30c^8d^3 - 3bc^6 d^2 + 6c^3 d divided by 12c^2 d (answer in standard form) (polynomial divided by a monomial)

The length of 175 metres and width of 87.5 metres will maximise the area 15312.5 square metres.

We have been given that Farmer Ed has 350 metres of fencing and wants to enclose a rectangle mat plot that borders on a river. Farmer Ed does not fence the side along the river.  

First of all we will make a relevant figure to represent the perimeter of fencing for 3 sides as shown in the attachment.

Since Ed will not fence the side along the river, fencing is needed for 3 sides and the perimeter of the fencing would be x + x + y = 2x + y.

Now we will equate perimeter with 350 as: 2x + y = 350

y=350-2x

We know that the area of the rectangle is width times length.

A = X•Y

Upon substituting the value of y in area equation, we will get:

A = x•(350-2x)

A(x) = 350x -2x²

Now we will find derivative of area function as:

A'(x) = d(350- 2)/dx

A'(x) = 350-4x

Now we will equate derivative with 0 and solve for x as:

0 = 350-4

4x = 350

x = 350/4 - 87.5

Upon substituting x = 87.5 in equation y = 350-2x, we will get:

y = 350 - 2x

 = 350 - 2(87.5)

 = 350-175

y = 175

Therefore, the length of 175 metres and width of 87.5 metres will maximise the area.

on substituting x = 87.5 in area function, we will get:

A(87.5) = 350(87.5)-2(87.5)²

A(87.5) = 30625-2(7656.25)

A(87.5) = 30625-15312.5

A(87.5)= 15312.5

Therefore, the largest possible area enclosed would be 15312.5 square metres.

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—--------- CORRECT QUESTION FORMAT IS GIVEN BELOW —----------

(Q).

Farmer Ed has 350 meters of fencing and wants to enclose a rectangle mat plot that borders on a river. If farmer Ed does not fence the side along the river find the length and width of the plot that will maximize the area. What is the largest area that can be enclosed ?

Answer: A random variable.

Step-by-step explanation:

a numerical description of the outcome of an experiment is called a random variable.

Answer:

the coordinates of the point that partitions the directed line segment from (-6,-2) to (9,-7) into a ratio of 3 to 2 are (0, -4).

Step-by-step explanation:

To find the coordinates of the point that partitions the directed line segment from (-6,-2) to (9,-7) into a ratio of 3 to 2, we can use the following formula:

P = ( (2bx + 3ax)/(2+3) , (2by + 3ay)/(2+3) )

where P is the point we are looking for, (ax, ay) and (bx, by) are the coordinates of the two endpoints of the line segment, and the numbers 2 and 3 represent the ratio in which the line segment is to be divided.

Substituting the given values, we get:

P = ( (29 + 3(-6))/(2+3) , (2*(-7) + 3*(-2))/(2+3) )

= ( (18 - 18)/5 , (-14 - 6)/5 )

= ( 0, -4 )

Therefore, the coordinates of the point that partitions the directed line segment from (-6,-2) to (9,-7) into a ratio of 3 to 2 are (0, -4).

Answer:

x = 24
y - 16

Step-by-step explanation:

Answer:

[tex]\huge\boxed{\sf x = 16, \ y = 24}[/tex]

Step-by-step explanation:

Let the smaller number be x and larger number be y.

x + y = 40 ----------------(1)

x = y - 8 ------------------(2)

Put Eq. (2) in (1)

y - 8 + y = 40

2y - 8 = 40

2y = 40 + 8

2y = 48

y = 48/2

Put y = 24 in Eq. (2)

x = 24 - 8

[tex]\rule[225]{225}{2}[/tex]

(2, -2) does not make the equation y = -5x - 2 true.

Why it is and what is an equation ?

We can check if the point (2, -2) satisfies the equation y = -5x - 2 by plugging in the values of x and y and seeing if the equation is true:

y = -5x - 2

-2 = -5(2) - 2

-2 = -12

Since -2 is not equal to -12, the equation is not true for the point (2, -2). Therefore, (2, -2) does not make the equation y = -5x - 2 true.

An equation is a mathematical statement that shows that two expressions are equal.

It typically consists of one or more variables, constants, and mathematical operations such as addition, subtraction, multiplication, division, exponents, and roots.

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Answer: -25

Step-by-step explanation:

Answer:

Step-by-step explanation:

16

Answer:

3%

Step-by-step explanation:

We know

In a shipment of 700 motors, 21 are defective.

Based on the shipment, what is the probability that a motor is defective?

We take

21 divided by 700, times 100 = 3%

So, the probability is 3%.

