3. Robinsport and Titusville are 324 mi apart on a railroad line. Trains
leave each of these depots at the same time headed for the other depot.
One travels at 43 mi/h, the other at 38 mi/h. How long will it take for
the two trains to pass one another?

Answer:

(x - \(\frac{5}{2} \) )² + \(\frac{7}{4} \)

Step-by-step explanation:

x² - 5x + 8

Using the method of completing the square

add/subtract ( half the coefficient of the x- term )² to x² - 5x

x² + 2(- \(\frac{5}{2} \) )x + \(\frac{25}{4} \) - \(\frac{25}{4} \) + 8

= (x - \(\frac{5}{2} \) )² - \(\frac{25}{4} \) + \(\frac{32}{4} \)

= (x - \(\frac{5}{2} \) )² + \(\frac{7}{4} \)

John has the greater total change in the amount of detergent in their bottle.

Given that, Brenda pours laundry detergent from a bottle into the cap and then into the washing machine.

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Every time she fills the cap, the amount of detergent in the bottle changes by -0.26 L. She fills the cap 314 times in all.

Now, the volume of bottle =314×0.26

= 81.64

≈ 82 L

Every time he fills his cap, the amount of detergent in his bottle changes by -0.21 L. He fills his cap 256 times in all.

Here, the volume of bottle =256×0.21

= 53.76

≈ 54 L

Hence, John has the greater total change in the amount of detergent in their bottle.

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Answer:

x = -9/5

DECIMAL FORM: -1.8

Step-by-step explanation:

Answer:

x=28/5

Step-by-step explanation:

need more help? im glad to

first we need to simplify both sides :

5x + 13 * -2 = 2

5x +  -26 = 2

5x - 26 = 2

Then we add 26 to both sides:

5x - 26 = 2

    +26   +26

5x = 28

Then  we divide both sides by 5:

5x/5  = 28/5

x = 28/5

TA-DA! lol happy to help!

Phil's final debt after 20 years will be around $320,679.

To purchase a home, Phil borrowed $150,000 from a bank at a 3.5% annual interest rate.

The annual compounding of interest causes the amount of interest for each year to rise in proportion to the debt. Phil will be required to pay the initial sum plus interest after the first year, which comes to

$150,000 + 3.5% of $150,000 = $155,250.

Since interest is charged on the new amount owed for the second year, Phil will owe

$155,250 + 3.5% of $155,250, which

= $160,551.75.

For the next 20 years, this procedure is repeated, with the amount owed rising yearly by the sum of the year before plus interest. Phil's debt after 20 years will be around $320,679.

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Answer:

-2

Step-by-step explanation:

\(\boxed{ slope = \frac{y _{1} - y_2 }{x_1 - x_2} }\)

where (x₁, y₁) is the first coordinate and (x₂, y₂) is the second coordinate

Slope

\( = \frac{14 - 4}{ - 8 - ( - 3)} \)

\( = \frac{10}{ - 8 + 3} \)

\( = \frac{10}{ - 5} \)

= -2

There are 5 full square and 6 triangles that are half squares.

      5 + (6)(1/2) = 5 + 3 = 8

You could also break this into smaller shapes (like a big triangle on the top and a smaller triangle and rectangle on the bottom and use area formulas to calculate the area.  But counting works well in this example.

Answer: 8

Step-by-step explanation:

First you split up this shape into two different shapes, a triangle and trapezoid

Put a line through the coordinates (-2,2) to  (-1,2); the top is a triangle and the other is a trapezoid

Area of the trapezoid is A = .5x (base1 + base2) x height

base1 of the trapezoid goes from -4 to -1 which is 3

base2 goes from -2 to -1 which is 1

height is 0 to 2 whcich is 2

A = .5 x (3+1) x 2 = 4

Now area of a triangle is A = .5 x base x height

the base goes from -2 to 2 which is 4

the height goes from 2 to 4 which is 2

A = .5 x (4) x (2) = 4

Area of the Trapezoid + Area of the Triangle = Total Area

4 + 4 = 8

Answer:

2.77083333333

Step-by-step explanation:

I assume. Do not hold me account for mistakes, I apologize if my work is incorrect. Have a good day/night :}

Answer:

$72

Step-by-step explanation:

im guessing

Answer:

true

Step-by-step explanation:

Answer: El precio unitario de las palomitas es de $60 y el precio unitario del refresco es de $70.

