Two trains leave the station at the same time, one heading east and the other west. The eastbound train travels 14 miles per hour slower than the westbound train. If the two trains are 480 miles apart after 3 hours, what is the rate of the eastbound train?

Answer:

1: y = 3/2 + 1/2

Step-by-step explanation:

y1 -y2/x1 - x2

8-2 / 5-1

6/4 = 3/2

y-2=3/2(x-1)

y-2=3/2x - 3/2

y-2 +2= 3/2x - 3/2 +2

y=3/2x + 1/2

Answer:

look at attached image, hope this helps! :)

Exact value:  [tex]c = \frac{-11+\sqrt{165}}{22}[/tex]

Approximate value:    c = 0.08387

Round the approximate value however you need to

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

Work Shown:

Let x = 1+c

[tex]\displaystyle S = \sum_{n=2}^{\infty}(1+c)^{-n}\\\\\\\displaystyle S = \sum_{n=2}^{\infty}x^{-n}\\\\\\\displaystyle S = \sum_{n=2}^{\infty}\frac{1}{x^n}\\\\\\\displaystyle S = \frac{1}{x^2}+\frac{1}{x^3}+\frac{1}{x^4}\ldots\\\\\\[/tex]

We have an infinite geometric series here. The first term is a = 1/(x^2). The common ratio is r = 1/x.

Each new term is found by multiplying the previous term by 1/x.

Assuming -1 < r < 1 is true, the infinite geometric sum is

[tex]S = \frac{a}{1-r}\\\\\\S = \frac{1/x^2}{1-1/x}\\\\\\S = \frac{1/x^2}{x/x-1/x}\\\\\\S = \frac{1/x^2}{(x-1)/x}\\\\\\S = \frac{1}{x^2}\div\frac{x-1}{x}\\\\\\S = \frac{1}{x^2}*\frac{x}{x-1}\\\\\\S = \frac{1}{x^2-x}\\\\\\[/tex]

Plug in S = 11 and solve for x

[tex]S = \frac{1}{x^2-x}\\\\11 = \frac{1}{x^2-x}\\\\11(x^2-x) = 1\\\\11x^2-11x = 1\\\\11x^2-11x-1 = 0\\\\[/tex]

Use the quadratic formula to find the two solutions

[tex]x = \frac{11+\sqrt{165}}{22} \approx 1.08387\\\\x = \frac{11-\sqrt{165}}{22} \approx -0.08387\\\\[/tex]

Using these x values, we find that the corresponding r values are

r = 1/x = 1/(1.08387) = 0.92262

r = 1/x = 1/(-0.08387) = -11.92321

The first r value makes -1 < r < 1 true, but the second r value does not. So we will be ignoring the solution x = -0.08387

----------------------------------------------

Using the solution that corresponds to x = 1.08387, we find the value of c is

[tex]x = c+1\\\\c = x-1\\\\c = \frac{11+\sqrt{165}}{22}-1\\\\c = \frac{11+\sqrt{165}}{22}-\frac{22}{22}\\\\c = \frac{11+\sqrt{165}-22}{22}\\\\c = \frac{-11+\sqrt{165}}{22}\\\\c \approx 0.08387\\\\[/tex]

Answer:

put your first point at 7 in y axis that point go down 3 to the rights side 1 and your point should be at (1,4) then connect the dots and that's how you graph it

Step-by-step explanation:

The equation of the line y = - 3x + 7 is drawn below.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.

The linear equation is given as,

x/a + y/b = 1

Where 'a' is the x-intercept of the line and ‘b’ is the y-intercept of the line.

The equation of the line is given below.

y = -3x + 7

Convert the line into intercepts form, then we have

y = - 3x + 7

3x + y = 7

x / (7/3) + y / 7 = 1

The equation of the line is drawn below.

More about the linear equation link is given below.

https://brainly.com/question/11897796

#SPJ2

Answer: Indep. is: $3 and the dependent is $1

Step-by-step explanation:

Every item is $3, but if you add more then you also add $1

Answer:

5/12

Step-by-step explanation:

Isn't this just a ratio?

Answer: 8 SUVs to 57 total

Step-by-step explanation: You add 34 + 15 + 8 which gives you 57 Then you see there are 8 SUVs. So the answer is 8 to 57.

Sorry. I kinda got ahead of myself and excited. Guess mistakes happen. I was right the first time. I'm just so tired right now

Answer:

0.06

Step-by-step explanation:

6% = 0.06

0.06  as a decimal Hope this helped!