Based on the given information, the following statements are true:

1. Line R S is perpendicular to lines A B and C G on the y plane.

2. Line R S is parallel to line D F on the x plane.

3. Lines A B and C G are perpendicular to each other on the x plane.

What is Right angle ?
A right angle is an angle that measures exactly 90 degrees, or a quarter of a complete turn. It is often represented by a small square drawn at the vertex of the angle, as shown in the symbol "∟".

Explanation:

Statement 1 is true because line R S lies in plane Y and is perpendicular to the intersection of planes X and Y, which is represented by the right angle between lines A B and C G in the x plane.

Statement 2 is true because line R S is horizontal on plane Y, and line D G is parallel to line A B on the x plane, so line R S is also parallel to line D F on the x plane.

Statement 3 is true because lines A B and C G are beside each other and do not intersect on plane X, so they must be parallel to each other and perpendicular to line R S in the y plane.

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The multiple of 2 means any number that is completely divisible by 2.

A multiple in mathematics is basically that number which is formed by multiplying a particular number and it is completely divisible by that number.

If we talk about the number 2, then the multiple of 2 will mean that any number that is formed by multiplying 2 into it.

For example, 6 is a number which can be written as 2 x 3.

Here, 3 is multiplying two times and it becomes 6, so, it is a multiple of 2. Also, if any number is appearing in the table of 2 then it is a multiple of 2.

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False. Comparing marginal distributions of two variables only gives information about each variable separately and not their relationship.

Comparing the marginal distributions of two variables only shows the distribution of each variable individually and not their relationship. For example, suppose we have two variables X and Y. If we compare the marginal distributions of X and Y separately, we may see that one variable has a higher frequency of a certain value than the other variable, but this does not necessarily imply that there is a relationship between the two variables. To determine whether there is a relationship, we need to look at the joint distribution of X and Y, which can be displayed in a scatterplot or analyzed using a correlation coefficient.

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Answer: 3.33 repeating

Step-by-step explanation: .

Nominal data have no inherent order or ranking, while ordinal data have categories that have a natural order or ranking.

Nominal and ordinal are two sorts of information that are utilized in measurements and information examination. The primary distinction between them is in the idea of the information.

Nominal information are all out information where the qualities address discrete classes or gatherings, however there is no inborn request or positioning among them. Instances of ostensible information incorporate tones, orientation, conjugal status, or sorts of natural product.

Ordinal information, then again, have a characteristic request or positioning to their qualities. They are straight out information, yet the qualities address a particular request or progressive system. Instances of ordinal information incorporate degrees of training, grades, or rankings of sports groups.

To sum up, ostensible information are portrayed by classes that have no intrinsic request or positioning, while ordinal information have classifications that have a characteristic request or positioning.

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Linear Equation and It's Application in Real Life

In the given problem, it is an application of linear equation and solving word problem about mathematical operation. It is a combination of general mathematics and algebra.

In word problem about time and work, the equation is 1/x + 1/y + 1/z + ... = 1/t, where

x is the amount of time consume by first person

y is the amount of time consume by second person

z is the amount of time consume by third person

t is the amount of time they consume working together.  

In this case, to solve for the amount of work that Rizal can finish the school project alone.

1/x + 1/y + 1/z + ... = 1/t

It can be derived as 1/x = 1/t - (1/y + 1/z + ... ), where x is the amount of work done by Joseph, and y for Maria.

Given

Joseph can finish the chores in 2 hours

Maria can finish the same chores in 4 hours.

Create  mathematical equation using the given formula for work problem.

1/x + 1/y = 1/t, where x = 2 hours, and y = 4 hours

½ + ¼ = 1/t, solve for t

The LCD of 2, 4 and t is 4t, the new equation will be

4t(1/2) + 4t(1/4) = 4t(1/t)

2t + t = 4

3t = 4

t = 4/3

t = 1 1/3 hours

Final Answer

1 1/3 hours to complete the task when they work together.  

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Therefore, 10/12 cups of fruit are required for the dish, which can be expressed as 5/6 cups.

An element of a whole is a portion. The number is represented mathematically as a fraction, where the numerator and denominator are split. Both are numbers in a straightforward fraction. A fraction appears in the sum or base of a complicated fraction. The numerator of a perfect proportion is smaller than the denominator.

Based on the given conditions, formulate: [tex]\frac{2}{4} +\frac{1}{3}[/tex]

Cross out the common factor: [tex]\frac{1}{2}+\frac{1}{3}[/tex]

Rewrite fractions using the Least Common Denominator: [tex]\frac{3+2}{6}[/tex]

Calculate the sum or difference: [tex]\frac{5}{6}[/tex]

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a) The coordinates of G are (3, -4)

b) The name of the line through G and E is y = (-3/2)x + 13/2

(a) Since the line x=1 is a line of symmetry for triangle EFG, we know that G must lie on the same line of symmetry, and hence its x-coordinate should be reflected across the line x=1 from the x-coordinate of E.