Primero, podemos descomponer el costo total de la primera visita al cine en el costo de las palomitas y el costo de los refrescos:

- 5 palomitas + 7 refrescos = $630

- Palomitas = $x, Refrescos = $y

- 5x + 7y = 630

Luego, podemos descomponer el costo total de la segunda visita al cine en el costo de las palomitas y el costo de los refrescos:

- 8 palomitas + 11 refrescos = $1000

- Palomitas = $x, Refrescos = $y

- 8x + 11y = 1000

Ahora podemos resolver este sistema de ecuaciones para encontrar el precio unitario de las palomitas y del refresco. Primero, despejamos y de la primera ecuación:

- 5x + 7y = 630

- 5x = 630 - 7y

- x = (630 - 7y) / 5

Luego, sustituimos esta expresión para x en la segunda ecuación:

- 8x + 11y = 1000

- 8[(630 - 7y) / 5] + 11y = 1000

- 504 - 45.6y + 11y = 1000

- 65.4y = 496

- y = 7.58

Finalmente, podemos sustituir este valor para y en la primera ecuación para encontrar el valor de x:

- 5x + 7(7.58) = 630

- 5x = 578.86

- x = 115.77

Por lo tanto, el precio unitario de las palomitas es de $60 y el precio unitario del refresco es de $70.

Step-by-step explanation:

Answer:

i guess 10 i hope this is the right answer

Answer:

Step-by-step explanation:

its 1 : 4

Answer:

P(x)=0.025x+100

Step-by-step explanation:

The 0.025 is 2.5% as a decimal. Then, the +100 is for the base pay amount Hailey receives.

Answer:

Lacy would earn a commission of $104.

Lacy would earn 0.06x dollars on phones sale and 0.02y dollars on computer sales.

Step-by-step explanation:

Hopefully this helped, if not HMU and I will try my best to get u a better aswer!

Have a great day! :)

And if u need help HMU and I got you, no points needed:)

Andf thanks  for the 25 points! :D

#1

\(\sf \longmapsto3x-4y=11\)

\(\sf \longmapsto3x−4y+4y=11+4y\)

\(\sf \longmapsto3x=4y+11\)

\(\sf \longmapsto \frac{3x}{3} = \frac{4y + 11}{3} \)

\(\sf \longmapsto{x} = \frac{4}{3} y + \frac{11}{3} \)

#2

\(\sf \longmapsto3x+2y=2\)

\(\sf \longmapsto3x+2y+−2y=2+−2y\)

\(\sf \longmapsto3x=−2y+2\)

\(\sf \longmapsto \frac{3x}{3} = \frac{ - 2y + 2}{3} \)

\(\sf \longmapsto \: x = \frac{ - 2}{3} y + \frac{2}{3} \)

Answer:

9y²+9 that's the answer

8 feets will the bottom of the ladder slip.

What is pythagora's theorem?

In ΔABC

AC² = AB² - BC² (∴Pythagoras theorem)

AC = √25² - 7²

AC = √625 - 49

AC = √576

AC = 24 feet

As after sliping length of ladder remains same ⇒ DE = 25 feet and feet 4 feet.

Let say x be the length of how much the ladder slips.

New height = DC = AC - AD = 20 feet

EC = (x + 7 ) feet

In ΔDEC,

DE² = DC² + EC²  (∴Pythagoras theorem)

25² = 20² + (x + 7)²

(x + 7)² = 225

x + 7 = 15

(∵ x+7)>0, We can't take negative value)

x = 8 feet

Hence, 8 feets will the bottom of the ladder slip.

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Answer:

a  c

Step-by-step explanation:

Answer:

8

Step-by-step explanation:

c(w)= 200 * 1/5^2.

1/5 * 1/5 = 1/25

1/25 * 200 = 8

Hope this helps!

:)

Answer:

hope this helps you. look it once

To find the amount of extra money Robert will have after two years if he compounds continuously instead of collecting simple interest monthly, we need to calculate the compound interest on the investment.

The compound interest is calculated by multiplying the principal (the initial amount invested) by the compound interest rate, raised to the power of the number of compounding periods. In this case, the compound interest rate is 1.9%/12 = 0.158% per month, and there are 12*2 = 24 compounding periods (12 months per year for 2 years).

