the satellite is in the shape of a rectangular prism. which polynomial represents the volume of the satellite? a rectangular prism with length 4 x minus 3 feet, a width of x plus 1 feet, and a height of x plus 2 feet.

Answer: y = x(x+1)(x-4)

Step-by-step explanation:

Answer:

Step-by-step explanation:

Given,y=x^3-3x^2-4x

taking x commonly

y=x(x^2-3x-4)

y=x(x^2+x-4x-4)

y=x[x(x+1)-4(x+1)]

y=x(x+1)(x-4)

Answer:

34 bricks is the greatest amount Mary could have used

Step-by-step explanation:

Answer:

74.90d + 0.13m = Total cost of the car rental

Step-by-step explanation:

Hmmm you didn't give enough information but....

let d represent the number of days

let m represent the number of miles driven

74.90d + 0.13m = Total cost of the car rental

For example Tyee rents the car for 2 days and drives 100 miles

149.8 + 13 = Total cost of the car rental.

$162.8 is the Total cost of the car rental.

Answer:

so im a little confused  3,5203,5203, is not a proper number and there is not enought yards to make a full mile could you reword it?

Step-by-step explanation:

Approximately one full tablespoon of coffee powder is required for each 200 ml cup of coffee. We advise using seven teaspoons of ground coffee to produce a full litre of filter coffee at once.

To create coffee, coffee beans must first be roasted. Coffee is a dark-colored, bitter, and slightly acidic beverage that stimulates individuals due to its high caffeine content. In terms of sales, hot beverages have the largest market worldwide. The roasted beans are ground into tiny particles, frequently steeped in hot water, and then filtered to create a cup of coffee. Despite the fact that coffee is typically served hot, it is frequently served cold or iced. Unroasted green coffee beans are made by separating the seeds from the fruits of the Coffea plant. To produce a cup of coffee, the roasted beans are ground into tiny particles, regularly soaked in hot water, and then filtered. Coffee is commonly served cold or iced even though it is traditionally served hot.

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The different values in the row of the table are: 1. l = 2π²r/ 2160, A = π²r²/ 2160. 2. α = 60/r and sector area A = πr/60.

The sector is essentially a section of a circle, and it may be described using the following three criteria:

The area of a disc that is surrounded by two radii and an arc is known as a circular sector.

The circle is divided into the Major Sector and the Minor Sector by a sector.

The region with a lesser extent is referred to as the Minor Sector, whereas the territory with a larger area is referred to as the Major Sector.

Given that,

Central angle = [tex]\frac{\pi}{6}[/tex].

The arc length is given as:

l = α/360 (2πr)

Where, α is the central angle.

Substitute the value of central angle we have:

l = (π/6)/360 2πr

l = 2π²r/ 2160

The sector area is given as:

A = α/360  πr²

A = (π/6)/360 πr²

A = π²r²/ 2160

Similarly, the arc length is given as:

l = π/3

Substituting the value of l in arc length we have:

π/3 = α/360 (2πr)

α = 360(π)/ 6πr

α = 60/r

The sector area is given as:

A = α/360  πr²

A = (60/r) 360 πr²

A = πr/60

Hence, the different values in the row of the table are: 1. l = 2π²r/ 2160, A = π²r²/ 2160. 2. α = 60/r and sector area A = πr/60.

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If the sum of 3 consecutive even numbers is 114, we can represent the numbers as x, x+2, and x+4.

The sum of the three numbers is:

x + (x+2) + (x+4) = 3x + 6

We know that the sum is 114, so we can set up the equation:

3x + 6 = 114

Subtracting 6 from both sides gives:

3x = 108

Dividing both sides by 3 gives:

x = 36

Therefore, the three consecutive even numbers are 36, 38, and 40.

Answer:

37, 38, 39

Step-by-step explanation:

let the 3 consecutive numbers be

n , n + 1 , n + 2

then summing and equating to 114

n + n + 1 + n + 2 = 114

3n + 3 = 114 ( subtract 3 from both sides )

3n = 111 ( divide both sides by 3 )

n = 37

n + 1 = 37 + 1 = 38

n + 2 = 37 + 2 = 39

the 3 consecutive numbers are 37 , 38 , 39

The ratio of cups of flour to water for 6 batches is 18:6

18:6 = 3:1

The ratio is maintained.

The ratio shows how many times one value is contained in another value.

Example:

There are 3 apples and 2 oranges in a basket.

The ratio of apples to oranges is 3:2 or 3/2.

