Water leaking onto a floor forms a circular pool. The circumference of the pool increases at a rate 24 cm/min. How fast is the area of the pool increasing when the radius is 5 cm

the value of x would be 22/3 after simplification.

The acts or process of simplifying something such that it is simpler to accomplish or understand, or the item that is the consequence of such simplifying: The group offers suggestions on how to make trade procedures simpler. In mathematics, we generally use the PEMDAS method to simplify the values.

Given, the equation in the form of x is  3/4(x−8)= −1/2

For the value of x

3/4(x−8)= −1/2

multiply by 4 on both sides

3(x - 8) = -2

divide by 3 into both the sides

x - 8 = -2/3

add 8 on both sides

x = -2/3 + 8

x =  22/3

therefore, the value of x for the given equation 3/4(x−8)= −1/2 is 22/3.

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In each shape there are 4 wholes hence the answer is yes.

A fraction is referred to as the portion of a whole in mathematics. There are two components to a fraction: a numerator and a denominator. The numerator is the number at the top, and the denominator is the number at the bottom.

13a. There are 4 wholes, hence the answer is yes.

13b. Every whole is divided into 2 parts hence the total number of equal parts is 4 *2 = 8. Hence the answer is yes.

13c. The answer is yes.

13d. No

13e. No

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The  polynomial Y⁴+ 4y²+ 5 does not have zeroes.

Polynomials are an essential component of the "language" of mathematics and algebra. They are used to express numbers as a result of mathematical operations in nearly every field of mathematics. Polynomials can also be used as "building blocks" in other kinds of mathematical expressions, such as rational expressions.

Polynomials can be used to represent a wide range of everyday mathematical processes. A polynomial can be formed by adding the costs of items on a grocery bill. A polynomial can be used to calculate the distance travelled by a vehicle or object. Polynomials can be used to calculate the perimeter, area, and volume of geometric figures. These are just a few of the many uses for polynomials.

We know that,   (a +b)² = a² + b² + 2ab

Here given that,

⇒ y⁴ + 4y² + 5 = 0

⇒ y⁴ + 4y² + 4 + 1 = 0

⇒ (y² + 2)² + 1 = 0

Because the first term is a square, the expression (y² + 2)² + 1  will never be zero for any value of y.

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Using PEDMAS to solve the mathematical expression given, the value is 2

PEMDAS stands for Parentheses, Exponents, Multiplication, Division, Addition, Subtraction. It is an acronym used to remember the order of operations in math problems. It is also sometimes referred to as Order of Operations.

In this problem, we will need to use and apply the rules of PEMDAS.

We will need to break this into different components and then bring them together afterwards.

[(3/5 + 0.425 - 0.005) ÷ 0.1] / [30.5 + 1/6 + 3(1/3)] + [6(3/4) + 5(1/2)] / [(26 ÷ 3(5/7)] - 0.05

This becomes ;

[10.2 / 34] + [12.25 / 7] - 0.005

We can further resolve this into

2.05 - 0.005

And then we just subtract the values from one another

2.05 - 0.005 = 2

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The equation for the linear model in the scatter plot is Y = -2x + 56.

To calculate this equation, we need to find the slope (m) and the y-intercept (b). The slope is calculated with the formula m = (y2 - y1) / (x2 - x1), where x and y represent the coordinates of two points on the graph.

The two points closest to the line in the scatter plot are (2, 48) and (4, 52). Substituting these values into the formula gives us m = (52 - 48) / (4 - 2) = 4/2 = 2.

The y-intercept is the point where the line crosses the y-axis. To find it, we need to substitute the slope and one point's coordinates into the equation y = mx + b. For our equation, we will use the coordinates (2, 48). Substituting these values into the equation gives us 48 = 2x + b, and solving for b gives us b = 48 - 2(2) = 44.

Therefore, the equation for the linear model in the scatter plot is Y = -2x + 56.

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Spiders are arachnids with eight legs, as do all arachnids. Spiders differ from insects in that they have only six legs.

Crabs and prawns are also members of the phylum Arthropoda, which includes spiders. Spiders walk on eight legs, but they also have two additional legs that they utilise as hands. The front legs are called pedipalps, or palps for short.

Proteins are secreted by glands on spiders, which aid in the formation of the web. For a number of objectives, including prey capture, prey detection, tunnel lining, egg sacs, and prey wrapping, spiders can create a variety of webs or silks.

