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

12% of ___ shirts is 36 shirts

Answers

Answer: 3

Step-by-step explanation:

Answer:

300 shirts

Step-by-step explanation:

You can divide 12% by itself to find one percent, then divide the 36 shirts by 12 as well.

What you do to one side, you need to do to the other.

Now that we have our numbers after dividing (you should have 1% and 3 shirts) you can see what 100% would be. To do this you would multiply 1% by 100 and multiply 3 shirts by 100.

Now we know that 12% of 300 shirts is 36 shirts.

Sum of 5 and 9 less than 17

Answers

Answer:

15?

Step-by-step explanation:

Answer:

-3

Step-by-step explanation:

5+9=14

14-17=-3

Give the factors for the numerator [n] and denominator [d] after reducing.

Answers

Answer:

The factors for the numerator [n] and denominator [d] after reducing will be:

[tex]\frac{x^2-25}{x^2-4x}\div \:\frac{2x^2+2x-40}{x^3-x}=\frac{\left(x-5\right)\left(x+1\right)\left(x-1\right)}{2\left(x-4\right)^2}[/tex]

Step-by-step explanation:

Given the expression

[tex]\frac{x^2-25}{x^2-4x}\div \frac{2x^2+2x-40}{x^3-x}[/tex]

[tex]\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{a}{b}\div \frac{c}{d}=\frac{a}{b}\times \frac{d}{c}[/tex]

[tex]=\frac{x^2-25}{x^2-4x}\times \frac{x^3-x}{2x^2+2x-40}[/tex]

[tex]\mathrm{Multiply\:fractions}:\quad \frac{a}{b}\times \frac{c}{d}=\frac{a\:\times \:c}{b\:\times \:d}[/tex]

[tex]=\frac{\left(x^2-25\right)\left(x^3-x\right)}{\left(x^2-4x\right)\left(2x^2+2x-40\right)}[/tex]

[tex]=\frac{\left(x^2-25\right)x\left(x^2-1\right)}{\left(x^2-4x\right)\left(2x^2+2x-40\right)}[/tex]

[tex]\mathrm{Cancel\:the\:common\:factor:}\:x[/tex]

[tex]=\frac{\left(x^2-25\right)\left(x^2-1\right)}{2\left(x-4\right)\left(x^2+x-20\right)}[/tex]

∵ As factor  [tex]\left(x^2-25\right)\left(x^2-1\right)=\left(x+5\right)\left(x-5\right)\left(x+1\right)\left(x-1\right)[/tex]

so the expression becomes

[tex]=\frac{\left(x+5\right)\left(x-5\right)\left(x+1\right)\left(x-1\right)}{2\left(x-4\right)\left(x^2+x-20\right)}[/tex]

∵ As factor [tex]2\left(x-4\right)\left(x^2+x-20\right)=2\left(x-4\right)^2\left(x+5\right)[/tex]

so the expression becomes

[tex]=\frac{\left(x+5\right)\left(x-5\right)\left(x+1\right)\left(x-1\right)}{2\left(x-4\right)^2\left(x+5\right)}[/tex]

[tex]\mathrm{Cancel\:the\:common\:factor:}\:x+5[/tex]

[tex]=\frac{\left(x-5\right)\left(x+1\right)\left(x-1\right)}{2\left(x-4\right)^2}[/tex]

Therefore, the factors for the numerator [n] and denominator [d] after reducing will be:

[tex]\frac{x^2-25}{x^2-4x}\div \:\frac{2x^2+2x-40}{x^3-x}=\frac{\left(x-5\right)\left(x+1\right)\left(x-1\right)}{2\left(x-4\right)^2}[/tex]

what is the image of (6,-6) after a dilation by a scale factor of 4 centered at the origin

Answers

9514 1404 393

Answer:

  (24, -24)

Step-by-step explanation:

Dilation centered at the origin multiplies each coordinate by the dilation factor.

  image = 4 × (6, -6)

  image = (24, -24)

Armon has a prepaid cell phone. This month he will like to purchase a $9 message package. The rate plan for the talk time is $0.10 per minute. Write an inequality for the maximum amount of talk time that Armon can purchase for his bill to stay under $45.

Pls show step-by-step! :)

Answers

Equation formula: y = mx + b
0.10 per minute is the slope
9 would be the y intercept
Equation: 0.10x + 9 < 45

A single fair die is tossed. Find the odds in favor of rolling a number greater than 5

What are the odds in favor of rolling a number greater than 5?

Please help

Answers

Answer:

[tex]1 : 5\ or\ \frac{1}5[/tex]

Step-by-step explanation:

Given that:

A single fair die is tossed.

First of all, let us learn about a fair die.

A fair die is a 6 sided die numbered from 1, 2, 3, to 6 and each side has an equal probability of occurring OR we can say each side is equally likely to occur.

So, probability of rolling a number greater than 5 has only one possible outcome i.e. 6.

And total number of outcomes are 6.

So, probability of rolling a number greater than 5 = [tex]\frac{1}{6}[/tex]

Probability of not rolling a number greater than 5 = [tex]\frac{5}{6}[/tex]

Odds in favor of rolling a number greater than 5 = Probability of rolling a number greater than 5 : Probability of not rolling a number greater than 5

[tex]\dfrac{1}{6} :\dfrac{5}{6} = \bold{1:5}\ or\ \bold{\dfrac{1}{5}}[/tex]

Using the probability concept, the odds of rolling a number greater than 5 is 1 :5

The odd of a particular experiment is defined thus :

Number of possible outcomes greater than 5 : number of possible below or equal to 5

Sample space = {1, 2, 3, 4, 5, 6}

Outcomes greater than 5 = {6} = 1

Outcomes below or equal to 5 = {1, 2, 3, 4, 5} = 5

The odds equals to 1 : 5

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Counting up on a number line starting at 0 corresponds with what numbers

Answers

The number coryspimding is seventie

What is the value of a? Please solve this with the law of sine

Answers

Answer:

what chap is this

Step-by-step explanation:

Choose all the expressions that are equal to 0.7 × 0.41.
A. 7100×41100
B. 710×41100
C. 7100×4110
D. 710×4110
E. 70100×41100

Answers

Answer:

None of the expressions is equal to 0.7 x 0.41.

Step-by-step explanation:

Given that 0.7 x 0.41 is equal to 0.287, to determine which options are equal to said operation, the calculations set out for each of them must be performed:

A. 7,100 × 41100 = 291,810,000

B. 710 × 41100 = 29,181,000

C. 7100 × 4110 = 29,181,000

D. 710 × 4110 = 2,918,100

E. 70100 × 41100 = 2,918,100,000

Therefore, looking at all the results produced by the predisposed calculations, it is evident that none of the expressions is equal to 0.7 x 0.41.

There is no expression equivalent to the given expression and this can be determined by using the arithmetic operations.

Given :

Expression  --  0.7 × 0.41

The arithmetic operations can be used in order to evaluate the given expression.

[tex]0.7\times 0.41 = 0.287[/tex]

Now, check all the options in order to determine the correct option.

A) 7100×41100

Evaluate the above expression by using the arithmetic operations.

[tex]7100\times 41100 = 291810000[/tex]

Therefore, this option is incorrect.

B) 710×41100

Evaluate the above expression by using the arithmetic operations.

[tex]710\times 41100 = 29181000[/tex]

Therefore, this option is incorrect.

C) 7100×4110

Evaluate the above expression by using the arithmetic operations.

[tex]7100\times 4110 = 29181000[/tex]

Therefore, this option is incorrect.

D) 710×4110

Evaluate the above expression by using the arithmetic operations.

[tex]710\times 4110 = 2918100[/tex]

Therefore, this option is incorrect.

E) 70100×41100

Evaluate the above expression by using the arithmetic operations.

[tex]70100\times 41100 =2881110000[/tex]

Therefore, this option is incorrect.

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What is i2=-1 math test

Answers

Answer:

Your answer is: ↓

If your converting in Logarithmic Form then your answer is: [tex]log_{i}(-1)=2[/tex]

If you are trying to figure if that equation is determined T/F: The answer is T.

If you are trying to evaluate (expand) the question your answer is:[tex]-1=-1[/tex]

Step-by-step explanation:

Hope this helped : )

In a fruit basket there are 9 bananas 4 apples and 3 plums 1. The ration of bananas to apple is ________:_________. 2. The ration of plums to apples is __________to________. 3. For every __________apples, there are ______plums. 4. For every 3 bananas there is one _________.

Answers

Answer:

1. 9:4 2. 3:4 3. for every 4 apples there are 3 plums 4. plum

Step-by-step explanation:

1. there are 9 bananas and there are 4 apples.

2. there are 3 plums and there are 4 apples

3. there are 4 apples so there are 3 plums

4. 9 divided by 3 = 3. 3 divided by 3 = 1

A class has 48 minutes available to hear reports from 15 students. if the time is to be divided equally, how long may each student have?​

Answers

Answer:

No, every student will have 3.2 minutes

Answer:

Each student has approximately 3 minutes and 12 seconds.

Step-by-step explanation:

You divide the total amount of minutes by the total amount of students. 48/15=3.2

After you get your answer, you convert to minutes. There are 3 minutes and the .2 converts to 12 seconds

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 .

help please
3/11 × 4/9 =​

Answers

Answer:

4/33

Step-by-step explanation:

Multiply 3x4 across which equals 12

Multiply 11x9 across which equals 99

Simplify to equal 4/33

Hope this helps!! :)

Answer:

Exact Form:

433

Decimal Form:

0.¯¯12¯¯

Step-by-step explanation:

Where is the punctuation error in this sentence?

