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.

Answers

Answer 1

Answer:

The average speed of the car is 90 km/h

Step-by-step explanation:

The rule of the distance id D = v × t, where

v is the speedt is the time

∵ A car can travel 450 km in the same time it takes a train to travel

   350 km

→ That means the time of them are equals

Time of the car = Time of the train

→ From the rule above t = [tex]\frac{D}{v}[/tex]

D(car) = 450 km and D(train) = 350 km

∵ The car's average speed is 20 km/h faster than the average speed

   of the train

→ Assume that the average speed of the train is x km/h

v(train) = x km/h and v(car) = (x + 20) km/h

→ Use the rule of the time above to find the time of each one

∵ t(car) = [tex]\frac{450}{(x+20)}[/tex]

∵ t(train) = [tex]\frac{350}{x}[/tex]

t(car) = t(train)

∴ [tex]\frac{450}{(x+20)}[/tex] =  [tex]\frac{350}{x}[/tex]

→ By using cross multiplication

450 × x = 350 × (x + 20)

∴ 450x = 350(x) + 350(20)

∴ 450x = 350x + 7000

→ Subtract 350x from both sides

∴ 100x = 7000

→ Divide both sides by 100 to find x

x = 70

∵ x represents the average speed of the train

The average speed of the train = 70 km/h

∵ The average speed of the car = x + 20

∴ The average speed of the car = 70 + 20

The average speed of the car = 90 km/h


Related Questions

1
A line has a slope of 5 and a y-intercept of -2

Answers

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

Combine like terms, showing one step per line. Justify each step using a rule of algebra or "Combining Like Terms." You may need to add extra rows. Expression Justification 7x + 3 + 9x + 15 Given 7x

Answers

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

Which of the following graphs shows the set of points that represents the number of hours that Leah
can work in order to earn at least $120 and not work more than 20 hours per month?

Answers

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 .

What are the coordinates of the image of triangle ABC after dilation with the center (0,0) and the scale factor of 3?

Answers

Answer:

1.5

Step-by-step explanation:

Hailey is going to use a computer at a Internet cafe. The cafe charges $1.50 for every minute using a computer on top of an initial charge of $4. Make a table of values and then write an equation for C, in terms of t, representing the total cost of using a computer for t minutes at the Internet cafe.

Answers

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.

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Find the slope of the line that passes through the points (–2, 4) and (5, 4).

Answers

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

Please help what is the answer

Answers

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

Complete each ordered pair so that it is a solution of the given linear equation.
x-3y = -2;( ,1). (-8, )

Answers

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).

I need help please : )

Answers

Answer:

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

Help please ;-; The values in the table represent a linear function.

x 1 2 3 4
f(x) −3 −1 1 3
What is the function rule?

Write the rule in function notation, using the slope-intercept form of a line.

Enter your answer in the box.

Answers

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]


Arizona iced tea is manufactured in a warehouse by machines that bottles
the iced tea bottles and puts the caps and labels on them. There is a
special machine that bottles iced tea so that every 8th bottle gets a green
label and every 6th bottle gets a pink cap.
What number bottle will be the first bottle to get a green label and a
pink cap?
On the 100th year Anniversary every 10th bottle got a special edition bottle
that has a gold band.
What number bottle will be the first to get a green label, a pink cap
and a special edit

Answers

Answer:

to get a green and pink it would be 24

i cant find find the special edit sorry

Step-by-step explanation:

what is the 101st term for the sequence 13, 9, 5, 1... ?

Answers

Step-by-step explanation:

a=13d=13-9=4

[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_n=a+(n-1)d [/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]

what is an equation of the line that passes through the points (-2,-7) and (-1,-3)

Answers

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

What is the domain of the relation [(x,y):y=x(x-3)/(x+4)(x-7)

Answers

Answer:

i think its b

Step-by-step explanation:

Suppose you and your colleagues have identified three reliable and recent polls. Looking at the results of all three, you find their p-values to be: 0.058 0.026 0.045 Barring any major incidents between now and election day, how much evidence do you have to predict your candidate will win the election

Answers

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.

Find the area of the circle

Answers

If d = 12 the r = 6

3.14 * 6^2
3.14 * 36
113.04

Given the cos(θ) = 5/13 the ratio for sine of θ is
. Enter your answer as a fraction.

Answers

12/13 is the answer for sure

helppppp help help helppppp help help thanks

Answers

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%

2. What number is equal to five units + three tenths? Circle the correct answer.
0.53
0.35
5.3
3.5
53
35

Answers

Answer:

35

Step-by-step explanation:

5*1+3*10

5+30 = 35

Which ordered pair would form a proportional relationship with the point graphed below?

(10.-20)
(-30, 20)
(-10,5)
(35, -20

Answers

The third option but can also be the first option, The would proportionate properly.

How can I figure out my screentime password.
100 points to whoever can tell me exactly how to do it and maybe even brainless if it works and it has to be an actual answer not just a random one!!!

Answers

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:

Use the distributive property to write an equivalent expression without parentheses.

9 (a + 8)

Check all that apply.
Distribute 9, by multiplication, to the variable, a, and to the constant, 8.
Write the two multiplications, 9(a) + 9(8)
The expression 9(a) is written as 9a.
The expression 9(8) equals 72.
The equivalent expression is 9a + 8.
The equivalent expression is 9a + 72.



100 points if anyone can give me the RIGHT answers to this question!

Answers

Answer:

all except e

Step-by-step explanation:

Answer:

all of them acept number 1

Step-by-step explanation:

i just want points

Find the product 822x9=

Answers

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. :)

HELLPPPP PLEASEEE!!

A pack of gum costs $1.49. It has 25 pieces in a pack. How much does it cost to chew each piece of gum?

Answers

Answer:

$0.05

Step-by-step explanation:

<3

Kendrick caught 22 rainbow trout and 18 tiger trout while fishing last month. What percent of the trout were tiger trout?

Answers

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.                                                                                                                                                            

What type of sequence do these figures belong?​

Answers

Answer:

what figures? pls share the picture of the figures

Step-by-step explanation:

How do you do this question?

Answers

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.

If Sally makes $7.25 / hour and works 40 hours plus 8 hours overtime what will she get paid?

Answers

Answer:

$348

Step-by-step explanation:

40 + 8 = 48 x 7.25 = 348

I NEED THE ANSWER QUICK

Answers

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]

Please help me!!!!!​

Answers

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:

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