(3a²b-4ab²+a²b²)-(2ab²+a²b²+5a²b)

The relationship between the volume of the pyramid inscribed in a cube and the volume of the cube can be determined by comparing both. The volume of cube is three times the volume of the pyramid inscribed in the cube.

Let us say the cube is of side a. Then for a pyramid inscribed in the cube the base is the surface of the cube with dimensions a×a and is of height a.

Volume of a cube of side a is a³.

Vc = a³

Volume of a pyramid of base l×b and height h is given by

V = l×b×h/3

Therefore in this case volume of pyramid is

Vp = (a×a×a)/3

Vp = a³/3

Thus Vp = Vc/3, or we can say Vc = 3Vp.

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The equation for the quadratic function in standard form is 4x² - 16x - 9

From the question, we are to write an equation for the quadratic function in standard form.

From the given quadratic graph,

The roots of the function are -0.5 and 4.5.

That is,

x = -0.5 and x = 4.5

That is,

x = -1/2 and x = 9/2

Therefore,

2x = -1 and 2x = 9

The factors of the quadratic function are (2x + 1) and (2x - 9)

Thus,

We can write that

(2x + 1)(2x - 9) = 0

4x² - 18x + 2x - 9 = 0

Simplify

4x² - 16x - 9 = 0

Hence, the equation is f(x) = 4x² - 16x - 9

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A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain. The usual way to refer to a function is as f(x), where x is the input. A function is typically represented as y = f. (x).

A function can have a "hole" if it is not defined at a certain input value. For example, consider the following function:

f(x) = 1/x

This function has a hole at x=0 because it is not defined at that value. If you try to evaluate the function at x=0, you will get an error or an undefined result.

To determine whether a function has a hole, you can consider the domain of the function, which is the set of all input values for which the function is defined. If there are any values in the domain for which the function is not defined, then the function has a hole at those values.

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Answer: City fans = 33,264 fans

because City fans percentage = 100% - 37% = 63%

Multiplier = 0.63 (63/100)

So City fans = 0.63 x 52800 = 33,264

Hope this helps!

Answer:

Step-by-step explanation:

To find out how many fans at the match support City, we first need to find out how many fans support Rovers. We can do this by multiplying the total number of fans by the percentage of fans who support Rovers:

Total fans supporting Rovers = 52800 fans * 37% = 19296 fans

Since the total number of fans at the match is 52800, and 19296 of those fans support Rovers, then the number of fans who support City is:

Total fans supporting City = 52800 fans - 19296 fans = 33504 fans

Therefore, there are 33504 fans at the match who support City.

It will take at least 39.5 minutes to raise the temperature of the magnesium sample to its melting point.

B. m ≥ 39.5

Formula:

[tex]m ≥ (650 - 255)/10[/tex]

We can use the formula [tex]m ≥ (650 - 255)/10[/tex] to solve for the number of minutes (m) needed to raise the temperature of the magnesium from 255 degrees to the melting point of 650 degrees.

First, we subtract the initial temperature of 255 degrees from the melting point of 650 degrees. This gives us 395.

Then, we divide 395 by 10, which is the number of degrees the temperature is increasing every minute. This gives us the result of 39.5 minutes.

Therefore, the answer is m ≥ 39.5, which means that it will take at least 39.5 minutes to raise the temperature of the magnesium to the melting point.

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The elevation of point A is greater than 3350 feet.

The lines of equal elevation are known as contour lines. In relation to the mean sea level, it reflects the height of any specific site. The crucial elements on a topographic map are those that never cross each other.

Locations A and B are shown on the provided topographic map. By reading the contour and the contour interval, which is shown to be 50 feet, it is clear that Location A is higher up than Location B.

Location A is at a higher contour line, with respect to the contour 3250 feet, mentioned on the left side of location A.

Thus, the height of location A is slightly more than 3350 feet above the mean sea level.

(Refer to the image attached for the topographic map)

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Context lines are those lines that have the same elevation. It reflects the height of any particular site in relation to the average sea level. A topographic map's most important features are those that never cross one another.

The topographic map is displayed with the locations A and B. It is evident that Location A is higher up than Location B by reading the contour and the contour interval, which is indicated to be 50 feet.

In comparison to the contour line of 3250 feet listed on the left side of location A, position A is at a higher contour line.

As a result, position A is higher above the norm by about 3350 feet.

One-half squared is one-fourth. In other words , 1/ 4 is the square is 1/2 .

In mathematics, a square is the result of multiplying a number by itself. The verb "to square" is used to denote this operation. Squaring is the same as raising to the power 2, and is denoted by a superscript 2; for instance, the square of 3 may be written as 32, which is the number 9.

Squaring a number is simply multiplying the value by itself. When you take the square root of a number, you are figuring out what number had to be squared to get the original value.