The x-coordinate of E is 5, so the x-coordinate of G should be 5-2=3. That is, G has an x-coordinate of 3.

Similarly, since the line x=1 is a line of symmetry, the y-coordinate of G should be the same as the y-coordinate of F, which is -4. Therefore, G has a y-coordinate of -4.

Thus, the coordinates of G are (3, -4).

(b) To find the name of the line through G and E, we can first calculate the slope of the line:

slope = (y2 - y1)/(x2 - x1) = (-4 - 2)/(3 - 5) = -3/2

The line through G and E has a slope of -3/2.

Next, we can use the point-slope form of the equation of a line to find the equation of the line. We can use either point E or point G to write the equation, but it might be easier to use point G since we have already calculated its coordinates.

Using point-slope form with point G and the slope -3/2, we get:

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

Simplifying and rearranging, we get:

y = (-3/2)x + 13/2

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Answer:

Below

Step-by-step explanation:

I will assume this question has messed up syntax and is supposed to be :

x^5  *   x^4   * x    =

x^5   * x^4   * x^1

x^(5 + 4+ 1) =  x^10

Answer:

False

Step-by-step explanation:

This is the  POINT -SLOPE form

Answer: 5:50 PM

Step-by-step explanation:

5:15 PM + 0:35 minutes = 5:50 PM

The Correct answer will be B. f(x) is shifted π/4 units to the left.

The general equation for a sine and cosine curve is y = A sin ⁡ ( x − h ) + k and y = A cos ⁡ ( x − h ) + k , respectively. Similar to other function transformations, is the horizontal shift (also called a phase shift), and is the vertical shift.Changes to the amplitude, period, and midline are called transformations of the basic sine and cosine graphs. Changing the midline shifts the graph vertically. The graph is stretched or compressed vertically depending on the amplitude. The graph is stretched or compressed horizontally depending on the era.

To determine the transformation;

Dim x=t+π/4

so, f(t+π/4)=cos(t+π/4)=g(t)

t+π/4→t:units to the left.

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The area covered by 19, 602 square feet in acres is around 0.45, according to the relation between the two.

As per the known relation between acre and square foot, the two quantities are related through the formula -

1 acre is equal to 43, 560 square feet

Therefore, formula to convert square feet to acre will be -

Amount of area in acres = area covered in square feet/unit equivalent area in square feet

So, rewriting the above mentioned relation.

43, 560 square feet is equal to 1 acre

Thus, 19, 602 square feet will be equal to acres = 19, 602/43, 560

Performing division on Right Hand Side of the equation

The amount of area in acres = 0.45 acres

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n = 10

Her sister is 7 years old subtract that from 31 gets you 24, then double 7 is 14 so subtract 14 from 24, and that gets you the value of 10 which equals 10

In this case, we subtracted 7.5 kg from 4.5 kg and obtained a result of -3 kg.

Subtraction is a mathematical operation that involves taking one number away from another. It can be represented using the "-" symbol, and the number to the left of the symbol is called the minuend, while the number to the right is called the subtrahend.

In this case, we have 4.5 kg as the minuend and 7.5 kg as the subtrahend, which means that we need to take away 7.5 kg from 4.5 kg.

To perform the subtraction, we start by aligning the digits of both numbers in columns according to their place values (i.e., ones, tens, hundreds, etc.).

Since both numbers have the same unit of measurement (kg), we do not need to perform any conversions.

We then begin subtracting the digits in the subtrahend from the corresponding digits in the minuend, starting from the rightmost column and working our way leftwards.

So, it can be written as,

=> 4.5 - 7.5 =  -3 kg.

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So, in response to the above question, we can state that We obtain the inequality following system of inequalities by combining these three constraints:

[tex]x + y \geq 10\\x \leq 7\\y \leq 6[/tex]

An inequality in mathematics is a relationship between two expressions or values that is not equal. Thus, imbalance leads to inequality. An inequality creates the link between two values that are not equal in mathematics. Egality is distinct from inequality. When two values are not equal, most commonly use the not equal sign (). Different inequalities are used to contrast values, no matter how little or large. Many simple inequalities may be resolved by modifying the two sides until the variables are all that remain. But a number of things contribute to inequality: Negative values on both sides are divided or added. Trade off the left and right.

