A train leaves Philadelphia at 3:00 PM. A second train leaves the same city in the same direction at 9:00 PM. The second train travels 120mph faster than the first. If the second train overtakes the first at 11:00 PM, what is the speed of each of the two trains?

Complete Question: You are building a shelf that fits in a corner in the figure the entire shelf is XYZ each unit in the coordinate plane represents one inch find the area of the shelf.

Answer:

112.5 units²

Step-by-step explanation:

Area of the shelf = ½*base*height.

The base is the distance between Z(0, 5) and Y(15, 5)

The height is the distance between X(15, 20) and Y(15, 5).

Therefore area of the shelf = ½*ZY*XY

Use the distance formula to find ZY and XY.

Distance between Z(0, 5) and Y(15, 5):

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

Let,

[tex] Z(0, 5) = (x_1, y_1) [/tex]

[tex] Y(15, 5) = (x_2, y_2) [/tex]

[tex] ZY = \sqrt{(15 - 0)^2 + (5 - 5)^2} [/tex]

[tex] AB = \sqrt{(15)^2 + (0)^2} [/tex]

[tex] AB = \sqrt{225 + 0} = \sqrt{225} [/tex]

[tex] AB = 15 [/tex]

Distance between X(15, 20) and Y(15, 5):

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

Let,

[tex] X(15, 20) = (x_1, y_1) [/tex]

[tex] Y(15, 5) = (x_2, y_2) [/tex]

[tex] XY = \sqrt{(15 - 15)^2 + (5 - 20)^2} [/tex]

[tex] XY = \sqrt{(0)^2 + (-15)^2} [/tex]

[tex] XY = \sqrt{0 + 225} = \sqrt{225} [/tex]

[tex] XY = 15 [/tex]

Area of shelf = ½*15*15 = ½*225 = 112.5 units²

Answer:

-30√(t/a) cos(√(at)) + 30/a sin(√(at)) + C

Step-by-step explanation:

∫ 15 sin(√(at)) dt

Use substitution:

If x = √(at), then:

dx = ½ (at)^-½ (a dt)

dx = a / (2√(at)) dt

dx = a/(2x) dt

dt = (2/a) x dx

Plugging in:

∫ 15 sin x (2/a) x dx

30/a ∫ x sin x dx

Integrate by parts:

If u = x, then du = dx.

If dv = sin x dx, then v = -cos x.

∫ u dv = uv − ∫ v du

= 30/a (-x cos x − ∫ -cos x dx)

= 30/a (-x cos x + ∫ cos x dx)

= 30/a (-x cos x + sin x + C)

Substitute back:

30/a (-√(at) cos(√(at)) + sin(√(at)) + C)

-30√(t/a) cos(√(at)) + 30/a sin(√(at)) + C

Answer:

  8%

Step-by-step explanation:

If you subtract 1 times the original cost, the result is the tax rate:

  27/25 - 1 = tax rate = (27 -25)/25 = 2/25 = 8/100 = 8%

The tax rate is 8%.

Answer:

6 would be the overlined number

Step-by-step explanation:

Answer:

6 will be the overlined number.

Step-by-step explanation:

Answer:

one solution

Step-by-step explanation:

-2|3x − 1| = 0?

Divide each side by -2

|3x − 1| = 0

3x-1 = ±0

Since +0 = -0 =0

3x-1 =0

There will be only one solution

Answer:  All adults of United States.

Step-by-step explanation:

Here, the study is all about the problem have been facing by the population of U.S.

Since adults of a society are likely voters.

So, population = All adults of United States., as only they can address the current situation or problems because they live there.

Answer:

-8

Step-by-step explanation:

I've taken a picture of the way I solved the equation.

Answer:

[tex]f(2)=-7[/tex]

Step-by-step explanation:

So we have the function:

[tex]f(t)=-t-5[/tex]

To find f(2), substitute 2 for t. Thus:

[tex]f(2)=-2-5[/tex]

Subtract:

[tex]f(2)=-7[/tex]

And, we're done!

Answer:

2x + 8 = -14

Step-by-step explanation:

Twice​ x, plus 8 ​, is the same as -14.

2x + 8 = -14

Answer:

2x + 8 = -14

Step-by-step explanation

Because twice is 2 times and then you plus 8 i the same as -14

so 2 times= 2x then +8 so altoghther is 2x+8 and it says it's the same as -14

so the answer is 2x+8= -14

Brainly please!

Answer:

9

Step-by-step explanation:

If A = - 3, than A^2 is equal to (-3)^2

If a number is squared (to power of 2), it is multiplied by itself (there are two of that number being multiplied together) so it is - 3x-3

-3 x - 3 = 9,

Because 3x3 =9 and a negative multiplied by a negative makes a positive.

Hope this helped!

Answer:

9

Step-by-step explanation:

(A)^2 is a better way to write it. That way the answer is unambiguous (-3)^2 = -3 * - 3 = 9

That is the answer.

Answer:

[tex]2\frac{15909}{5000}[/tex]

Step-by-step explanation:

To make [tex]2.31818[/tex] into a fraction, you must first move it to the numerator and make 1 the denominator.

[tex]\frac{2.31818}{1}[/tex]

And then you multiply it by [tex]10,000[/tex] or you can say [tex]10^5[/tex]

[tex]\frac{2.31818}{1}*\frac{100000}{100000}[/tex]

After you multiply you divide the numerator and denominator by 2.

[tex]\frac{231818/2}{100000/2}[/tex]

And now this equals:

[tex]2\frac{15909}{5000}[/tex]

Hope this helps!

The number before the decimals always represents the whole number of a mixed number and the number after the decimals represents the fraction part of the mixed number.