The square of a number (let x) is given by the formula x².

According to the Question ,

Square of 1/2 is given by = (1/2)²

Since , the square of a number (let x) is given by the formula x².

  (1/2)²

= 1/(2)²

= 1/ 4

= 0.25

Hence, One-half squared is one-fourth. In other words , 1/ 4 is the square is 1/2 .

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Answer:6 quizzes over 1  week

Step-by-step explanation: because if u add 6 + 6+ 6 that 18 so ya

The graph of an inequality is shown below -

The graph of a two-variable inequality is the set of points that describe all solutions to the inequality. The coordinate plane is split in half by a boundary line created by a linear inequality, with one-half representing the solutions to the inequality.

It's a line with a shaded side on one side to show which x-y pairings are the inequality's solutions.

Example -

Let us take a equation, 4x + 8y ≤ -24

Now, solve the above equation in the form of slope-intercept.

4x + 8y ≤ -24

or, 8y ≤ - 4x - 24

or, y ≤ -(1/2)x - 3

Now, the graph becomes according to the slope-intercept form is:

Here we noticed that,

This side of the inequality is shaded below (instead of above) because y is lower than (or equal to) the other side.

Because working with a "or equal to" inequality, draw a solid line rather than a dashed one. Points on the solid line denote locations where the inequality has been solved.

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The expression y-3x-1 is not a direct variation as it does not satisfy the criteria.

It is a mathematical relationship between two variables shown by the form of an equation that says one variable is equal to the other variables that is multiplied by a factor.

Such as y =4x is an equation which express the direct variation between x and y as y is equal to four times of x

The formula for direct variation is given by the equation y = kx.

x and y are variables, k is the constant or factor.

Suppose we examine a number of linear equations and check the ratio of the variables such as x and y ratio. If we find a constant ratio, then it is termed as direct variation.

In the given expression, y-3x-1 that could not satisfy the criteria of direct variation because there is a constant -1 in the expression. And while writing in an equation form, we get y-3x-1 =0

 we never get constant ratio from x and y variables.

hence, this is not a direct variation.

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2+2+2+4+4+2+4 = 20 and It's written in the addition form.

What is addition ?

One of the four fundamental mathematical operations, along with addition, subtraction, multiplication, and division, is addition. This operator is used to combine two or more objects or numbers.

Given,  2+2+2+4+4+2+4

The result can be found by applying addition,

So, 2+2+2+4+4+2+4  = 20

We can also find the sum of the above numbers by applying multiplication,

We've,  2+2+2+4+4+2+4

We will rearrange it in such a way that all the same numbers come together,

So, 2+2+2+2+4+4+4

Now, we can see that the number 2 is occurring 4 times and the number 4 is occurring 3 times,

So, It can be written as,

 (2 × 4) + (4 × 3)

= 8 + 12

= 20.

Hence, We get the same answer in both the cases.

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Rigid body motion is a change that preserves space's geometric characteristics. It is a distance-preserving map or isometric since Euclidean qualities may be described in terms of distance.

The separation between each pair of the geometric object's points is preserved during a rigorous change of the object. In other words, a rigid transformation maintains the object's size and shape. For instance, the rigid transformation of a triangle retains the angles and lengths of the triangle. Imagine a stiff shape distortion, similar to a cardboard shape. The form remains the same after being pushed left and right, rotated, and flipped. When the mold was created using putty, the opposite was true. The thing can then be twisted and stretched. These conversions, nevertheless, are not exact. Stretching a form alters the distances between each pair of its points.

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Answer:

24 6/7

Step-by-step explanation:

​5/14+24 1/2​

24 1/2 = 49/2

5/14 + 49/2

The common factor is 14

5/ 14 + 343 / 14 = 348 /14 = 174 / 7

174/ 7 = 24 6/7

Step-by-step explanation:

1. Convert the mixed number 24 1/2 to an improper fraction by multiplying the whole number (24) by the denominator of the fraction (2) and adding the numerator (1). This gives us an improper fraction of 49/2.

2. Find a common denominator for the fractions ​5/14​ and ​49/2​. The least common multiple of 14 and 2 is 14, so we can rewrite the fractions as ​7/7​ and ​49/14​, respectively.

3. Add the numerators and keep the denominator the same: ​7/7​ + ​49/14​ = ​(7+49)/7​ = ​56/7​

4. Simplify the fraction ​56/7​ by dividing both the numerator and the denominator by their greatest common factor, which is 7. This gives us a simplified fraction of ​8/1​, or 8.

5. The sum of ​5/14+24 1/2​ is equal to 8.

Option B. It represents a nonlinear function because its points are not on a straight line.

What is linear and non-linear functions?

When plotted on a graph, a linear function produces a straight line. Therefore, any non-linear functions are those that are functions. The quickest way to tell if a function is linear or non-linear is probably by graphing it, but we can also tell if a function is linear by looking at its input/output table or equation.