We have,

Two batches:

The ratio of cups of flour to water.

= 6: 2

= 3:1

Now,

For 1 batch.

The ratio of cups of flour to water.

= 3 : 1

Now,

For m batches.

The ratio of cups of flour to water.

= 3m : 1m

So,

For m = 6

The ratio of cups of flour to water.

= 18 : 6

Thus,

The ratio of cups of flour to water for 6 batches is 18:6.

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The complete question.

For two batches the ratio is 6 cups of flour to 2 cups of water,

This means for every 3 cups of flour, you need 1 cup of water.

The ratio 3:1 is maintained.

Find the ratio for 6 batches

Distributive property is expressed as:

Apply this to the given expression and simplify

The solution of the linear equations y = 2x + 56 and y = 9x will be (8, 72).

The possible value of the variables that satisfy the equation which is known as the solution of the equation.

The equations are given below.

y = 2x + 56       ....1

y = 9x               ....2

From equations 1 and 2, then we have

9x = 2x + 56

7x = 56

 x = 8

Then the value of the variable 'y' is given as,

y = 9(8)

y = 72

The solution of the linear equations y = 2x + 56 and y = 9x will be (8, 72).

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Ten pounds of chopped walnuts would total cost $30.00. That is because 3/4 pound of chopped walnuts costs $3.75, and 10 pounds would be 13.33 times as much.

1. 3/4 pound of chopped walnuts costs $3.75

2. 1 pound of chopped walnuts costs $5.00 (3.75 x 1.33)

3. 10 pounds of chopped walnuts costs $50.00 (5.00 x 10)

To calculate the cost of 10 pounds of chopped walnuts, we need to first calculate the cost of 1 pound of chopped walnuts. We know that 3/4 of a pound of chopped walnuts costs $3.75. To calculate the cost of 1 pound, we can multiply 3.75 by 1.33, which gives us the result of $5.00. We then multiply $5.00 by 10, which gives us the result of $50.00. Therefore, 10 pounds of chopped walnuts would cost $50.00. This is because 3/4 pound of chopped walnuts costs $3.75, and 10 pounds would be 13.33 times as much.

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Equation of line DC is y = -1/2 x - 8

Equation of line AD is y = 2x + 2

Equation of line BC is y = 2x - 8

The equation of the line 2y + x = 4 is arranged in slope intercept form to have

y = -x/2 + 2

The slope is -1/2

with a slope of -/2 and points (0, -8) line DC is written as

y - -8 = -1/2 (x - 0)

y + 8 = -1/2 x

y = -1/2 x - 8

Equation of line AD

line AD is a perpendicular line  to line DC hence the slope is negative reciprocal of the slope of line DC

slope = 2

point A(0, 2) line AD is written as

y - 2 = 2 (x - 0)

y - 2 = 2x

y = 2x + 2

Equation of line BC

line BC is a parallel to line AD hence the slopes are equal

slope = 2

point C (0, -8) line AD is written as

y - - 8 = 2 (x - 0)

y + 8 = 2x

y = 2x - 8

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Answer

Step-by-step explanation:

The addition and subtraction of the fractions by finding the LCD gives:

NUMBER 1: (8y-49) /(y²-49)

NUMBER 2: (x+10) /(2x+8)

NUMBER 3: (7a-2)/10b

NUMBER 4: 1

Least Common Denominator (LCD) refers to the smallest multiple that two or more denominators have in common, and is used in operations involving fractions.

NUMBER 1

y/(y²-49) - 7(y+7) = y/[(y+7)(y-7)] - 7(y+7)

LCD of (y+7)(y-7) and (y+7) is (y+7)(y-7):

                          = [y + 7(y-7)] / [(y+7)(y-7)]

                          = [y + 7y-49)] / [(y+7)(y-7)]

                          = (8y-49) / (y+7)(y-7)

                          = (8y-49) /(y²-49)

NUMBER 2

1/2 + 3/(x + 4) = [1(x+4) + 3*2] /[2(x+4)]

                      = [x+4 + 6] /[2(x+4)]

                      = (x+10) /(2x+8)

NUMBER 3

(a+2)/4b + (a-1)/10b + (a-3)/5b = [5(a+2) + 2(a-1) + 4(a-3)]/20b

                                                 = [5a+10 + 2a-2 + 4a-12]/20b

                                                 = (14a-4)/20b

                                                 = 2(7a-2)/20b

                                                 = (7a-2)/10b

NUMBER 4

x/(x+1) - 1/(x-1) + 2x/(x²-1) = [x(x-1) - 1(x+1) + 2x]/(x²-1)

                                         = [x²-x -x-1 + 2x]/(x²-1)

                                         = (x²-1)/(x²-1)

                                         = 1

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The shortest distance is 5.83 miles as we calculate this by distance formula.