2.31818 = 2.0 + 0.31818

In  2.31818

2 represents the whole number  and

0.31818 represents the fraction  31818/100000

Dividing the  fraction  31818/100000 by 2 gives

15909/50000 which cannot be further reduced.

2.31818 = 2 [tex]\frac{15909}{50000}[/tex]

https://brainly.com/question/1369626

Answer:

≈ 0.39

Step-by-step explanation:

Area of circle:

Area of triangle:

Probability of the point within red shaded area:

Answer:

The unit rate is 5 ft/1 second

Step-by-step explanation:

Unit rates must always be a fraction with a denominator of 1

Our unit rate is 125/25

To get to a denominator of 1 divide 25 by 25

25 ÷ 25 = 1 second

What we do to one side we have to do to the other so also divide 125 by 25

125 ÷ 25 = 5 ft

Answer:

-9

Step-by-step explanation:

1−15−(−5)

−14−(−5)

−9

Answer:

-15-(-5)

= - 15 +5 (Multiplying - and - we get a plus(+))

=-10 ( - stg + stg means to subtract and since 15 is greater than 5 and it's sign is - we should keep that)

Answer:

[tex]\huge\boxed{D) \ f^{-1}(x) = (x-3)^2+2}[/tex]

Step-by-step explanation:

[tex]f(x) = \sqrt{x-2} + 3[/tex]

Replace f(x) by y

[tex]y = \sqrt{x-2} + 3[/tex]

Interchange x and y

[tex]x = \sqrt{y-2} + 3[/tex]

Solve for y

[tex]x = \sqrt{y-2} + 3[/tex]

Subtracting 3 to both sides

[tex]x - 3 = \sqrt{y-2}[/tex]

Taking square on both sides

[tex](x-3)^2 = y-2[/tex]

Adding 2 to both sides

[tex]y = (x-3)^2 + 2[/tex]

Replace [tex]y = f^{-1}(x)[/tex]

[tex]f^{-1}(x) = (x-3)^2+2[/tex]

so first we need to find the total number of crayons

to do that we're going to multiply 6 by 24 cause each box has 24 crayons

24 × 6 = 144

so the answer of total number of crayons is 144 crayons

next we're going to find the total number of paint brushes

to do that we're going to multiply 9 by 15 cause each package has 15 paint brushes

9 × 15 = 135

so the answer of total number of paint brushes is 135 crayons

finally we're going to calculate the difference

so its 144 crayons subtracted by 135 paint brushes

144 - 135 = 9

so the difference of total number of crayons and total number of paint brushes is 9

hope that helped :))

The difference between the crayons and the paintbrush the total. I just see which one is greater

if sum of any two angles 90 then they are called complementary

A +B =90 let the complement of A is B

4x+2 +B =90

B= 90-4x-2

B = 88-4x

complementary angle = B = 88-4x

♡Hope it helps♡

Answer:

x = 17/6

Step-by-step explanation:

First of all remove parenthesis by using distribution

6x + 9 - 12x + 24 = 16

Then collect all like terms

-6x + 33 = 16

After that move the constant to the right

- 6x = 16 - 33

Calculate 16 - 33

-6x = -17

Divide both sides

x = 17/6

Hope this helps!

Answer:

10 months

Step-by-step explanation:

3500 - 2000 = 1500

1500/150 = 10

Answer:

On the 23rd month

Step-by-step explanation:

Answer:

First, frank buys 3 packs on 3 different days, so in those first 3 days he buys:

3*3 = 9 packs.

Then on other 3 days he buys 4 packs each day, so he has:

3*4 = 12 packs.

In total he haves:

9 + 12 = 21 packs.

Now he divides the packs with his 2 brothers (So we divide 21 packs between 3 people)

Then each brother gets:

N = 21/3 = 7 packs each.

Answer:

54.18

Step-by-step explanation:

Answer:

Step-by-step explanation:

.....

an image please   because there is nothing explainign what you need                                                                                                                                                                  

Without the screenshot, it's fairly difficult to know what your teacher wants exactly. I found this similar problem

https://brainly.com/question/13583475

which might help. It sounds like you have 4 semicircles which can be thought of as a division problem 12/3 = 4. Note how I'm dividing by 3 which is the width of each section (eg: from 6 to 9 is 9-6 = 3 units)

Answer:

Which division problem does the number line below best illustrate?

A number line going from 0 to 2. Arrows go from 0 to 2, from 2 to 4, from 4 to 6, from 6 to 8, and from 8 to 10.

10 divided by 2 = 5

15 divided by 3 = 5

50 divided by 5 = 10

20 divided by 10 = 2

Step-by-step explanation:

which means its a

Answer:

Sam is 15; Owen is 5.

Step-by-step explanation:

Let s denote Sam's age and let o denote Owen's age.

So, Sam is three times older than Owen. Thus:

[tex]s=3o[/tex]

In 5 years, Sam will be twice as old as Owen. In other words, Sam's current age plus 5 years will be Owen's current age plus five years times 2. Thus:

[tex]s+5=2(o+5)[/tex]

We have a system of equations. Solve for substituting the first equation into the second. Thus:

[tex]3o+5=2(o+5)[/tex]

Distribute the right:

[tex]3o+5=2o+10[/tex]

Subtract 2o from both sides:

[tex]o+5=10[/tex]

Subtract 5 from both sides:

[tex]o=5[/tex]

So, Owen is currently 5 years old.

Sam is 3 times older than Owen, so Sam is 15 years old.

And we're done :)

Answer:

think the answer is E but not 100%. been a while. let me know either way

Answer:

Step-by-step explanation:C