Spiders are venomous carnivores who hunt their prey with poison.In Everglades National Park, arachnids such as spiders, scorpions, mites, ticks, whip scorpions, and pseudoscorpions are all common.

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Answer: 1/4

Step-by-step explanation:

Method 1

this method only works when there is a visual graph, but you can oick 2 points. then go to the point farthest to the left ide of the graph. then count up to be on the same y coordinate as the other point. then count over to be on the same x point, hence 1/4 (up 1 over 4)

Method 2

You can also pick 2 points, and put them into this formula to find slope ([tex]\frac{x2-x1}{y2-y1} }[/tex] then you plug in so the point farthest left would be x1 and y1 and the other point would be y1 and y2 so when you plug in and solve you get 1/4

Answer:

Step-by-step explanation:

rise/run

=1/4

Its equation in the slope-intercept form will be y = -3 because the y coordinates of both points are equal.

Given points in terms of coordinates so let's try to understand what are coordinates.

Coordinates are a pair of integers (Cartesian coordinates), or sporadically a letter and a number, that identify a certain place on a grid, also referred to as a coordinate plane. The x-axis (horizontal) and y-axis(vertical) are the two axes that make up a coordinate plane. (Telling children that the x-axis crosses because "x" is a cross helps them remember which of these is which.)

We have total 4 coordinates

First Coordinate both x and y are positive.

Second Coordinate x is negative and y is positive.

Third Coordinate both x and y are negative.

Fourth Coordinate x is positive and y is negative.

Point A is (14, -3)

Point B is (-10, -3) both have the same y coordinate.

So line AB is parallel to the x-axis.

The formula for the equation in the slope-intercept formula is

y = mx + c.

m is the slope of the line and c is the intercept on the y-axis.

Line AB is parallel to the x-axis the equation is y = -3.

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Assuming the bags are filled at a constant rate, the average time it takes to fill one bag of leaves is 5 minutes.

To calculate the average time it takes to fill one bag of leaves, we need to know the total amount of time spent filling bags and divide that by the number of bags filled.

First, we know that the staff works an average of six hours per day. Since mowing and raking typically take four hours, we can assume that the remaining two hours are spent filling bags.

To find out how long it takes to fill one bag, we divide the total time spent filling bags by the number of bags filled. In this case, it would be:

(2 hours) / (24 bags) = 0.083 hours (or 5 minutes)

So the average time it takes to fill one bag of leaves is 5 minutes.

It's important to note that this is an average time and may not reflect the exact time it takes for each bag to be filled. Factors such as the size of the bag, the type of leaves being filled, and the skill level of the staff could all affect the time it takes to fill a bag.

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The solution to the equation is g = 4π² ( L / T² )

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

The formula to determine the time period of a simple pendulum is given by

T = 2π √ ( L / g )   be equation (1)

where L = length of string

g = acceleration due to gravity

On simplifying the equation , we get

Divide by 2π on both sides of the equation , we get

√ ( L / g ) = T / 2π

Squaring both sides of the equation , we get

( L / g ) = T² / ( 2π )²

( L / g ) = T² / 4π²

Now , taking reciprocals on both sides of the equation , we get

g / L = 4π² / T²

Multiply by L on both sides of the equation , we get

g = 4π² ( L ) / T²

On simplifying the equation , we get

g = 4π² ( L / T² )

Therefore , the value of A is 4π² ( L / T² )

Hence , the equation is g = 4π² ( L / T² )

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Answer:

x = - 2 or x = - 4

Step-by-step explanation:

Via completing the square:

x^2 + 6x + 8  = x^2 + 6x + (6/2)^2 - (6/2)^2 + 8

                     = (x + 3)^2 - 3^2 + 8

                     = (x + 3)^2 - 9 + 8

                     = (x + 3)^2 - 1

Since x^2+6x+8=0,

(x + 3)^2 - 1 = 0

(x + 3)^2 = 1

x + 3 = +- sqrt(1)

x + 3 = +- 1

x + 3 = 1 or x + 3 = -1

x = -2 or x = -4

The value of A in A## = ( A - 2 )## if x## = x² - x is 2 Or 3.

Topics in the reasoning part include coding, decoding, and reasoning. One of the most frequently occurring portions in all of the important competitive exams specifically created for employment procedures and higher education is this one. Because Coding-Decoding and Reasoning problems can be difficult for some applicants to complete, they avoid them and lose some quick and simple marks.

Given, x## is defined as x## = x² - x.