A distance formula is a formula used to find the distance between any two points only if the coordinates are known. These coordinates can be on the x-axis, y-axis, or both. Suppose we have two points, P and Q, in the XY plane. Point P has coordinates (x1,y1) and Q has coordinates (x2,y2). Then the formula for the distance PQ between two points is:

PQ = √([tex](x2 - x1)^{2}[/tex] + [tex](y2-y1)^{2}[/tex])

The school is located 5 miles west of your home the co ordinate is (-5,0)

The playground is 3 miles south of the school so co - ordinate is (0,-3)

shortest distance  = PQ = √([tex](x2 - x1)^{2}[/tex] + [tex](y2-y1)^{2}[/tex])

√([tex]5^{2} +3^{2}[/tex]) = √34

=5.830 miles

And this Question also can be do by right angle triangle method

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Answer:

To solve it, you need to use compound interest. Let me show you how.

Let P be the initial amount that Terry invested. Then after 4 years, the amount in the account is:

P × (1 + 0.037)^4

After withdrawing $2000, the remaining amount is:

P × (1 + 0.037)^4 - 2000

This amount is then moved to another account earning 4.5% p.a. compounded annually. After 3 more years, the amount in the account is:

(P × (1 + 0.037)^4 - 2000) × (1 + 0.045)^3

We are given that this amount is equal to $5635.66. So we can write an equation:

(P × (1 + 0.037)^4 - 2000) × (1 + 0.045)^3 = 5635.66

Simplifying the equation, we get:

P × 1.1597 - 2000 = 5635.66 / 1.1406

Adding 2000 to both sides, we get:

P × 1.1597 = 5635.66 / 1.1406 + 2000

Dividing both sides by 1.1597, we get:

P = (5635.66 / 1.1406 + 2000) / 1.1597

Using a calculator, we get:

P ≈ 5000.01

Therefore, Terry initially invested about $5000.01.

Step-by-step explanation:

The measure of angle NOP is found by solving an equation that is obtained by using the fact that the sum of the angles in a triangle is 180 degrees. The solution is m∠NOP to obtain the answer of 53.13 degrees.

In the problem, we are given a triangle NOP, where \overline{NP} is extended through point P to point Q. We are given the measures of three angles: m∠OPQ, m∠PNO, and m∠NOP.

We are asked to find the measure of angle NOP.To find the measure of angle NOP, we can use the fact that the sum of the angles in a triangle is always 180 degrees. So, we add up the measures of the three angles we know:

m∠OPQ + m∠PNO + m∠NOP = 180

We are given the measures of m∠OPQ, m∠PNO, and m∠NOP in terms of x. We substitute these values and get an equation in terms of x:

(9x-19) + (2x+5) + (3x+16) = 180

Simplifying the left side of the equation, we combine like terms:

14x + 2 = 180

We can then isolate x by subtracting 2 from both sides of the equation:

14x = 178

And then we can solve for x by dividing both sides of the equation by 14:

x = 12.71

Now that we know x, we can use it to find the measure of angle NOP, which is what we were asked to do. We substitute x = 12.71 into the equation for m∠NOP:

m∠NOP = 3x + 16 = 3(12.71) + 16 = 53.13

Therefore, the measure of angle NOP is 53.13 degrees.

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As per the discount, the customer will only need to pay P4,950 on May 12.

Discounts are a common practice in business transactions, where the seller offers a reduction in the price of goods or services as an incentive for the buyer to make a purchase.

The terms of the sale are as follows: 2/10, 1/15, n/30. This means that the customer is entitled to a 2% discount if they pay within 10 days, or a 1% discount if they pay within 15 days. Otherwise, the full amount is due within 30 days.

The customer makes a partial payment of P1,000, which means that they still owe P5,000. However, since the discount is only given upon full payment, the customer is not eligible for any discounts at this point.

Assuming that the customer pays the balance on May 12, they will have taken 11 days to make the payment. Since this is within the 15-day discount period, they are entitled to a 1% discount.