Answer:

9 nickels .   7 dimes

Step-by-step explanation:

i take the same class so i know where u got it from

Answer:

C.1/12

Step-by-step explanation:

Divide 5/12 by 5 since he cut it into 5 equal pieces

Answer:c

Step-by-step explanation:

The measures of the angles in triangle ABC are; m∠A ≈ 73.7°, m∠B ≈ 16.3°, m∠C ≈ 90°

It follows that the right angle is between the two shorter sides;

On this note, the angle, m∠A is opposite side BC;

Therefore, from sine formula;

m∠A ≈ 73.7°

And from sum of angles in a triangle;

m∠A ≈ 16.3°

Read more on right triangle;

https://brainly.com/question/2437195

Answer:

27

Step-by-step explanation:

The area of the triangle is 30.9 square units.

We have,

From the figure,

Height = Distance between (-2, 6) and (-2, 0).

Base = Distance between (-2, 0) and (7, -5).

To find the distance between two points in a Cartesian coordinate system, use the distance formula:

Distance = [tex]\sqrt{((x_2 - x_1)^2 + (y_2 - y_1)^2)[/tex]

Height:

Distance = √((-2 - (-2))² + (0 - 6)²)

Distance = √(0² + (-6)²)

Distance = √(0 + 36)

Distance = √36

Distance = 6

Base:

Distance = √((7 - (-2))² + (-5 - 0)²)

Distance = √((7 + 2)² + (-5)²)

Distance = √(9² + (-5)²)

Distance = √(81 + 25)

Distance = √106

Distance ≈ 10.3

Now,

The area of the triangle.

= 1/2 x base x height

= 1/2 x 10.3 x 6

= 10.3 x 3

= 30.9 square units

Thus,

The area of the triangle is 30.9 square units.

Learn more about triangles here:

https://brainly.com/question/25950519

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Answer:  It is irrational.

Step-by-step explanation:

√18 is an irational number. Multiplying most rational numbers by an irrational number results in an irrational number.

Answer:

6h

Step-by-step explanation:

If he drove 72 mph and you know how long he drove, just need to divide:

[tex]Distance / Speed = Time[/tex]

Therefore:

[tex]432 / 72mph = 6h[/tex]

Answer:

hi its just like the dood above me said *dude sorry if i was late

Step-by-step explanation:

Answer:

x=2

Step-by-step explanation:

hope it helps

please mark as Brainliest

Answer:

x = 2

Step-by-step explanation:

For me it's easier to work with decimals than fractions, so I converted 3/4 to .75

.75(x + 18) = 15

.75x + 13.5 = 15  

That was just distributing the .75 but here is where it gets a bit confusing.

.75x + 13.5 = 15

       -13.5     -13.5

.75x = 1.5

Divide both sides by .75 to isolate the variable.

x = 2

Hope that helps and have a great day!

Answer:

Supplementary

Step-by-step explanation:

84 plus 96 equals 180 degrees

supplementary angles are angles that add up to 180 so their relationship is supplementary

Answer:

Bro this has no solution

Answer: 4(x−5)

Step-by-step explanation: I think this is right. If it’s not Im sorry. But if it is hope this helps!

Answer:

The constant of proportionality is the ratio between two directly proportional quantities

Step-by-step explanation:

Two quantities are directly proportional when they increase and decrease at the same rate.

Answer:The constant of proportionality is the constant value of the ratio of two proportional quantities x and y, typically the equation is Y=KX.

Step-by-step explanation:

Answer:

-7

Step-by-step explanation:

-3x+7=28

     -7=28

           -7

-3x/21

x=-7

Answer:

3.2 hours

Step-by-step explanation:

Answer:

a) -7/9

b) 16 / (n² + 15n + 56)

c) 1

Step-by-step explanation:

When n = 1, there is only one term in the series, so a₁ = s₁.

a₁ = (1 − 8) / (1 + 8)

a₁ = -7/9

The sum of the first n terms is equal to the sum of the first n−1 terms plus the nth term.

sₙ = sₙ₋₁ + aₙ

(n − 8) / (n + 8) = (n − 1 − 8) / (n − 1 + 8) + aₙ

(n − 8) / (n + 8) = (n − 9) / (n + 7) + aₙ

aₙ = (n − 8) / (n + 8) − (n − 9) / (n + 7)

If you wish, you can simplify by finding the common denominator.

aₙ = [(n − 8) (n + 7) − (n − 9) (n + 8)] / [(n + 8) (n + 7)]

aₙ = [n² − n − 56 − (n² − n − 72)] / (n² + 15n + 56)

aₙ = 16 / (n² + 15n + 56)