If A(0, 0), B(1, 0) and C(2, 4).

We know that,

If point A,B and C are on a straight line then the slope of AB must be equal to the slope of AC

The formula to calculate the slope between two points is equal to

[tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex]

Find the slope AB

A(0, 0) and B(1, 0)

[tex]m = \frac{0-0}{1-0} = 0[/tex]

Find the slope AC

A(0, 0) and C(2, 4)

[tex]m = \frac{2-0}{4-0} = \frac{1}{2}[/tex]

Slope of AB ≠ Slope of AC

Points A, B and C are not on a straight line.

Hence, it represents a nonlinear function because its points are not on a straight line.

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The equations allow us to compare the slopes of two lines to determine if they are parallel. The lines are parallel if the slopes are the same and the y-intercepts are different. The lines are not parallel if the slopes differ.

Perpendicular lines do meet, but parallel lines do not. They meet at a straight angle, or 90 degrees.Different perpendicular lines have different slopes. There is a distinct difference in the slopes of perpendicular lines.

One line's slope is equal to the other line's slope's negative reciprocal. A number's reciprocal and its product equal one. If m 1 and m 2 are negative reciprocals of one another, then multiplying them together will result in the number 1.

As with parallel lines, we can determine whether two lines are perpendicular by comparing their slopes. The slope of each line below is the negative reciprocal of the other so the lines are perpendicular.

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The slope of one line is equal to the negative reciprocal of the slope of the other line. The product and reciprocal of a number are both one. The outcome of multiplying m 1 and m 2 together if they are the negative reciprocals of one another is 1.

Similar to parallel lines, we can compare the slopes of two lines to determine if they are perpendicular. Each of the lines below has a slope that is the negative reciprocal of the other, making them perpendicular.

An asymptote function is called such because it is a line that a curve approaches but never touches, or "asymptotically" approaches.

An asymptote is a line that a curve approaches but never actually touches. It is called an asymptote because the word comes from the Greek asymptōtos, which means "not falling together." Asymptotes are used in mathematics to describe curves that approach a particular line without ever intersecting it. For example, in a graph of a function, an asymptote is a line that the graph of the function approaches, but never intersects with, as it approaches infinity. Asymptotes are also used to describe straight lines in a plane that approach each other at a certain angle, but never meet. In both cases, the idea is that the line or curve approaches the asymptote, but never actually touches it, thus the name asymptaote.

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Answer:

A. The graph is nonlinear.

D. The graph is a function

E. The graph is increasing in two intervals.

Step-by-step explanation:

        We will review each answer choice to decide on our answer to this question.

✓ A. The graph is nonlinear.

             Since the graph has a change in it's rate of increase, it's nonlinear.

✗ B. The function increases at the same rate.

             As stated below, the rate increases after x = 2 so the function is not increasing at the same rate.

✗ C. The rate decreases after x = 2.

             No, the rate increases after x = 2.

✓ D. The graph is a function.

             Yes, there is only one output for every input, so this is a function.

✓ E. The graph is increasing in two intervals.

             The graph is only increasing in two intervals. These intervals change at x = 2.

Answer:

adult ticket $16

child ticket $12

Step-by-step explanation:

let x = price of adult tix

y = price of child tix

1)  3x + 4y = $96

2) 2x + 3y = $68

Subtract equation 2 from equation 1 to get:

3) x + y = 28

x = 28 - y  (now substitute this into equation 1)

3(28-y) + 4y = 96

84 - 3y + 4y = 96

y = 96 - 84 = 12 (price of child tickets)

Now that you know the value of y, plug it into equation 3:

x + 12 = 28

x = 28 - 12 = 16 (price of adult tickets)

When a system has no solution it is called inconsistent equation

When a system has infinitely many solution it is called consistent and dependent equations

A system is considered to be inconsistent if there is no solution. There is no solution because the line graphs are parallel and not intersecting.

x + 5y = 4   and x + 5y = −2

subtracting gives

0 = -6 no solution  

this is an instance

A consistent system is dependent if there are an endless number of possible solutions. The two equations represent the same line when you graph them. An instance of the situation is

3x + y = 4

−6x − 2y = −8

subtracting gives

9x + 3y = 12 - none eliminates, meaning infinite many solutions

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Answer:

An equation with a degree of 3 is called a cubic function.

Step-by-step explanation:

Functions are named by their degree.

Examples:

[tex]y = ax^2 + bx + c[/tex] is named a quadratic function because it has a degree of 2.

Similarly, [tex]y = ax^3 + bx^2 +cx + d[/tex] is named a cubic function because it has a degree of 3.

The preimage of a value z by the function f are all the values for which the function f(x)=z.

What is preimage?

The preimage of a value z by the function f are all the values for which the function f(x)=z.