The calculation of the discount is as follows: P5,000 x 1% = P50. Therefore, the customer will only need to pay is calculated as,

=> P5,000 - P50 = P4,950

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Complete Question:

On May 1, RVQ Company sold goods for P6,000 on terms of 2/10, 1/15, n/30. Customer made a partial payment of P1,000 discounts are given only upon full payment of an account. The customer pays the balance on May 12, RVQ will receive on May 12 the amount of

Answer:

0.0256x^4y^4

Step-by-step explanation:

Answer:

So, the rational number is [tex]\frac{52}{12}[/tex] .

Step-by-step explanation:

Let x be the other number.

We know ,

[tex]\frac{7}{36}[/tex] + x = [tex]\frac{5}{6}[/tex]

To find x, we need to convert both to have a common denominator.

So, if we multiply [tex]\frac{7}{36}[/tex] by [tex]\frac{10}{36}[/tex]  ,

[tex]\frac{10}{1}[/tex] × [tex]\frac{7}{36}[/tex] + x = [tex]\frac{56}{10}[/tex]

After multiplication the fraction  [tex]\frac{7}{36}[/tex] becomes [tex]\frac{70}{360}[/tex]  .

[tex]\frac{70}{360}[/tex]+ x =  [tex]\frac{56}{10}[/tex]

Now we have common denominator of 360in both fraction,

Now,

we can simplify the equation ,

[tex]\frac{70}{360}[/tex]  + x = [tex]\frac{56}{10}[/tex]

70 + 360x = 56 × 36

2520 + 360x = 2016

504 + 360x = 2016

360x = 1512

x = [tex]\frac{1512}{360}[/tex]

   =[tex]\frac{52}{12}[/tex]

So, the rational number is [tex]\frac{52}{12}[/tex] .

Answer:

Step-by-step explanation:d = 14t + 21t = 35t

So, after 3 hours, the distance between the boats will be:

d = 35 * 3 = 105 miles

Therefore, the Serenity and the Mystic will be 105 miles apart after traveling for 3 hours.

He earns $184 in commission yesterday on sold 5 watches for $60 each and 4 watches for $40 each.

A sales commission is a sum of money paid to an employee upon completion of a task, usually selling a certain amount of goods or services. Employers sometimes use sales commissions as incentives to increase worker productivity. A commission may be paid in addition to a salary or instead of a salary.

A salesman earns a commission 40%

He sold yesterday 5 watches for $60 each

and, 4 watches for $40 each.

We have to find the how much he earn commission?

Now, According to the question:

Price of 5 watches = 60.00 × 5 = $300

4 watches = $40.00 each

Price of 4 watches = 40.00 × 4 = $160

Total sales made = 300 + 160 = $460

His commission is 40% of the sales = 40% × 460

                                                       = 0.40 × 460 = $184

Hence, He earns $184 in commission.

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A quarterback completed 59% of his passes for a total of 265 yards and 2 touchdowns. The value "59%" is a statistic.

In this scenario, a sample of the quarterback's passes was taken during the championship football game, and the completion percentage was calculated based on that sample. Since the percentage was calculated based on a sample, it is a statistic. A parameter, on the other hand, is a value that describes a characteristic of an entire population. For example, if we were to consider the completion percentage of all quarterbacks in the league, then the mean or median completion percentage would be a parameter because it would describe a characteristic of the entire population of quarterbacks. In summary, statistics are values that describe a characteristic of a sample, while parameters are values that describe a characteristic of a population.

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Complete Question

Determine whether the underlined value is a parameter or a statistic. In a championship football game, a quarterback completed 59% of his passes for a total of 265 yards and 2 touchdowns. Is the value a parameter or a statistic?

The perimeter of the rectangle in the given diagram is: D. 42 units.

In order to determine the perimeter of this rectangle, we would have to find the length of the third side of the right-angled triangle by using Pythagorean's theorem. Mathematically, Pythagorean's theorem is given by this mathematical expression:

a² + b² = c²

Where:

a, b, and c represents the side lengths of a right-angled triangle.

9² + b² = 15²

81 + b² = 225

b² = 225 - 81

b = √144

b = 12 units.

Mathematically, the perimeter of a rectangle can be calculated by using this mathematical expression;

P = 2(L + W)

Where:

P = 2(9 + 12)

P = 42 units.

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The reference angle would be 155 degrees.

An angle's reference angle is the measure of the smallest, positive, acute angle formed by the terminal side of the angle and the horizontal axis.

The positive reference angles have terminal sides that lie in the first quadrant and can be used as models for angles in other quadrants.

The reference angle is acute angle, it must be < 90°.

The terminal side lies in Quadrant II.

The positive measure is:

=180-25

=155°.

And the negative measure is:

= 155-360

= -205°.

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