Two trains leave the same station at the same time but are headed in opposite directions. One train travels at 80 mph and the other train travels at 65 mph. How much time passes until the trains are 580 miles apart?

a: 4 hours
b : 6.4 hours
c: 7.7 hours
d: 8 hours
e: 38.7 hours

The equation of the plane that goes through these points is:

6x + 2y + z = 10.

The equation of the plane is found replacing the points into the following equation:

ax + by + c = z.

For point A, we have that:

3b + c = 4.

For point B, we have that:

a + 2b + c = 0.

For point C, we have that:

-a + 6b + c = 4.

Hence the system is:

From the first equation, we have that:

c = 4 - 3b.

Replacing in the second, we have that:

a + 2b + 4 - 3b = 0

a - b = -4.

Replacing in the third, we have that:

-a + 6b + 4 - 3b = 4.

-a + 3b = 0.

a = 3b.

We have that a - b = -4, hence:

3b - b = -4

2b = -4

b = -2.

a = 3b, hence a = -6.

c = 4 - 3b -> c = 10.

Hence the equation is:

ax + by + c = z.

z = -6x - 2y + 10

6x + 2y + z = 10.

More can be learned about the equation of a plane at https://brainly.com/question/13854649

#SPJ1

The possible graph for two points have the same y-coordinate but opposite x-coordinates is shown below.

In a general point (x,y) , the value x represents the distance from origin to point along x - axis,

and

the value y represents the distance from origin to point along y axis.

It is given in the question that

There are two points in which the y coordinate of both the points is same

the x coordinate is of opposite signs.

Let us take an Example  

let the points be A(a,b) and B(c,d)

According to the question

b = d and -a = c

So the points will become (a,b) and (-a,b)

For Example ;

let a=2, b=3

the two points will become (2,3) and (-2,3).

Therefore , the possible graph of these points is shown below .

Learn more about Graphs here https://brainly.com/question/4619801

#SPJ1

The following issues have the following needed probabilities: 1.) 1 / 3 2.) 1 / 5, and 3.) 1 / 4.

Here,

Four red marbles, five yellow marbles, three green marbles, and three blue marbles make up a jar.

There are 15 marbles in all.

1) Chance that the result exclusively includes green and/or blue marbles,

= 2 / 6 = 1 / 3

2.) Chance that the result solely contains green marbles

= 3 / 15 = 1 / 5

3.) the likelihood that there won't be any green marbles in the result,

= 3 / 12 = 1 / 4

As a result, the needed probability for the following issues is given: 1.) 1 / 3. 2.) 1 / 5, and 3.) 1 / 4.

Here is additional information about probability:

brainly.com/question/14290572

#SPJ1

Answer:

the answer would be 5a+2b-10

Answer:

14/15

Step-by-step explanation:

Answer:

your right

Step-by-step explanation:

the answer is k and l thats right pls mark brainliest

or hit the thanks button!!!!!!!

pls and thank you!

The image of the point (-9,7) after a rotation of 180 counterclockwise about the origin is at (9, -7).

Dilation is a process for creating similar figures by changing the size.

Rotation of a point P(x, y) 180 counterclockwise about the origin produces an image at P'(-x, -y).

Here, the point counterclockwise about the origin → (-(-9), -7).

Therefore, the image of the point (-9,7) after a rotation of 180 counterclockwise about the origin is at (9, -7).

Learn more about the Dilation here:

brainly.com/question/13176891

#SPJ1

Answer:

3 7/100

Step-by-step explanation:

3007/1000 = 3 7

1000

The relation is not a function if its domain is on the x-axis and its range is on the y-axis. However, if the relation's domain is on the y-axis and its range is on the x-axis, it is a function.

If so, what kind of function is it?

Relationships are defined by three factors:

1. domain is a set of inputs.

2. an output set referred to as range.

3 . relationships between domain and range-related items.

If and only if each element of the domain is associated to just one member of the range, is a relation a function. It must be noted that the solution may vary based on the domain and range that we assume.

The provided relation is a function if the x-axis is the range and the y-axis is the domain, as opposed to when the x-axis is the domain and the y-axis is the range.

To learn more about this visit , https://brainly.com/question/28574205

#SPJ9

The value of the given algebraic expression 6x(y²z)  is (D) 6.

So, substitute the values of x, y, and z in the given expression:

6x(y²z)

When x = 0.5, y = -1 and z = 2

Therefore, the value of the given algebraic expression is (D) 6.

