 15

16x + 18

Answer:

i think its b

Step-by-step explanation: