Two cars leave at the same time from points A and B, the distance between them is 280 km. If the cars meet each other, they’ll meet in 2 hours. But if they go in the same direction, then the car going from point A will catch up with the car going from point B in 14 hours. What is the speed of both of the cars?

Answers

Answer 1

Set up the following equations:

[tex]2x + 2y = 280[/tex]

[tex]14x - 14y = 280[/tex]

x represents car A's speed, and y represents car B's speed.

We'll use elimination to solve this system of equations. Multiply the first equation by 7:

[tex](2x + 2y = 280) * 7 = 14x + 14y = 1960[/tex]

[tex]14x - 14y = 280[/tex]

Combine both equations:

[tex]28x = 2240[/tex]

Divide both sides by 28 to get x by itself:

[tex]x = 80[/tex]

The speed of car A is 80 mph.

Since we now know the value of one of the variables, we can plug it into the first equation:

[tex]2(80) + 2y = 280[/tex]

[tex]160 + 2y = 280[/tex]

Subtract 160 from both sides.

[tex]2y = 120[/tex]

Divide both sides by 2 to get y by itself:

[tex]y = 60[/tex]

The speed of car B is 60 mph.

Related Questions

Simplify the expression 6sqrt2/sqrt3

Answers

The answer would be 2√6 and in decimal form 4.898979, I hope this helps!

Hello!

First you factor the 6

[tex] \frac{2 * 3 \sqrt{2} }{ \sqrt{3} } [/tex]

Simplify

[tex]2 \sqrt{2} * \sqrt{3} [/tex]

Multiply the square roots

[tex]2 \sqrt{6} [/tex]

The answer is [tex]2 \sqrt{6} [/tex]

Hope this helps!

Sunny's garden has 9 tomato plants, 5 pepper plants, 3 squash plants, and 6 pumpkin plants. For every 3 tomato plants in Sunny's garden, there is 1 ____ plant.

Answers

9 total tomato plants / 3 plants = 3

from the list of plants there are 3 squash plants

3 squash plants x 3 tomato plants = 9 total tomato plants

the answer is Squash Plants

Answer: Squash plant is the right answer to fill the blank.

Step-by-step explanation:

Since we have given that

Number of tomato plants = 9

Number of pepper plants = 5

Number of squash plants = 3

Number of pumpkin plants = 6

Since the ratio of tomato plants to squash plants is 9 : 3 = 3 : 1.

So, for every 3 tomato plants in Sunny's garden, there is 1 squash plant.

Hence, Squash plant is the right answer to fill the blank.

A) suppose you will receive $200 in 16 years. how much money in year 6 is equivalent to this amount?

Answers

$200=16
simplify
200/16=12.5
12.5*6=75
Answer = 75

Find the area of the circle in terms of Pi

Answers

Let's start with the area of a circle formula: A = pi * r^2, where r is the radius. The radius is half the diameter. Since the diameter here is 6, the radius is 3. Now we can start solving!
1) A = pi* (3^2)
2) A = 9pi
The area in terms of pi is 9pi cm^2.
I got 9pi cm^2, but it is always helpful to double check work. Hope this helps!

The area of the circle: [tex]A=\pi r^2[/tex]

r - the radius

We have the diameter of the circle: d = 6cm.
d = 2r, therefore

2r = 6cm → r = 3cm

Substitute to the formula:

[tex]A=\pi\cdot3^2=9\pi\ cm^2[/tex]

How do I answer this dot plot?

Answers

It would seem the problem requires you compute the mean, median, and standard deviation of each of the data sets. This is nicely done using the statistics functions of your graphing calculator.

Data Set A (mean, median, standard deviation) = (29.7, 29.5, √12.71)
Data Set B (mean, median, standard deviation) = (27.95, 27, √6.1475)

1. False. Data Set B is skewed to the right.
2. TRUE. 27.95 is within 3 of 29.7.
3. False. √12.71 ≠ √6.1475
4. False. The mean of Data Set A is 29.7.
5. False. Data Set A has the higher standard deviation.
6. TRUE. 29.7 is close to 29.5.

The true statements are
• the 2nd one
• the 6th one

The scores on a university examination are normally distributed with a mean of 62 and a standard deviation of 11. if the bottom 5% of students will fail the course, what is the lowest mark that a student can have and still be awarded a passing grade? give the answer that is closest to the exact number.

Answers

The lowest score will be obtained as follows:
the z-score is given by:
z=(x-μ)/σ
where:
σ-standard deviation
μ- mean

we are required to evaluate for x, given that P(x<X)=0.05
The value of z that corresponds to 5% will be:
z=-1.65
thus plugging our values we obtain:
-1.65=(x-62)/11
solving for x we get:
-18.15=x-62
thus
x=-18.15+62
x=43.85
x~44
Thus the lowest score is 44

The lowest marks that a student can have and still be awarded a passing grade is 44.

Step-by-step explanation:

Given :

Mean, [tex]\mu = 62[/tex]

Standard Deviation, [tex]\sigma = 11[/tex]

Calculation :

z score is given by,

[tex]z = \dfrac{x-\mu }{\sigma}[/tex] ----- (1)

Value of z corresponds to 5% is,

[tex]z =-1.65[/tex]

from equation (1) we get,

[tex]-1.65=\dfrac{x-62}{11}[/tex]

[tex]x=43.85[/tex]

[tex]\rm x = 44 \;\;(Approx)[/tex]

The lowest marks that a student can have and still be awarded a passing grade is 44.

For more information, refer the link given below

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The dot plot shows the number of goals that the Springlane High School soccer team scored per game last season. How many games did the team play?

Answers

Answer:

Step-by-step explanation:

it shows 16 dots but it keeps saying i get it wrong

Answer:

Step-by-step explanation:

Plato ( just put 16 nothing extra “

On the assembly line it takes 2 ½ minutes to complete task one, 3 minutes 10 seconds to complete task two and 1 minute to complete the last task to make an item.How many items can be completed in 25 minutes?

Answers

Task 1 ----- [tex]2 \frac{1}{2} [/tex]minutes
Task 2 ----- 3 min 10 sec = 3+10/60 = [tex] 3\frac{1}{6} [/tex] minutes
Task 3 ----- 1 min
Total time to make 1 item = [tex]2 \frac{1}{2} [/tex] + [tex]3 \frac{1}{6} [/tex] +1 = [tex]6 \frac{2}{3} [/tex]minutes

In 25 minutes;

Number of items made = 25/(6 2/3) = 3.75 items = 3 items (since only a fully assembly can be regarded as an item).

Given: ΔSTQ, ST = TQ
Line SD is perpendicular to TQ
m∠1=32°
Find: m∠S, m∠T, m∠Q

Answers

Answer: m∠S = 58 ° ; m∠T = 64 ° ;  m∠Q = 58 ° .
__________________________________________________________

Explanation:
__________________________________________________________

To find "m∠Q" :

Consider the triangle formed by ∠D , ∠1, and ∠Q ;

Given m∠1 = 32° ;

and m∠D = 90° (a "right triangle" ; as shown in "image attached" ;

and by definition, all triangles have 3 angles and 3 sides; and all 3 angles of a triangle add up to 180° ;

→ m∠Q =  180 − (90 + 32) = 180 − 122 = 58 ;
_______________________________________________________

Since this is an "isosceles triangle" ;

→ m∠S = m∠Q = 58° .

Since all angles of any triangle add up to " 180° " ;

→ m∠T = 180 − (58 + 58) = 180 − 116 = 64 ;
____________________________________________

Answer: m∠S = 58 ° ; m∠T = 64 ° ;  m∠Q = 58 ° .
____________________________________________

Answer:

s=58 degrees, Q=58 degrees, T=64 degrees

Step-by-step explanation:

Consider the triangle formed by ∠D , ∠1, and ∠Q ;

Given m∠1 = 32° ;

and m∠D = 90° (a "right triangle" ; as shown in "image attached" ;

and by definition, all triangles have 3 angles and 3 sides; and all 3 angles of a triangle add up to 180° ;

→ m∠Q = 180 − (90 + 32) = 180 − 122 = 58

"suppose that it is decided to reject the null hypothesis if the sample mean time lag is less than 18.5 days. what is the probability of type i error if the population mean time lag is 20 days?"

Answers

answer : 17
.......... .

Answer:

Step-by-step explanation:

The product of two consecutive even integers is 120. Find the interfere

Answers

the correct question is
The product of two consecutive even integers is 120. Find the integers

let
x-----------> first even integer
x+2-------> second consecutive even integer

we know that
x*(x+2)=120-------> x²+2x-120=0

using a graph tool----> to resolve the second order equation
see the attached figure

the solution is
x=10

therefore
first even integer is 10
second consecutive even integer is (10+2)----> 12

the answer is
10 and 12

20 POINTS!!!

a point is translated 2 units to the right and five units down on the coordinate plane, how will this affect the x- and y- coordinates of the point?

Answers

Let x start out as x
Let y start out as y

The original point is (x , y)
Start with moving the x 2 units to the right.
To the right means going more positive.
x would become x + 2

down means the value is going in the minus y direction you are subtracting 5 from the original y
y - 5 is what you get.

The answer is
(x + 2, y - 5) <<<<<< answer

hey can you please help me posted picture of question

Answers

The statement is False,

The function and its inverse are reflected about the line y=x. This means that the x and y values are replaced.

So, if a function has a point (2,3) the same point on its inverse will moved be (3,2). This happens for all the points.

Therefore, the statement is false.

Please help !!!!!!!!

Answers

f(x) = 1/2x +4
replace f(x) with y
y = 1/2x+4

switch x and y
x = 1/2y +4

solve for y

multiply both sides by 2
2x = y+8

subtract 8 from both sides
2x-8 = y

rewrite with y on the left side: y = 2x-8

replace y with f(x)^-1 (inverse notation)
f(x)^-1 = 2x-8

solve for f^-1(4)
replace x with 4 in the equation and solve:
2(4) -8 = 8-8 = 0

hello can you please help me posted picture of question

Answers

There are 4 seats in total.

There are 4 ways to fill 1st seat.
When 1st seat is filled, there will be 3 ways to fill the second seat.
Similarly there will be 2 ways to fill the third seat and 1 way to fill the last seat.

So, total number of ways the seats can be filled = 4 x 3 x 2 x 1 = 24 ways.

Therefore, the correct answer is option A

1. Ten slips of paper labeled from 1 to 10 are placed in a hat. The first slip of paper is NOT replaced before selecting the second slip of paper. What is the probability of selecting and odd number and then a number greater than 9? 1/2 1/18 6/10 3/25

2. The probability of drawing two white cards without replacement is 14/95, and the probability of drawing one white card is 2/5. What is the probability of drawing a second white card, given that the first card is white? 52/95 7/19 7/38 28/475

3. Kim rolls a 6-sided number cube. What is the probability she rolls a number greater than 3 or a 1? 2/3 1/2 1/12 1/3

Answers

1. If we get an odd number first (probability 5/10 = 1/2), then the only way to get a number greater than 9 is the 10 (probability 1/9, since only 9 papers remain). This gives 1/2 * 1/9 = 1/18.

2. We would expect that P(2 white cards) = P(1 white card)*P(2nd white card given 1 white card).This gives the equation 14/95 = 2/5 * x
Solving for x gives x = 7/19.

3. There are a total of 4 favorable results: 1, 4, 5, 6. Out of the 6 possibilities, this is a probability of 4/6 = 2/3.

List two school activities that u do in the morning time and afternoon time.write time for these two activities

Answers

1. I complete some of my cyber: 7:00am to 10:00am

2. I spend time doing assignments in votech: 12:00pm to 2:30pm

- arrive at school at 7:00
- go to class at 7:05

-leave class at 3:15
-do homework for 45 minutes
-debate club in the afternoon at 4:00

Mason earns $70,000 per year and puts 7% of his earnings into a savings account. What is the total amount in Mason's account after 1 year if the interest rate is 3%?
A. $147
B. $72,100
C. $5,047
D. $2,100

Answers

The answer is B. $5,047.

Annual income of Mason is 70,000 dollars.

He saves 7% of his annual earnings into a saving account.

So, his savings would be 7% of 70,000 = 0.07 x 70,000 = 4,900 dollars.

The saving account gives an interest rate of 3% per annum.

So the interest accrued on 4900 dollars over the year would be 3% of 4,900 = 0.03 x 4,900 = 147 dollars.

Total amount in the saving account would be sum of principal amount and interest accrued.

Total balance = principal amount + interest accrued.

Total balance = 4900 + 147 = 5,047 dollars.

Hence, option C is correct i.e. 5,047 dollars.

Factor the Following Expression using the greatest common monomial factor. (x^p+2)(y^p+2) + (x^p+2)(y^p-1) + (x^p+1)(y^p+1) + (x^p+1)(y^p-1)

Answers

As written, there is no common monomial factor. We assume you intend to factor ...
[tex]x^{p+2}y^{p+2}+x^{p+2}y^{p-1}+x^{p+1}y^{p+1}+x^{p+1}y^{p-1}\\\\=(x^{p+1}y^{p-1})(xy^{3}+x+y^{2}+1)[/tex]

John's monthly salary is 7,000. If John deposits 0.75 of his paycheck into a savings account. How much money does he put in his savings account every month?

Answers

John deposits $5,250 into his savings account every month, which is 75% of his monthly salary.

The student's question is about how much money John deposits into his savings account from his monthly salary. To solve this, we calculate 0.75 (or 75%) of John's monthly salary of 7,000.

Calculation: 0.75 imes 7,000 = 5,250

So, John deposits $5,250 into his savings account every month.

You are laying an asphalt driveway. How much area must you cover if the driveway is 21 feet long and 10.5 feet wide?

Answers

we know that

An asphalt driveway has the shape of a rectangle
so
area of rectangle=long*wide
area=21*10.5-----> 220.5 ft²

the answer is
220.5 ft²

The pyramid shown has a square base that is 14 centimeters on each side. The slant height is 15 centimeters. What is the surface area of the pyramid?

Answers

we know that

[surface area of the pyramid]=area of the base+4*[area of one lateral triangle]
area of the base=14*14------> 196 cm²

area of one lateral triangle=b*h/2
b is the length side of the square
b=14 cm
h is the slant height
h=15 cm
area of one lateral triangle=14*15/2-----> 105 cm²

[surface area of the pyramid]=196 cm²+4*[105 cm²]-----> 616 cm²

the answer is
616 cm²

Jaimie purchased a condo at naples Florida for 699000. She put 20 % down and financed the rest at 5% for 35 yrs what are Jaime total finance charges

Answers

Asked and answered elsewhere.
https://brainly.com/question/10177253

Finance charges are about $626,128.20.

T-Shirts R Us advertises shirts as shown below. mc002-1.jpg Which quantities in the advertisement represent a unit rate?

Answers

Answer:

C.) $10 per shirt

Step-by-step explanation:

have a nice day

The option C is more simplified answer for given condition, unit rate is $10.

What is unit rate?

When comparing two different kinds of numbers with distinct units, a rate is a ratio that is employed. The unit rate, on the other hand, shows how many units of one quantity are equal to one unit of another. When the rate's denominator is 1, we refer to the rate as a unit rate.

Given

There are 5 shirts in the image given to us composed of 3 white shirts and 2 black shirts.

A rate with 1 as its denominator is known as a unit rate.

Option A: A ratio of 3:2 or a fraction of 3/2 is indicated by 3 white shirts and 2 white black shirts.

The denominator is not 1, hence this cannot be a unit rate.

Option B: 5 white shirts to 2 black shirts. This cannot be a unit rate because the fraction 2/5 will not have 1 as the denominator.

Choice C: $10 for each shirt. Because it represents a ratio of 10:1 or a fraction of 10/1, this rate is a unit rate. Therefore, the price of 5 shirts will be $50.

D: $50 for each shirt. Because option C has provided us with a more straightforward sum of $10, which we must accept as we are dealing with unit rates, this would not be a unit rate in this question.

Hence Option C is most suitable answer.

Learn more about unit rate;

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The complete question is in image.

the dump truck weighs 18 tons when filled. at the same time the dump truck is being filled, an identical truck filled to capacity is being emptied at a rate of 1/8 ton per minute. how much sad is in each dump truck when the trucks are the same weight

Answers

2.25 tons would be without sand

Answer:2 .25 Tons

Step-by-step explanation:

Weight of truck + sand when filled= 18 tons

Discharge rate per minute= 1/8 tons/ minute

Quantity of sand in the truck will be:

1/8tons per minute×18tons = 9/4 = 2.25tons

G a family has five children. if it is just as likely to have a boy as a girl, what is the probability that 3 of the children are girls and 2 are boys?

Answers

there is a 3/5 or 60% probability that there will be 3 girls and a 2/5 or 40% probability that there will be boys

Simplify 5(7y+2) can someone help me with the steps on how to simplify this problem and answer as an expression

Answers

5(7y + 2)

Distribute (multiply) the 2 to the numbers in the parentheses.

35y + 10

Eya is 7 less than threee times bills age.if eya is 17 how old is bill

Answers

(17+7)(3)=x (bills age)
24(3)=x
x=72
bill is 72

Hello!

We do the opposite than what is says in the problem

Eya is 7 less than three times bills age

We add 7 to Eya age

17 + 7 = 24

It says three times bills age so we divide by 3

24 / 3 = 8

Bill is 8

Hope this helps!

Solve the system of equations. -6y+11x = -36
-4y+7x=-24 −6y+11x=−36 −4y+7x=−24 x= y=

Answers

If you divide the first equation by -6 and the second by -4, you have ...
y -(11/6)x = 6
y -(7/4)x = 6
Subtracting one of these from the other tells you x=0, so you know immediately that y=6.

The solution is ...
x = 0
y = 6

The solution to the system of equations is:

x = 0

y = 6

To solve the system of equations:

-6y + 11x = -36

-4y + 7x = -24

You can use the method of substitution or elimination. I'll use the elimination method here.

First, multiply the second equation by 3 to make the coefficients of y in both equations equal:

-6y + 11x = -36

-12y + 21x = -72

Now, you can subtract the first equation from the second equation to eliminate x:

(-12y + 21x) - (-6y + 11x) = (-72) - (-36)

Simplify:

-12y + 21x + 6y - 11x = -72 + 36

Combine like terms:

-6y + 10x = -36

Now, divide both sides by 2 to simplify:

(-6y + 10x) / 2 = (-36) / 2

-3y + 5x = -18

Now you have a simplified system of equations:

-6y + 11x = -36

-3y + 5x = -18

You can solve this system using either the substitution or elimination method. Let's use the elimination method again. Multiply the second equation by 2 to make the coefficients of x equal:

-6y + 11x = -36

-6y + 10x = -36

Now, subtract the first equation from the second equation:

(-6y + 10x) - (-6y + 11x) = (-36) - (-36)

Simplify:

-6y + 10x + 6y - 11x = -36 + 36

Combine like terms:

-1x = 0

Now, solve for x:

x = 0

Now that you know the value of x, you can substitute it into one of the original equations to find the value of y. Let's use the first equation:

-6y + 11x = -36

-6y + 11(0) = -36

Simplify:

-6y = -36

Now, solve for y:

y = (-36) / (-6)

y = 6

for such more question on system of equations

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Can someone tell me if I got this answer correct? If not, what is the correct answer?

Answers

replace x with the given value and solve each:

A) 9^2 *9-2 = 81 * 7 =567

B) 2^2 * 2-2 = 4 *0 = 0

C) 4^2 * 4-2 = 16 * 2 = 32

D) 2-2 *2^2 = 0*4 = 0

the correct answer is D

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