According to the given question:

As a simple example, consider the function f(x) = √x . The preimage of 5 is 25; for ℕ(the set of natural numbers) it is the set of all perfect squares in ℕ

PREIMAGES OF SET: The pre Given a function f:A→B , and  D⊆B , the preimage   D  of under   f  is defined as

f−1(D)={x∈A∣f(x)∈D}.(5.4.5)

Hence,  f−1(D)  is the set of elements in the domain whose images are in  C . The symbol  f−1(D)  is also pronounced as “ f  inverse of  D .”

The preimage of a value z by the function f are all the values for which the function f(x)=z.

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3.5% percent does the number of Salmonella cells increase each minutes when y = a(4.7[tex])^{t/45}[/tex].

Given that,

The number of y of Salmonella cells on an egg after t minutes is

y = a(4.7[tex])^{t/45}[/tex]

Here,

y is the number of salmonella cells.

a is the initial number of cells.

t is the time in minutes.

We have to find what percent does the number of Salmonella cells increase each minutes.

We know that,

Take the original function,

y = a(4.7[tex])^{t/45}[/tex]

Take the power of proportionality

y = [a(4.7[tex])^{1/45}]^{t}[/tex]

Evaluating the power

y = [a(4.7[tex])^{1/45}]^{t}[/tex]

y = a(1.035[tex])^{t}[/tex]

y = a(1-0.035[tex])^{t}[/tex]

Therefore, 3.5% percent does the number of Salmonella cells increase each minutes when y = a(4.7[tex])^{t/45}[/tex].

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Let x=(i+1)^2. So the square of given expression will be x= 2i.

A square in mathematics is produced by multiplying a number by itself. To describe this operation, the term "to square" is employed. For example, the square of 3 may be expressed as 3^2, which is the number 9, since squaring is the same as raising to the power 2. Squaring is indicated by a superscript 2.

We'll examine the square of any number, which we'll refer to as "n." The square of the digit "n" is represented by the symbol "n^2," and it can be determined by multiplying n by n.

(i+1)^2= i^2+1+2i

         = -1+1 +2i

         =2i.

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Answer: 3/10 cup of water

Step-by-step explanation:

Take 3 divided by 5 = 0.6

So, we know to get from 3 to 5 we need to times 0.6

So, we take 1/2 times 0.6

1/2 = 0.5

0.5 times 0.6 = 0.3 cup of water

0.3 = 3/10

So, the answer is 3/10 cup of water

3/4 is the lowest form of the given fraction.

if the highest common factor of numerator and denominator if equals to 1. then  that fraction can't be reduced further and is said to be in the lowest form.

so suppose we are having any fraction of the form [tex]\frac{a}{b}[/tex]

the lowest form of the given fraction is  given by   [tex]\frac{x}{y}[/tex]

where x = [tex]\frac{a}{gcd(a,b)}[/tex] , y = [tex]\frac{b}{gcd(a,b)}[/tex]

where gcd is greatest common divisor of a , b

we are given fraction = 3/4

=> a = 3 and b = 4

gcd(3,4) = 1

so x = 3/(gcd(3,4)) = 3

y=  4/(gcd(3,4)) = 4

so the lowest form of 3/4 =  [tex]\frac{x}{y}[/tex]

and x=3 and y=4

and hence lowest form = 3/4

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The median for the next batch of observations is 2.

The median is the value in the middle of a data set, which indicates that 50% of the data points have a value less than or equal to the median, and 50% have a value greater than or equal to the median. The median is the number in the middle of a set of numbers. The median represents the 50th percentile of the set of numbers. In other words, the median is the value in the center of a set of numbers where half are less than the median and half are more than the median.

Here,

given set of observation,

=1,1,2,4,6,8

n=6

median=6/2

=3rd term

=2

The median for following set of observation is 2.

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Answer:

squares : triangles

1:2 or 1/2

Step-by-step explanation:

⭐What is a ratio?

⭐ How can we write a ratio?

For this problem, we can write the ratio of squares to triangles as:

[tex]\frac{2}{4}[/tex], or [tex]2:4[/tex].

But, we can further simplify this ratio.

To simplify the ratio, divide the numerator and denominator or both sides of the colon by the number they are both divisible by.

2 is divisible by 2, and 4 is divisible by 2:

[tex]\frac{2}{4}[/tex]

[tex]\frac{2 /2}{4/2}[/tex]

Simplified is: [tex]\frac{1}{4}[/tex]

[tex]2:4[/tex]

[tex]\frac{2}{2} : \frac{4}{2}[/tex]

Simplified is: [tex]1:4[/tex]

Answer:

no

Step-by-step explanation:

the factors of 6 are

1, 2, 3, 6

that is 6 has 4 factors

Answer:

“If none of the input values are repeated, the relation is a function” because one input must have one output.