Therefore,

A## = (A - 2)##

= (A - 2)² - (A - 2).

= A² - 4A + 4 - A + 2.

= A² - 5A + 6.

Let, A² - 5A + 6 = 0.

A² - 3A - 2A + 6 = 0.

A(A - 3) - 2 (A - 3) = 0.

(A - 3)(A - 2) = 0.

A = 3 Or A = 2.

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In algebra, a symbol is used to denote an unknown numerical value in an equation or algebraic expression.

A variable in mathematics is a letter that is substituted for an unknown integer in equations, expressions, and formulas.

An unknown numerical value in an equation or algebraic expression is represented by a symbol (often a letter) in algebra. A variable is, to put it simply, a quantity that may be altered and is not fixed.

The two primary categories of variables are categorical and numeric. Then, for categorical and numerical variables, respectively, nominal or ordinal and discrete or continuous subcategories are created for each category. This section provides a quick overview of these types.

A.) (x) ≈ 0.572[tex]$$x^4[/tex] − 15.63x³ + 146.273x² − 523.325x + 687.334

Approximately 203 automobiles were produced in 2007, according to estimates.

B.) f(x) ≈ 0.423x³ − 12.463x2 + 123.485x − 223.309

Approximately 178 automobiles were produced in 2007, according to estimates.

C.) f(x) ≈ 0.572[tex]$$x^4[/tex] + 15.63x³ − 146.273x² − 523.325x + 687.334

Approximately 203 automobiles were produced in 2007, according to estimates.

D.) f(x) ≈ 0.423x³ + 12.463x² − 123.485x + 223.309

Approximately 178 automobiles were produced in 2007, according to estimates.

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Number of cars manufactured in 2007 will be equal to 178 or 203 based on quartic model.

A variable in mathematics is a letter that is substituted for an unknown integer in equations, expressions, and formulas.

An unknown numerical value in an equation or algebraic expression is represented by a symbol (often a letter) in algebra. A variable is, to put it simply, a quantity that may be altered and is not fixed.

The two primary categories of variables are categorical and numeric. Then, for categorical and numerical variables, respectively, nominal or ordinal and discrete or continuous subcategories are created for each category. This section provides a quick overview of these types.

A.) (x) ≈ 0.572 − 15.63x³ + 146.273x² − 523.325x + 687.334

Approximately 203 automobiles were produced in 2007, according to estimates.

B.) f(x) ≈ 0.423x³ − 12.463x2 + 123.485x − 223.309

Approximately 178 automobiles were produced in 2007, according to estimates.

C.) f(x) ≈ 0.572 + 15.63x³ − 146.273x² − 523.325x + 687.334

Approximately 203 automobiles were produced in 2007, according to estimates.

D.) f(x) ≈ 0.423x³ + 12.463x² − 123.485x + 223.309

Approximately 178 automobiles were produced in 2007, according to estimates.

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The altitude of the right circular cone is 13.5 inches.

What is volume?

Volume is a term used in mathematics to describe the volume of three-dimensional space occupied by an object or a closed surface. The measurement of volume is done in cubic units, like m3, cm3, in3, etc. Volume is also referred to as capacity on occasion.

Here, the volume of a right circular cone varies jointly as the altitude and the square of the radius of the base

So our equation for volume becomes

V = c*h*r^2

where 'h' is altitude and

'r' is radius of base and

'c' is constant

Putting the values of V, h, r, in the volume equation.

we get,

154 = c*12*3.5*3.5

  c = 22/21

Now we have volume = 77 cu and radius of the base =7/3, so putting the values we get,

 77 = 22/21*h*7/3*7/3

or, h = 13.5 inches

Hence, the altitude of the right circular cone is 13.5 inches.

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The formula for finding the height of an isosceles triangle is h = (2*A)/b, where h is the height, A is the area of the triangle, and b is the base of the triangle.

The formula for finding the height of an isosceles triangle is h = (2*A)/b, where h is the height, A is the area of the triangle, and b is the base of the triangle. To use this formula, the area of the triangle must first be calculated. To do this, multiply the base of the triangle by its altitude, or the perpendicular distance from the base to the vertex opposite it. Once the area is known, the height of the triangle can be calculated by multiplying the area by two and dividing it by the base. This will give the height of the triangle. For example, if a triangle has a base of 5 and an area of 10, then the height of the triangle is (2*10)/5, or 4.

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The 30-60-90 triangle is shaped like half of an equilateral triangle.