The compound interest is therefore calculated as follows:

Compound interest = $20,000 * e^(0.158%*24) - $20,000

= $20,000 * e^0.3832 - $20,000

= $20,000 * 1.454 - $20,000

= $4,080 - $20,000

= -$15,920

So the amount of extra money Robert will have after two years if he compounds continuously instead of collecting simple interest monthly is -$15,920. Therefore, the correct answer is [A] $800.

The electrician needs a ladder that is 25 feet long to reach the spotlight. The answer is 25ft.

A right triangle's three sides are related in Euclidean geometry by the Pythagorean theorem, also known as Pythagoras' theorem. According to this statement, the areas of the squares on the other two sides add up to the area of the square whose side is the hypotenuse.

The electrician needs to place a ladder against the house so that it reaches the spotlight. The ladder will form a right triangle with the ground and the wall of the house, with the length of the ladder being the hypotenuse.

We can use the Pythagorean theorem to find the length of the ladder:

\($ladder^2 = 7^2 + 24^2$\)

\($ladder^2 = 49 + 576$\)

\($ladder^2 = 625$\)

\($ladder = \sqrt{625}$\)

ladder = 25

Therefore, the electrician needs a ladder that is 25 feet long to reach the spotlight. The answer is 25ft.

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Answer:

required formula: πr^2h

Solution

Formula to find volume of cylinder= πr^2h

= 22/7 ×3×3×4

= 113.14cm^3

Answer:

Step-by-step explanation:

$183.20/(8 hours) = $22.90/hour

13 hours × $22.90/hour = $297.70

Answer:

32

Step-by-step explanation:

Answer: I agree with the first one the answer should be 32hope this helps

Step-by-step explanation:

Based on common factors, Fatoumata can increase each dimension of the deck by 2 feet so that the deck's new area is increased by 50% to 126 ft².

Common factors are the numbers that can divide another number evenly without a remainder.

In this situation, 9 and 14 can divide 126 equally and the product of 9 and 14 are 126.

The old dimensions of the deck:

Width = 7 feet

Length = 12 feet

Area = 84 ft² (7 x 12)

The expected new area of the deck:

Increase in the new area = 5%

Increased factor for the area = 1.5 (100% + 50%)

Area = 126 ft² (84 x 1.5)

The common factors of 126 include 9 and 14 and the product of 9 and 14 = 126.

Therefore, we can increase each length of the deck by 2 feet.

Check:

Width = 9 feet

Length = 14 feet

Area = 126 ft² (9 x 14)

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The chain rule is a formula used in calculus to find the derivative of a composition of functions. It is an important tool for solving problems in many areas of mathematics and science.

The chain rule formula can be stated as follows:

If y = f(g(x)), then the derivative of y with respect to x is given by:

dy/dx = (df/dg) * (dg/dx)

In other words, the derivative of y with respect to x is equal to the derivative of f with respect to g, multiplied by the derivative of g with respect to x.

Here, f and g are functions of x, and y is a function of g. The chain rule formula tells us how to find the derivative of y with respect to x, by taking into account the effect of both f and g on the function y.

The chain rule can be extended to more complex compositions of functions, by applying the formula repeatedly. For example, if y = f(g(h(x))), then the chain rule can be applied twice, as follows:

dy/dx = (df/dg) * (dg/dh) * (dh/dx)

This formula tells us how to find the derivative of y with respect to x, by taking into account the effects of all three functions f, g, and h on the function y.

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Answer:

That would be 2/7.

Step-by-step explanation:

By finding the GCD between 14 and 49, you can reduce the fraction.

The GCD between 14 and 49 is 7.

By dividing both 14 and 49 by 7, you'll reduce your answer.

14/49 ---> 2/7

Answer:

Find the volume of the rectangular prism and

divide by the volume of the cube.

Volume of cube = side measure ^3

Cube = (1/8)3 = 1/512

Volume of prism = Ixwxh

Prism (1/4)(1/2)(3/8) =3/64

3/64/1/512

3/64 x 512/1

3x 512/64

1536/64

24

Kemar weighs the fruit before making the biscuits to ensure accurate measurements.

Weighing the fruit is important because it helps Kemar to calculate the amount of fruit needed for each batch of biscuits. This helps him to avoid using too much or too little fruit, which can affect the taste and texture of the biscuits.

Additionally, by weighing the fruit, Kemar can also keep track of his inventory and ensure that he has enough fruit to make the biscuits for the entire event. This helps him to avoid running out of ingredients and disappointing customers who want to purchase his delicious fruit biscuits.
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Writing linear equations given two points can be a useful skill when graphing linear equations.

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