[tex]x + y \geq 10[/tex]

Next, we know that Sam works out his cardiovascular system for no more than 7 hours. Thus, x must be less than or equal to 7. This restriction can be shown by the inequality:

[tex]x \leq 7[/tex]

Finally, we are aware that Sam only devotes a maximum of 6 hours to weight training. This implies that y should be between -6 and -6. This restriction can be shown by the inequality:

[tex]y \leq 6[/tex]

We obtain the following system of inequalities by combining these three constraints:

[tex]x + y \geq 10\\x \leq 7\\y \leq 6[/tex]

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The distance between points A and B is 11785.2 ft.

In mathematics, an algebraic expression is an expression built up from constant algebraic numbers, variables, and the algebraic operations.

Given is that the plane maintains a constant altitude of 6350 feet. Mei Mei initially measures an angle of elevation of 17° to the plane at point A. At some later time, she measures an angle of elevation of 36° to the plane at point B.

We can write -

tan (17°) = 6350/AC

tan (36°) = 6350/BC

Now, we can write -

AC = 6350/tan (17°)                                ... { 1 }

AC = 20483.9 ft

&

BC = 6350/tan (36°)                              ... { 2 }

BC = 8698.7 ft

We can write -

AB = AC - BC                                        ... { 3 }

AB =  20483.9 - 8698.7

AB = 11785.2 ft

Therefore, the distance between points A and B is 11785.2 ft.

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She can compare the original design with its reflection by plotting both designs on the same graph. If the two designs are identical, then the design is symmetric across the x-axis.

To show that a design is symmetric across a line using coordinates, you can use the following steps:

Here's an example of how to use coordinates to show that a design is symmetric across the x-axis:

Suppose Yuson has a design with three points: A(2, 4), B(4, 6), and C(6, 4), and she drew a dashed line along the x-axis to represent the line of symmetry.

To check if the design is symmetric across the x-axis, she can reflect each point across the x-axis to obtain the following new coordinates: A'(2, -4), B'(4, -6), and C'(6, -4).

She can then compare the original design with its reflection by plotting both designs on the same graph. If the two designs are identical, then the design is symmetric across the x-axis.

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The length of B'C' is 15k.

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

ABCD is the original image and A'B'C'D' is the dilated image.

BC is having length of fifteen units.

We need to find B'C'

Let k be the scale factor.

A dilation is a transformation which preserves the shape and orientation of the figure, but changes its size.

B'C'=kBC

B'C'=15K

Hence, the length of B'C' is 15k.

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Answer:5 feet 4.567 in hes

Step-by-step explanation:

The conversion of one unit i.e., 164 centimetres to other feet is equals to the 5.37 feet.

Unit conversion, is the conversion between different units and measurements of the same quantity done in the process of multiplication or division. In mathematics, conversion is the process of changing a value from one form to another, such as converting a value from inches to millimeters, for distance from miles to kilometers, feet or other units.

How to convert centimeters to feet : One meter is a measure of length and equals approximately 3.28 feet. So, 164 meters = 164 × 3.28 feet

= 537.92 feet --(1)

But we need to convert 164 centimeters to feet. So, change meters to centimeters. As you know, 1 meter = 100 centimeters, so 164 meters = 16400 centimeters --(2). Now from equations (1) and (2),

16400 centimeters = 537.92 feet,

Divide both parts by 100,

=> 164 centimetres = (537.92/100 ) feet

= 5.37 feet

Hence required value is 5.37 feet.

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five-ninths times four equals two and two-ninths.

What is an Algebraic Expression?

An algebraic expression is a combination of numbers, variables, and mathematical operations such as addition, subtraction, multiplication, and division. It is a mathematical phrase that can contain one or more terms separated by mathematical operators.

For example, 3x + 4y - 2z is an algebraic expression that contains three terms: 3x, 4y, and -2z. Each term is made up of a coefficient and a variable, where the coefficient is the numerical value that multiplies the variable.

In algebraic expressions, variables are used to represent unknown values, and the expression can be evaluated by substituting known values for the variables. For instance, if x = 2, y = 3, and z = 1, then the expression 3x + 4y - 2z can be evaluated as 3(2) + 4(3) - 2(1) = 12.

Algebraic expressions can also include exponentiation, roots, and other advanced mathematical operations. They are widely used in mathematics and other fields, such as physics and engineering, to represent relationships between variables and to model real-world situations

To solve five-ninths times four, we multiply 5/9 by 4, which gives:

5/9 x 4 = 20/9

So, the expression "five-ninths times four" is equal to 20/9.

Out of the options given, the answer closest to 20/9 is "two and two-ninths," which can be written as 20/9. Therefore, the answer is:

Therefore, five-ninths times four equals two and two-ninths.

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