More people came to the meeting1 than had been expected. They were standing2 in the aisles3 in the hall,4 and on the front steps.

Answers

Answer:

That is that It is Most not More

Answer:

It is number 3

Step-by-step explanation:

What is 0.62x10 yo the power of 3

Answers

Answer:

62

Step-by-step explanation:

Answer:

238.328

Step-by-step explanation:

The product of 0.62 x 10 is 6.2. So, I did 6.2 to the power of 3, which is 238.328.

5 Carla packs 4 pairs of pants, 2 pairs of shorts, and 3 skirts for her vacation.
What is the ratio of skirts to pants? (1 point)
A 4:3
B 4:9
C 3:9
D 3:4
Curriculum Associates, LLC
SHOW YOUR WORK

Answers

Answer: 3:4
Explanation : there are 3 skirts and 4 pants. These numbers do not reduce down more so the ratio is 3:4

asia is a chef in a restaurant to prepare for dinner service she chopped 7 1/2 onions into 1/6 of an hour what is Asia's rate of chopping in onions per hour ​

Answers

We’re is the question that I can answer it for you? Can you please say the question

The measure of angel B is (3x - 4)º and the measure of angel D is (2x - 6)°. What are the measures of angles B and D?​

Answers

Answer:

b=110 d=70

Step-by-step explanation:

Answer:

110 70

Step-by-step explanation:

let f(x) = x^4 -4x^2 +3x find f(-3) a.-54 b.36 c.-126 d.108

Answers

Answer:

b. 36

Step-by-step explanation:

Evaluate x^4 - 4 x^2 + 3 x where x = -3:

x^4 - 4 x^2 + 3 x = (-3)^4 - 4×(-3)^2 - 3×3

Hint: | Evaluate (-3)^2.

(-3)^2 = 9:

(-3)^4 - 49 - 3×3

Hint: | Determine the sign of (-3)^4.

(-3)^4 = (-1)^4×3^4 = 1×3^4:

3^4 - 4×9 - 3×3

Hint: | Compute 3^4 by repeated squaring.

3^4 = (3^2)^2:

(3^2)^2 - 4×9 - 3×3

Hint: | Evaluate 3^2.

3^2 = 9:

9^2 - 4×9 - 3×3

Hint: | Evaluate 9^2.

9^2 = 81:

81 - 4×9 - 3×3

Hint: | Multiply -4 and 9 together.

-4×9 = -36:

81 + -36 - 3×3

Hint: | Multiply 3 and -3 together.

3 (-3) = -9:

81 - 36 + -9

Hint: | Group the negative terms in 81 - 36 - 9 together and factor out the minus sign.

81 - 36 - 9 = 81 - (36 + 9):

81 - (36 + 9)

Hint: | Evaluate 36 + 9 using long addition.

| 1 |  

| 3 | 6

+ | | 9

| 4 | 5:

81 - 45

Hint: | Subtract 45 from 81.

| 7 | 11

| 8 | 1

- | 4 | 5

| 3 | 6:

Answer: 36

What is the slope of the line?answer

Answers

Answer:

Whenever the equation of a line is written in the form y = mx + b, it is called the slope-intercept form of the equation. The m is the slope of the line. And b is the b in the point that is the y-intercept (0, b). For example, for the equation y = 3x – 7, the slope is 3, and the y-intercept is (0, −7).

Step-by-step explanation:

Answer:

The slope of the line is -2.

Step-by-step explanation:

Because the line is going down from left to right it is considered a negative slope. The rise is -2 and the run is 3, so the slope of the line in integer form is -2.

But, if it was in fraction form the slope would be -2/3.

Hope this helps! If you have any additional questions please don't hesitate to ask me or your teacher to be sure you master the subject. :) Stay safe and please mark brainliest!

An average pen manufactured by the F&M Corporation lasts 400 days with a standard deviation of 40 days.
Assuming that pen life is normally distributed, what is the probability that such a pen will last at least 440
days?

Answers

Answer:

The probability that the pen will last at least 440 days is 0.1587

Step-by-step explanation:

Given that

Mean = μ = 400 days

SD = σ = 40 days

Now we have to find the probability of a data point X = 440

For that first of all we have to find the z-score of the value

z-score is found using the formula

[tex]z-score = \frac{x-Mean}{SD}[/tex]

Putting the values of x, mean and SD we will get,

[tex]z = \frac{440-400}{40} = \frac{40}{40} = 1[/tex]

At least 440 means that either 440 or greater than this, hence, we have to find area to the right of z=1

For that

[tex]P(z<1) = 0.8413\\P(z>1) = 1-P(z<1) = 1-0.8413 = 0.1587[/tex]

Hence,

The probability that the pen will last at least 440 days is 0.1587

Consider the statement: "The president of the United States is a United States citizen."

Is the statement a grammatically correct sentence?

What is the subject of the sentence? What is the verb in the sentence?

Is the sentence true?

Answers

Yes this statement is grammatically correct , subject- president
Verb- is
And yes
The sentence should capitalize the word “President” because “President of the United States” is a complete title.

The subject is The President of the United States.

The verb in this sentence is “is”.

This sentence is true.

Which is the better buy?
7-pound bag of barley for $6.72
312-ounce bag of barley for $28.08

Answers

Answer:

7-pound bag of barley for $6.72 is a better buy.

Step-by-step explanation:

7-pound bag of barley for $6.72

6.72 : 7 = 0.96

check your work: 0.96 x 7 = 6.72

so for the first offer you will be paying $0.96 per pound

312-ounce bag of barley for $28.08

1 pound = 16 ounces

312 ounces = 19.5 pounds

28.08 : 19.5 = 1.44

for the second offer you will be paying $1.44 per pound of barley. 7-pound bag of barley for $6.72 is a better buy because you will be less for each pound.

hope this helps!

Answer:

7-pound bag of barley for $6.72

Step-by-step explanation:

A fairly good estimate for a long-term loan with a moderate or high interest rate is that the monthly payment is _____ as large as the principal times the monthly interest rate.

Answers

Answer:

at least

Step-by-step explanation:

A fairly good estimate for a long-term loan with a moderate or high interest rate is that the monthly payment is AT LEAST as large as the principal times the monthly interest rate.

The correct word that missing in the statement is at least.

Given that, a statment is given we have to determine which word is missing the statment.

What is the investment?

Investment is defined as when an individual spends money on something that returns him or her higher money than the money they or invest.

The monthly payment being at least equal to the principal multiplied by the monthly interest rate is a reasonable estimate for a long-term loan with a moderate or high-interest rate. So the correct statement is given as,
"A fairly good estimate for a long-term loan with a moderate or high-interest rate is that the monthly payment is at least as large as the principal times the monthly interest rate."

Thus, the correct word that missing in the statement is at least.

Learn more about investments here:

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Un ingeniero realiza las siguientes observaciones sobre las ventas de impresoras en una tienda: Hay impresoras Epson, Hp y Cannon. El número de impresoras Epson y HP es cinco veces el número de las Cannon. Además, el número de impresoras Epson es el triple que el de la Cannon y El total de impresoras Cannon y Hp asciende a 123​

Answers

Answer:

En la tienda hay 123 impresoras Epson, 82 impresoras HP y 41 impresoras Cannon.

Step-by-step explanation:

Para determinar el número de impresoras de cada marca, se deben plantear las siguientes ecuaciones:

E + HP = 5 x C

E = 3 x C

C + HP = 123

Así, teniendo en cuenta estas ecuaciones y los valores de cada marca dentro del stock de la tienda, se puede plantear la siguiente equivalencia:

Si E = 3C y E + HP = 5C, entonces HP = 2C, ya que 5C - 3C = 2C.

Entonces, las equivalencias son las siguientes:

E = 3C

HP = 2C

Si C + HP = 123, podríamos decir que 3C = 123. Por ello, dado que 123 / 3 es igual a 41, el número de impresoras Cannon asciende a 41 unidades.

A su vez, el número de impresoras HP es de 82 unidades (41 x 2), mientras que el número de impresoras Epson asciende a 123 unidades (41 x 3).

4(3x + 2) = 4(2x + 3) + 4x

Answers

Answer:

x = -4

Step-by-step explanation:

4(3x + 2) = 4(2x + 3) + 4x (distribute the 4's on both sides)

12x + 8 = 8x + 12 + 4x (collect like terms)

12x + 8 = 13x + 12 (subtract 12x on both sides)

8 = x + 12 (subtract 12 on both sides)

-4 = x

Hope this helps ya!

PLEASE YALL I need HELP ASAP PLEASE PLEASE PLEASE I WILL MARK YOU AS BRANLIEST IF CORRECT

White an equation in slope intercept form whose slope is 10 and y intercept is -3.

Answers

Answer:

y = 10x - 3

Step-by-step explanation:

Answer:

f(x)=10x+-3

f(x)=mx +b

m= slope

b= y intercept

Step-by-step explanation:

what is the slope (5,7) and (2,-2)​

Answers

Answer:

slope = 3

Step-by-step explanation:

to find the slope you do (y2-y1)/(x2-x1)=m

so we can plug the points into this formula

(5,7)     (2,-2)

x1 y1    x2 y2

-2-7/2-5=m

-9/-3=m

Simplifies to

3=m

May u please help me ill give out the brainly

Answers

Answer: The answer that I think is A

sry if wrong

It’s A your welcome
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