The infinite sum is:

∑₁°° aₙ = lim(n→∞) sₙ

∑₁°° aₙ = lim(n→∞) (n − 8) / (n + 8)

∑₁°° aₙ = 1

Answer:

The slope is 2. As x increase y is increase and as x decrease y decrease

Answer:

true

Step-by-step explanation:

Because it is

Answer: x=10

Step-by-step explanation:

5x+3=53 subtract 3 from 3 and 53

5x=50 divide both sides by 5

50/5=10

now lets check to be sure

5*10=50+3=53

the solution is correct

hoped this help =)

Answer:6.03*10^3

Step-by-step explanation:

(3.1 *10^2)(2*10^3)

2*10^3=20*10^2

(3.1*10^2)(20*10^2)

(60.3*10^2)=

6.03*10^3

Answer:

*The Museum and the Coffee Shop lie on the opposite sides of the transversal and form a pair of alternate exterior angles

*The Day Care and the Community Center are supplementary angles and on opposite sides of the transversal.

*The Fire Station and the Community Center are consecutive interior angles lying on the same side of the transversal

Step-by-step explanation:

The transversal is the major road that crosses the other two roads shown in the diagram above.

Applying the knowledge of properties of lines, let's consider each statement given, to ascertain which is true and which is untrue:

Statement 1: 'The Fire Station and the Worship Center lie on the same side of the transversal and form a linear pair."

The fire station and the Worship center are on the same side of the transversal, however, they do not form a linear pair. They are corresponding angles.

Statement is NOT TRUE.

Statement 2: "The Museum and the Coffee Shop lie on the opposite sides of the transversal and form a pair of alternate exterior angles."

This statement is TRUE.

The Museum and the Coffee shop form alternate exterior angles pair.

Statement 3: "The Bank, the Museum, the Coffee Shop, the Worship Center are interior angles."

This is NOT TRUE.

They are all EXTERIOR angles.

Statement 4: "The Day Care and the Park are on the same side of the transversal and form a linear pair."

This is NOT TRUE.

They are consecutive interior angles.

Statement 5: "The Day Care and the Community Center are supplementary angles and on opposite sides of the transversal."

This is TRUE.

Statement 6: "The Bank and the Community Center are on opposite sides of the transversal and form a pair of alternate interior angles"

This is NOT TRUE.

They are on opposite side of the transversal but one the bank is an exterior angle while the community center is an interior angle.

Statement 7: "The Park and the Museum are adjacent angles and form a vertical pair of angles."

This is NOT TRUE.

They do not share the same side, so they can't be adjacent angles. They only share the same vertex, which makes them vertical angles.

Statement 8: "The Fire Station and the Community Center are consecutive interior angles lying on the same side of the transversal."

This is TRUE.

Answer:

12x - 12

Step-by-step explanation:

-2(x  + 6)

open the parenthesis

-2 * x + -2 * 6

-2x - 12

-2x - 12

Answer:

The proportion of the population believes that passwords should be replaced with biometric security is not more than 50%.

Step-by-step explanation:

In this case we need to test the claim that more than half of the population believes that passwords should be replaced with biometric security.

Assume that the significance level of the test is, α = 0.05.

The hypothesis can be defined as follows:  

H₀: The proportion of the population believes that passwords should be replaced with biometric security is 50%, i.e. p = 0.50.  

Hₐ: The proportion of the population believes that passwords should be replaced with biometric security is more than 50%, i.e. p > 0.50.  

The information provided is:

[tex]n = 510\\\hat p=0.53[/tex]

Compute the test statistic value as follows:

 [tex]z=\frac{\hat p-p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]

    [tex]=\frac{0.53-0.50}{\sqrt{\frac{0.50(1-0.50)}{510}}}\\\\=1.354991\\\\\approx 1.35[/tex]

The test statistic value is 1.35.

The decision rule is:

The null hypothesis will be rejected if the p-value of the test is less than the significance level.

Compute the p-value as follows:

 [tex]p-value=P(Z>1.35)[/tex]

                 [tex]=1-P(Z<1.35)\\=1-0.91149\\=0.08851\\\approx0.088[/tex]

p-value = 0.088 > α = 0.05.

The null hypothesis will not be rejected at 5% significance level.

Thus, there is not enough evidence to support the claim.

Conclusion:

The proportion of the population believes that passwords should be replaced with biometric security is not more than 50%.