The Fenwick family filled their new in-ground swimming pool with 75,700 liters of water. One gallon of water is about 3.785 liters. About how many gallons of water are in the pool?

gallons

Step 1: Write the dividend and divisor:

\(\sf\:\frac{{x^3 - 8x^2 + 6x + 41}}{{x - 4}} \\ \)

Step 2: Divide the first term of the dividend by the first term of the divisor:

\(\sf\:\frac{{x^3}}{{x}} = x^2 \\ \)

Step 3: Multiply the divisor (x - 4) by the result (x^2):

\(\sf\:(x - 4) \cdot (x^2) = x^3 - 4x^2 \\ \)

Step 4: Subtract the result from the original dividend:

\(\sf\:(x^3 - 8x^2 + 6x + 41) - (x^3 - 4x^2) = -4x^2 + 6x + 41 \\ \)

Step 5: Bring down the next term from the dividend:

\(\sf\:\frac{{-4x^2 + 6x + 41}}{{x - 4}} \\ \)

Step 6: Repeat steps 2-5 with the new dividend:

\(\sf\:\frac{{-4x^2}}{{x}} = -4x \\ \)

\(\sf\:(x - 4) \cdot (-4x) = -4x^2 + 16x \\ \)

\(\sf\:(-4x^2 + 6x + 41) - (-4x^2 + 16x) = -10x + 41 \\ \)

Step 7: Bring down the next term from the dividend:

\(\sf\:\frac{{-10x + 41}}{{x - 4}} \\ \)

Step 8: Repeat steps 2-5 with the new dividend:

\(\sf\:\frac{{-10x}}{{x}} = -10 \\ \)

\(\sf\:(x - 4) \cdot (-10) = -10x + 40 \\ \)

\(\sf\:(-10x + 41) - (-10x + 40) = 1 \\ \)

Step 9: There are no more terms to bring down, so the division is complete.

Step 10: Write the final result:

The quotient is \(\sf\:x^2 - 4x - 10\\\) and the remainder is 1.

Therefore, the division of \(\sf\:(x^3 - 8x^2 + 6x + 41) by (x - 4) \\\) is:

\(\sf\:(x^3 - 8x^2 + 6x + 41) ÷ (x - 4) \\ \) \(\sf\:= x^2 - 4x - 10 + \frac{{1}}{{x - 4}} \\ \)

Answer:

-14

4(6-10)+2

6-10 = -4

-4(4)=-16

-16+2=-14

Answer:

The answer is -14.

Step-by-step explanation:

First, you substitute 6 for x.

4(6-10)+2 = -14

Then, you subtract 6 from 10 in the parenthesis.

4(-4)+2= -14

Then, you multiply 4 x -4.

-16+2= -14

Then you add -16 + 2.

-14 = -14

I hope this helped you. If it did, please feel free to rate and press thanks! Have a great day!

It would cost approximately $52.18 to drive from Statesville, NC to Washington, DC with a car that gets 29 miles per gallon on the interstate, considering a gas cost of $3.89 per gallon.

To calculate the time it would take to drive from Statesville, NC to Washington, DC, we can divide the distance of 389 miles by the average speed of 65 mph.

Time = Distance / Speed

Time = 389 miles / 65 mph

Time ≈ 5.98 hours

Therefore, it would take approximately 5.98 hours to drive from Statesville, NC to Washington, DC on interstates with an average speed of 65 mph.

To calculate the cost of driving to Washington, DC, we need to know the number of gallons of gas required for the trip. We can find this by dividing the distance by the car's mileage, which is 29 miles per gallon.

Number of gallons = Distance / Mileage

Number of gallons = 389 miles / 29 miles per gallon

Number of gallons ≈ 13.41 gallons

The cost of gas can be calculated by multiplying the number of gallons by the cost per gallon, which is $3.89.

Cost = Number of gallons * Cost per gallon

Cost ≈ 13.41 gallons * $3.89/gallon

Cost ≈ $52.18

Therefore, it would cost approximately $52.18 to drive from Statesville, NC to Washington, DC with a car that gets 29 miles per gallon on the interstate, considering a gas cost of $3.89 per gallon.

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Answer:

36

Step-by-step explanation:

a) The distance from point P to the pole  is: 6.2 m

b) The height of the Pole is: 6.2 m

The triangle attached shows us the triangle formed as a result of the given word problem about angle of elevation and distance and height.