Know more about algebraic expressions here:

https://brainly.com/question/2164351

#SPJ9

The complete question is given below:
What is the value of the algebraic expression if x= 1/2 , y = -1, and z = 2? 6x(y²z)

A. -12

B. -6

C. 1

D. 6

Answer:

x = 4

Step-by-step explanation:

Perimeter of triangle: P = (5x -1) + (5x -1) + (2.2x + 10)

Perimeter of square: P = 4(6.5x - 11.8)

so (5x -1) + (5x -1) + (2.2x + 10) = 4(6.5x - 11.8)

5x - 1 + 5x - 1 + 2.2x + 10 = 26x - 47.2

12.2x + 8 = 26x - 47.2

26x - 12.2x = 8 + 47.2

13.8x = 55.2

x = 55.2/13.8 = 4

The two numbers are 6 and 8.

The first step is to determine the simultaneous equations that would be used to determine the answer. The simultaneous equations would be derived from the information provided in the question.

x + y = 14 equation 1

x - y = 2 equation 2

Where:

x = larger number

y = smaller number

The simultaneous equations would be solved using the elimination method

Now, subtract  equation 2 from  equation 1

2y = 12

Divide both sides of the equation by 2

y = 12 / 2

y = 6

Substitute for y in  equation 2

x - 6 = 2

Add 6 to both sides of the  equation

x = 2 + 6

x = 8

To learn more about simultaneous equations, please check: https://brainly.com/question/15165519

#SPJ1

The number of cans of paint which it would take to paint one given the premise that; it takes 4 cans of paint to paint 1/3 of a room is; 12 cans of paint.

It follows from the task content that the number of cans of paint that would be required to paint one room according to the task content be determined.

Hence, since it takes 4 cans of paint to paint 1/3 of a room.

Hence, since there are 3 One-thirds in a whole, it follows from proportion that the number of cans of paints required is;

= 3 × 4 cans of paint

= 12 cans of paint.

The number of cans of paint which it would take to paint one given the premise that; it takes 4 cans of paint to paint 1/3 of a room is; 12 cans of paint.

Read more on proportion;

https://brainly.com/question/18437927

#SPJ1

The expression is simplified to x - 147

Algebraic expressions are defined expressions made up of terms, factors, variables, constants , coefficients.

They are also made up of arithmetic operations such as addition, subtraction, multiplication, division, etc.

Given the expressions;

−3 (5x + 1) + 16(x − 9)

First, we have to expand the bracket

-15x -3 + 16x - 144

collect like terms, we have;

-15x + 16x - 144 - 3

Add or subtract like terms as seen in the expression

x - 147

Note that the expression is simplified to x - 147

Thus, the expression is simplified to x - 147

Learn more about algebraic expression here:

https://brainly.com/question/4344214

#SPJ1

The amount spent on pants based on the information illustrated is 45 soles.

Let the amount spent of shirt = x

Amount spent on sweaters = 2x

Amount spent on pants = 3x

Amount spent = 90

Therefore, the value will be:

x + 2x + 3x = 90

6x = 90

Divide

x = 90/6

x = 15

Therefore, the amount spent on pants will be:

= 3x

= 3 × $15

= 45 soles.

Learn more about numbers on:

brainly.com/question/24644930

#SPJ1

The equation containing the point  (9,12) is y = 4/3x.

So, perpendicular = m1 × m2 = -1:

Now,

Therefore, the equation containing the point  (9,12) is y = 4/3x.

Know more about equations here:

https://brainly.com/question/2972832

#SPJ9

The correct question is given below:
Find the equation of the line that is perpendicular to y = -3/4x+1 and contains the point (9,12).

The finance charge for a credit card that has given the average daily balance and interest rate is 11.170$.

The finance charge is the cost of credit in dollars. It is calculated on a credit card's unpaid balance. A finance charge, the cost of having the debt a longer time, is added to the outstanding credit card balance.

Given:

Average daily balance: $118.18,

monthly interest rate: 1.15%

According to given question we have

A common way of calculating a finance charge on a credit card is to multiply the average daily balance by the annual percentage rate (APR) and the days in your billing cycle. The product is then divided by 365 .

i.e

[tex]\frac{118.18*1.15*30}{365} \\=11.170[/tex]

Therefore, the finance charge for a credit card that has given the average daily balance and interest rate is 11.170$.

Learn more details about  finance charge  here:

https://brainly.com/question/2588555

#SPJ1

Answer:

b

Step-by-step explanation:

state 3 fractors other than $/ hours

Answer: $0.65

Step-by-step explanation:

She can have all nickels since at least 3 nickels means that there is a possibility that all 13 of her coins are nickels.

100 cents=1 dollar

Nickel=5 cents

5 cents * 1 dollar/100 cents=

5*1/100=0.05 dollars

Hence, the least total amount of money she could have is:

13*0.05=$0.65

This is equivalent to 140 cents.