A special right triangle with angles 30°, 60°, and 90° is called a 30-60-90 triangle. Since 30° is the smallest angle in the triangle, the side opposite to the 30° angle is always the smallest.

The side opposite to the 60° angle is the longer leg, and finally, the side opposite to the 90° angle is the largest side of the right triangle, also known as the hypotenuse.

30°-60°-90° Triangle Rule:

In a 30-60-90 triangle, we can find the measure of any of the three sides by knowing the measure of at least one side in the triangle. This is known as the 30-60-90 triangle rule.

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The missing information, considering the volume of the cone and the cylinder, is given as follows:

The volume of a cylinder of radius r and height h is given as follows:

Vcy = πr²h.

The volume of a cone is one third that of the cylinder, hence:

Vco = πr²h/3.

At the second row, the volume of the cylinder is three times that of the cone, hence:

40π x 3 = 120π.

Considering the volume of the cylinder and the radius, the height is obtained as follows:

πr²h = 120π

9h = 120

h = 120/9

h = 13.3.

For the third row, we have that the base area is of 36π squared units, hence the radius is obtained as follows:

πr² = 36π

r = 6. (as the base is circular).

Hence the diameter is of 12 units, as the length of the diameter is twice that of the radius.

The volume of the cylinder is three times that of the radius, hence:

3 x 48π = 144π

Meaning that the height is then calculated as follows:

πr²h = 144π

36h = 144

h = 144/36

h = 4.

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The length and width of the rectangle will be 16 centimeters and 13 centimeters, respectively.

Let W be the rectangle's width and L its length.

The perimeter of the rectangle will be defined as the total length of all of its sides. So the rectangle's perimeter will be

Perimeter of the rectangle = 2(L + W) units

The length of a rectangle is 3cm longer than its width. If the perimeter of the rectangle is 58 cm. Then the equations are given below.

L = 3 + W                ...1

2(L + W) = 58

L + W = 29                ...2

From equations 1 and 2, then we have

3 + W + W = 29

2W = 26

W = 13 cm

Then the length of the rectangle will be given as,

L = 3 + 13

L = 16 cm

The length and width of the rectangle will be 16 centimeters and 13 centimeters, respectively.

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The value of y in the equation is y = x / 100.

Subject of the formula is a variable which is expressed in terms of other variables involved in the formula.

Therefore, let's make y the subject of the formula in the equation x = 100y.

Hence, we will find y in terms of x.

Therefore,

x = 100y

divide both sides of the equation by 100

100y  / 100 = x / 100

y = x / 100

Therefore,

y = x / 100

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The cost of filling the cone to its full capacity would be = 189.4 cents

A cone is a three-dimensional figure in geometry that tapers from a flat base (usually a circular base) to a point called a vertex or longitude (which forms an axis through the center of the base).

The formula for the volume of a cone = πr²h/3

Height (h) = 5 inches

Radius (r) = 3 inches

π = 3.14

volume = 3.14 × 3² × 5/3

= 3.15 × 9 × 1.67

= 47.35 in³

But 1 in³ = 4 cents

47.35 in³ = X

Make X the subject of formula;

X = 47.35 × 4 = 189.4 cents.

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The number of subscriber is increasing by factor 1,12 every month. The number of subscribers m months since the beginning of the year can expressed by the growth model equation S(m) = 150 . e^(0.12m)

The problem can be solved using exponential growth model.

1) The relation between growth rate and doubling time is given by:

doubling time = 70 / growth rate

In this case, doubling time = 6 months.

Hence,

growth rate = 70/6 = 11.67% = 0.1167 ≈ 0.12

Growth factor is defined as:

Growth factor = 1 + growth rate

                       = 1 + 0.12 = 1,12

2) The growth model of the number of subscribers is given by:

S(m) = So . e^(r.m)

Where:

S(m) = number of subscriber after m months

So= initial number of subscriber

r = growth rate

t = time period

Substitute So = 150 and r = 0.12

S(m) = 150 . e^(0.12m)

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The proportion that is solved correct using cross products is given as follows:

4/6 = 12/18 = 4x18 = 6x12

A proportion represents a fraction of a total amount, hence it is written as follows:

p = x/y.

In which the terms are given as follows:

For cross products, we have two proportions that are equal, hence the numerator of the first fraction multiplies the denominator of the second fraction, while the denominator of the first fraction multiples the numerator of the second fraction.

The proportion in this problem is given as follows:

4/6 = 12/18.

Hence the cross product is applied as follows:

4 x 18 = 6 x 12

72 = 72 (which is a true statement).

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The graph that is not a straight line does not represent a direct variation.

Direct variation of a quantity {y} with respect quantity {x} means that the value of {y} increases as the the value of {x} increases. Mathematically -

y = Kx

K = y/x

where -

{K} is scale factor.

Given are the graphs representing direct variation.

Direct variation is represented by the equation -

y = kx

The graphs representing the direct variation are straight lines. Since all the graphs are not given, any graph that is not a straight line does not represent a direct variation.

Therefore, the graph that is not a straight line does not represent a direct variation.

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[tex]x^2[/tex] - (b+c)x +bc=0  is the quadratic equation whose roots are b,c.

If the roots of a quadratic equation are given, the equation can be written by factoring the equation using the roots.

Given the roots, let's say r1 and r2, the quadratic equation can be written as (x - r1)(x - r2) = 0.

Expanding the above equation x^2 - (r1 + r2)x + r1r2 = 0

Therefore, if the roots of a quadratic equation are given as r1 and r2, the quadratic equation can be written as:

x^2 - (r1 + r2)x + r1r2 = 0

since we are given that the root of the equation are b,c;

so r1=b,r2=c;

putting the value in the above equation we get the equation with b and c as root:

[tex]x^2[/tex] - (b+c)x +bc=0

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Complete question :

The coefficient b and c in the equation [tex]x^2+bx+c[/tex] is also root of another equation where c≠0 .

please write the equation

Answer: To find an equation of the line that passes through the point (-5,-6) and is parallel to the line 4x−5y=35, we can use the fact that two lines are parallel if and only if they have the same slope.

The slope of the line 4x−5y=35 is -4/5. Therefore, we can find an equation of the line that passes through (-5,-6) and is parallel to 4x−5y=35 by using the slope-intercept form of a linear equation, y = mx + b, where m is the slope of the line and b is the y-intercept (the point where the line crosses the y-axis).

Substituting the values into the slope-intercept form, we get:

y = (-4/5)x + b

To find the value of b, we can substitute the coordinates of the point (-5,-6) into the equation:

-6 = (-4/5)(-5) + b

-6 = 8/5 + b

-6 - 8/5 = b

-24/5 = b

Therefore, the equation of the line that passes through the point (-5,-6) and is parallel to the line 4x−5y=35 is:

y = (-4/5)x - 24/5

This can also be written as:

y = -4/5x - 24/5

Step-by-step explanation:

So the solution to the system of equations is:

c = 4, d = 1

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, separated by the 'equal' sign.

x ax2 + bx + c = 0 is a quadratic equation, which is a second-order polynomial equation in a single variable. a 0. It has at least one solution since it is a second-order polynomial equation, which is guaranteed by the algebraic basic theorem.

Given equation I is [tex]3c+6d=18[/tex] and equation II is [tex]6c-2d=22[/tex]

We can start by multiplying the first equation by -2 and adding it to the second equation. This will eliminate the d variable:

[tex]-6c - 12d = -36[/tex]

[tex]6c - 2d = 22[/tex]

[tex]0c - 14d = -14[/tex]

solving this we know value of [tex]d=1[/tex]

So we know that d = 1, and we can substitute that into the first equation to find the value of c:

[tex]3c + 6d = 18[/tex]

[tex]3c + 6(1) = 18[/tex]

[tex]3c = 12[/tex]

[tex]c = 4[/tex]

So the solution to the system of equations is:

[tex]c = 4, d = 1[/tex]

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Answer:y=1x-7

Step-by-step explanation:

Answer:

The fraction representing the number of bad oranges can be written as 6/30. This fraction can be simplified by dividing both the numerator and the denominator by 2, which gives us 3/15. This fraction is already in its lowest terms, so 3/15 is the final answer.

Step-by-step explanation:

The probability that the product has a shelf life of at least 1 week and at most 2 weeks is 0.30.

Potential is described by probability. This branch of mathematics deals with the occurrence of a random event. The value's range is 0 to 1. Probability is a concept in mathematics that helps predict the likelihood of certain events. Probability generally refers to the degree to which something is likely to occur.

A standard normal variable with a mean of 0 and a variance of 1 can be created from a normally distributed random variable with a defined mean and variance.

Thus, The probability that the product has a shelf life of at least 1 week and at most 2 weeks is 0.30.

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