Now, we are given that:

The angle of elevation of the top of the pole =  45°

Angle of elevation of the top of the pole = 58°.

|PQ|= 10m

a) PR is distance from point P to the pole and using trigonometric ratios, gives us:

PR/sin 58 = 10/sin(180 - 58 - 45)

PR/sin 58 = 10/sin 77

PR = (10 * sin 58)/sin 77

PR = 8.7 m

b) P O can be calculated with trigonometric ratios as:

P O = PR * cos 45

P O = 8.7 * 0.7071

P O = 6.2 m

Now, the two sides of the isosceles triangle formed are equal and as such:

R O = P O

Thus, height of pole R O = 6.2 m

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Answer:

-8b^2 + 4b

Step-by-step explanation:

To simplify the expression (-6b^2 2b-1) + (-2b^2 + 4b), we need to combine like terms.

First, let's distribute the negative sign to the terms inside the first set of parentheses:

(-6b^2) + (-2b^1) = -6b^2 - 2b^1

Now let's combine the terms inside the second set of parentheses:

(-2b^2) + (4b) = -2b^2 + 4b

Finally, let's add the two expressions:

(-6b^2 - 2b^1) + (-2b^2 + 4b) = -6b^2 - 2b^1 - 2b^2 + 4b

Simplifying, we get:

-8b^2 + 4b = -8b^2 + 4b

The final simplified expression is: -8b^2 + 4b.

The equation that represents the cost, c, of n sets is c = 63.74n

from the question, we have the following parameters that can be used in our computation:

Each volleyball set costs $63.74.

Let the total number of sets be n

So we have

Cost of n = 63.74 * n

This gives

c = 63.74n

Hence, the equation is c = 63.74n

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The value of the S & P 500 before the open on June 22nd, 2010 is 1,113.20 points.

The percent change points is -1.61%/

The value of the S & P 500 before the open would be higher than the value at the close of June 22nd, 2010. This was because the index declined over the day.

Value before the open of June 22nd, 2010 = value at the close + change

17.89 + 1095.31 = 1,113.20 points

Percentage change = (change in points / points before open) x 100

(-17.89 /1,113.20) x 100 = -1.61%

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Answer:

7 Ways

Step-by-step explanation:

Have a Nice Day!

Answer:

64 ways

Step-by-step explanation:

Basic possibility table/using math, and calculating

Answer:74

Step-by-step explanation:

DCB arc's degree is equal to 2*<DAB so,

arc DCB=106*2=212 degrees

cicle is 360 degrees total, so,

360-212=148 degrees

and it is arc DAB which is arc for <DCB and same rule applies here:

arc DAB=2*<DCB

<DCB=DAB/2=148/2=74

The expected value  that  this broker assign to this stock's end-of-the-year price is $58.50.

Using this formula

Expected value=Stock worth at $50+ Stock worth at $60+ Stock worth at $70

Where:

Stock worth at $50=40% chance

Stock worth at $60=35% chance

Stock worth at $70=25% chance

Let plug in the formula

Expected value=(40%×$50)+($35%×$60)+($25%×$70)

Expected value=$20+$21+$17.5

Expected value=$58.50

Inconclusion the expected value  that  this broker assign to this stock's end-of-the-year price is $58.50.

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Answer:

Given that f(x) contains the discrete points of{(0, 3), (1, 4), (2, 0), (3, 1), (4, 2)}, the value of (f of)(0) is5.

Answer:

Step-by-step explanation:

Let h and s represent the numbers in the House and Senate, respectively. Then we have ...

  h + s = 88

  h - s = 54

Subtracting the second equation from the first gives ...

  (h +s) -(h -s) = (88) -(54)

  2s = 34 . . . . . simplify

  s = 17 . . . . . . . divide by 2

  h = 88 -17 = 71 . . . . find the other value using the sum equation

There were 71 females in the House of Representatives, and 17 females in the Senate.

Fundamental Trigonometric Identities are listed below:

Fundamental Trigonometric Identities can be defined as the basic identities or variables that can be used to proffer solutions to any problem relating to angles and trigonometry.

In conclusion, A few Fundamental Trigonometric Identities are listed above.

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The area of the shaded region of the rectangle is approximately 573.92 square feet.

The figure in the image is that of a rectangle with a semi-circle inscribed in it.

The area of rectangle is expressed as:

Area = Length × Width

The area of semi-circle is expressed as:

Area = 1/2 × πr²

To determine the area of the shaded region, we simply subtract the area of the semi-circle from the area of the rectangle.