==========================================================

Explanation:

"she has at least three each of quarters, dimes, and nickels"

Let's say she has exactly 3 of each for now

So far she has 75+30+15 = 120 cents (aka $1.20) with the 3*3 = 9 coins mentioned. There are 13-9 = 4 coins remaining

To achieve the least money possible, those missing four coins must be the smallest denomination allowed, i.e. the nickel. We can't go for penny since it states "none of them are pennies". So we add 4*5 = 20 more cents onto 120 to get 120+20 = 140 cents aka $1.40

Answer:

21 7/8 in^2

Step-by-step explanation:

explantation up top

The minimum and maximum numbers of hours the truck driver will drive before stoping for a rest will be 3.6 hours and 2.4 hours respectively.

From the information, the truck driver is driving on an interstate and is about 150 miles from his planned exit and he is traveling at a speed of 50 miles per hour and plans to stop for a rest within 30 miles of the exit on either side.

Therefore, the appropriate equation be:

50h - 150 = 30

50h = 30 + 150

50h = 180

Divide

h = 180 / 50

h = 3.6 hours.

The minimum hours will be:

50h = 150 - 30

50h = 120

h = 120/50

h = 2.4 hours.

Learn more about time on:

brainly.com/question/10428039

#SPJ1

The measures of the angles are:

m<7 = 47°

m<8 = 62°

m<1 = 62°

m<2 = 71° [vertical angles theorem]

m<5 = 109°

m<3 = 109°

m<4 = 35°

m<6 = 29°

The alternate interior angles theorem states that two interior angles that are formed along a transversal and lie alternate to each other on two parallel lines are congruent to each other.

Measure of angle 7 = 47° [based on the alternate interior angles theorem]

Measure of angle 8 = 180 - 47 - 71 [triangle sum theorem]

Measure of angle 8 = 62°

Measure of angle 1 = measure of angle 8 = 62° [based on the alternate interior angles theorem]

Measure of angle 1 = 62°

Measure of angle 2 = 71° [vertical angles theorem]

Measure of angle 5 = 180 - 71 [linear angle theorem]

Measure of angle 5 = 109°

Measure of angle 3 = measure of angle 5 = 109° [vertical angles theorem]

Measure of angle 4 = 180 - measure of angle 3 - 36 [linear angle theorem]

Measure of angle 4 = 180 - 109 - 36

Measure of angle 4 = 35°

Measure of angle 6 = 180 - measure of angle 5 - 42 [linear angle theorem]

Measure of angle 6 = 180 - 109 - 42

Measure of angle 6 = 29°

Learn more about the alternate interior angles theorem on:

https://brainly.com/question/24839702

#SPJ1

Answer:

W' (2, 4 )

Step-by-step explanation:

a translation of 4 units right means add 4 to the x- coordinate, that is

W (- 2, 4 ) → W' (- 2 + 4, 4 ) → W' (2, 4 )

Answer:

Step-by-step explanation:

n^2 - 18. n=8

Simply plug 8 in place of n. The ^ sign refers to the power of the number, so in this case we square it. Review order of operations if needed.

8^2 - 18

(8×8) - 18

64 - 18 = 46

So the answer is 46

Answer:

h = 3V /b

Step-by-step explanation:

V=1/3bh

Solve for h

Multiply each side by 3

3V = 3*1/3bh

3V = bh

Divide each side by b

3V/b = bh/b

3V /b = h

h = 3V /b

Answer:

[tex]3v = bh \\ bh = 3v \\ h = \frac{3v}{b} [/tex]

The land area of North America is 9,455,941.77 square miles.

Percentage can be described as the fraction of an amount expressed as a number out of hundred. Percentage is a measure of frequency. The sign used to represent percentages is %.

In order to determine the land area of North America, multiply the total land area of the Earth by the percentage of the land area of North America.

Land area of North America = percentage of the land area of North America x total land area

16.5% x  57,308,738

0.165 x 57,308,738 = 9,455,941.77 square miles

To learn more about percentages, please check: https://brainly.com/question/25764815

#SPJ1

According to the solving the beginning value of retained earnings:

= $1,60,000.

Retained earnings are usually included in the shareholders' equity portion of a company's balance sheet. Retained earnings are computed by adding beginning-period retained earnings to net income (or loss), then deducting dividend distributions.

To calculate retained earnings, subtract a company's liabilities from its assets to obtain stockholder equity, then locate the common stock line item on your balance sheet and multiply the total stockholder equity by the common stock financial statement figure (if the only two items in your stockholder equity were also common stock).

Retained earnings, ending = $240,000.

Net income = $110,000.

Preferred stock dividend = $30,000.

Retained earning, beginning = ?

Retained earnings, ending = Retained earning, beginning + Net income - Preferred stock dividend

$240,000 = Retained earning, beginning + 110,000 - 30,000

Retained earning, beginning = 1,60,000

According to the solving the beginning value of retained earnings:

= $1,60,000.

To know more about retained earnings visit:

https://brainly.com/question/13980094

#SPJ9

[tex] \chi - 0 = \chi \\ 2 - 0 = 2 \\ y - 0 = y\\ .....[/tex]

Any number take away zero, is still that number.