Area of shaded region = area of rectangle - area of semi-circle

Area of shaded region = ( Length × Width ) - ( 1/2 × πr² )

From the image:

Length = 40 ft

Width = 20 ft

Radius r = 12 ft

Plug the values into the above formula:

Area of shaded region = ( Length × Width ) - ( 1/2 × πr² )

Area of shaded region = ( 40 × 20 ) - ( 1/2 × 3.14 × 12² )

Area of shaded region = ( 800 ) - ( 226.08 )

Area of shaded region = 573.92 ft²

Therefore, the area is approximately 573.92 square feet.

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Answer: 2/7 of a gallon (in decimal it’s 0.286)

Step-by-step explanation: This one’s really easy.

2/7 of 1 gallon. Checking: so that if you multiply it by 7 it equals to 2

The gallon he used each hour he works is 2/7.

What is unit rate?

A rate is a ratio that is used for comparing two different kinds of quantities which have different units. On the other hand, the unit rate illustrates how many units of quantity correspond to the single unit of another quantity.

The common examples used are:

Distance per second

Kilometer per hour

Meter per second

Earning per month

Given,

he used 2 gallons liquid for every 7 hours he works.

gallons used for per hour = 2/7

Hence, He used 2/7 gallons per hour.

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The algebraic rule for the transformation is B' = (Bx + 15, By - 12)

Given data ,

To determine the algebraic rule for the transformation from point B to point B', we need to find the equations that relate the coordinates of the preimage point B to the image point B'.

Let's denote the translation amounts in the x-direction and y-direction as (dx, dy). The coordinates of B' can be obtained by adding these translation amounts to the coordinates of B:

B' = (Bx + dx, By + dy)

Given that B is located at (5, -4) and B' is located at (20, -16), we can calculate the translation amounts:

dx = 20 - 5 = 15

dy = -16 - (-4) = -12

Hence , the algebraic rule for the transformation is B' = (Bx + 15, By - 12)

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Answer:

2=a

7=b

Step-by-step explanation:

a+14=6a+4

-a  

14=5a+4

-4

10=5a

/5

2=a

9b+8=10b+1

-1

9b+7=10b

-9b

7=1b

/1

7=b

Answer:

WZ=7

XY=7

WX=2

ZY=2

Step-by-step explanation:

9b+8=10b+1

Take 9b to 10b and 1 to 8 to form the equation

8 - 1 =10b - 9b

7 = b

a + 14 =6a + 4

Take a to 6a and 4 to 14 to form the equation

14 - 4 =6a - a

10 =5a

Simplify the answer

10/5 =5a/5

Five divide by five 1 and 10 divided by 5 is 2

Answer is therfore

2 = a

The final parametric equations describing the plane's motion are:

x(t) = 0 + (425 km - 0) * t = 425t

y(t) = 0 + (736.6 km - 0) * t = 736.6t

z(t) = 1650 meters

where t varies from 0 to 1.36 hours.

Let's set up a coordinate system with the origin at sea level beneath Denver.

We'll use the x-axis to point east, the y-axis to point north, and the z-axis to point upward.

The plane starts directly above Denver at an altitude of 1650 meters.

We can represent this as the initial point P₀(0, 0, 1650).

The plane then flies to Bismark, which is about 850 km in the direction 60° north of east from Denver.

Let's represent the position of Bismark as the point P₁(x, y, z), where x and y are the horizontal displacements (east and north, respectively), and z is the altitude above sea level.

Since the plane flies at a constant height of 7500 meters above the line joining Denver and Bismark, the altitude z remains constant at 7500 meters.

Let's calculate the horizontal displacements x and y:

The eastward displacement x can be found using the cosine of the angle (60°) and the distance to Bismark (850 km):

x = 850 km * cos(60°) ≈ 425 km

The northward displacement y can be found using the sine of the angle (60°) and the distance to Bismark (850 km):

y = 850 km * sin(60°) ≈ 736.6 km

Now, we can write the parametric equations for the plane's motion:

x(t) = x₀ + (x₁ - x₀) * t

y(t) = y₀ + (y₁ - y₀) * t

z(t) = z

where:

x₀ = 0 (initial x-coordinate at Denver)

y₀ = 0 (initial y-coordinate at Denver)

z = 1650 meters (altitude above sea level at Denver)

x₁ = 425 km (x-coordinate at Bismark)

y₁ = 736.6 km (y-coordinate at Bismark)

The parameter t represents the time in hours.

The plane's motion is constant, so t will vary from 0 to the time it takes to travel from Denver to Bismark at a speed of 625 km/hour.

To find the time it takes, we can use the distance formula:

Distance = Speed * Time

850 km = 625 km/hour * Time

Time = 850 km / 625 km/hour ≈ 1.36 hours

A plane directly above Denver, Colorado, (altitude 1650 meters) flies to Bismark, North Dakota (altitude 550 meters).

It travels at 625 km/hour at a constant height of 7500 meters above the line joining Denver and Bismark. Bismark is about 850 km in the direction 60∘ north of east from Denver.

Assume the origin is at sea level beneath Denver, that the x-axis points east and the y-axis points north, and that the earth is flat. Measure distances in kilometers and time in hours.

So, the time it takes for the plane to travel from Denver to Bismark is approximately 1.36 hours.

The final parametric equations describing the plane's motion are:

x(t) = 0 + (425 km - 0) * t = 425t

y(t) = 0 + (736.6 km - 0) * t = 736.6t

z(t) = 1650 meters

where t varies from 0 to 1.36 hours.

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The number of days which it would take 1000 people to sign the petition as required in the task content is; 4.35 days.

It follows from the task content that the number of days which it would take Jan to get 1000 signatures on the petition be determined.

Since it is given in the task content that 230 people sign the petition each day.

It therefore follows from proportion that the number of days needed for 1000 people to sign the petition is;

= 1000/230

= 4.3478 days.

Hence, the number of days which it would take 1000 people to sign the petition is approximately; 4.35 days.

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Answer:

I think its answer A I think so

Answer:

40

Step-by-step explanation:

P=2(l+w)

2·(10+10)

          =40

Answer:

3/7 is the slope and -5 is the y intercept

Step-by-step explanation:

y=3/7x-5

The equation is written in slope intercept form

y = mx+b where m is the slope and b is the y intercept

3/7 is the slope and -5 is the y intercept

Answer:

B

Step-by-step explanation:

The slope is always the coefficient of the x value in the linear equation. And the y intercept is the constant in the equation.

I need the table to help you with the answer. wish I could help.

Answer:

\(y=-\frac{1}{5} x-1\)

Step-by-step explanation:

Hi! Welcome to brainly!

So slope intercept form - y = mx + b

where m = slope and b = y intercept

First lets find the y intercept

The y intercept is at (0,-1)

B would equal the y value of the y intercept so b = -1

now lets find the slope

To do so we can pick 2 points on the line and use the slope formula

\(m = \frac{y_2-y_1}{x_2-x_1}\)

the points can vary but i chose the points (5,-2) and (10,-3)

having found the points we plug them into the formula

\(m = \frac{-3-(-2)}{10-5} \\-3-(-2)=-1\\10-5=5\\m=-\frac{1}{5}\)

now that we have found all of the information we plug the values into the equation and get that the answer is

\(y=-\frac{1}{5} x-1\)

Answer:2^1 × 3^2 × 13^1

Step-by-step explanation:

Answer: A, 4 inches.

Step-by-step explanation: 36 divided by 9 is 4.

The cost of each pound of grass seed is $6.

A graph of the solution for the cost of each pound of grass seed is shown below.

In order to determine the cost of each pound of grass seed, we would assign a variable to the cost of each pound of grass seed and then translate the word problem into an algebraic linear equation.

Let the variable x represent the cost of each pound of grass seed.

Since Lori bought 3.6 pounds of grass seed and she was charged $22.90, including a tax of $1.30, an algebraic linear equation that best represent this situation is given by;

3.6x + 1.30 = 22.90

3.6x = 22.90 - 1.30

3.6x = 21.60

x = 21.60/3.6

x = $6.

In conclusion, we would sue an online graphing calculator to plot the solution for the cost of each pound of grass seed as shown in the image attached below.

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The solution is: Piece-wise function

f(x)=x+6 , x≤1

f(x) = x^2 + 3 , x>1, the following functions is graphed below.

Option C is correct.

Explanation:

We are given a graph of piece-wise function which break at x=1

We need to choose correct option for graph.

Function is break at x=1.

We will get two function

For x≤1 and x>1

As we can see x≤1, graph is linear and x>1 graph is parabolic.

Equation of linear graph, x≤1

Take two point of graph (0,6) and (-6,0)

Equation of line:

y-y1/y2-y1 = x-x1/x2-x1

y = x+1

f(x)=x+6 , x≤1

Equation of parabolic graph, x>1

f(x) = x^2 + 3

Piece-wise function

f(x)=x+6 , x≤1

f(x) = x^2 + 3 , x>1

Please see the attached figure.

Hence, The option C is correct.

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