Which polynomial function could be represented by the graph below?

If you have three side lengths, you should find the angle opposite the smallest side to determine the lowest angle, the angle opposite the medium-sized side to determine the greatest angle, and the angle opposite the largest side to determine the greatest angle.

Two rays that have a common terminal and are referred to as the angle's sides and vertices, respectively, make up an angle in Euclidean geometry. Two rays can form angles in the plane where they are positioned.

Angles are also produced when two planes intersect.

These are what are known as dihedral angles.

Consequently, if you have three side lengths, you should discover the lowest angle by finding the angle that is opposite the smallest side, the medium-sized angle by finding the angle that is opposite the medium-sized side, and the greatest angle by finding the angle that is opposite the largest side.

Therefore, if you have three side lengths, you should find the angle opposite the smallest side to determine the lowest angle, the angle opposite the medium-sized side to determine the greatest angle, and the angle opposite the largest side to determine the greatest angle.

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All the rational roots of the polynomial f(x) = 20x4 + x3 + 8x2 + x - 12 are 3/4 and -4/5.

We have the given polynomial:

f(x) = 20x4 + x3 + 8x2 + x - 12

All potential polynomial roots are represented by rational numbers, according to the Rational Root Theorem:

x = a/b

Where a is a factor of a constant term

b is the factor of coefficient of leading term

From the given polynomial:

-12 is the constant term and 20 is the coefficient of leading term

The possible factors of -12 are ±1, ±2, ±3, ±4, ±6, ±12

The possible factors of 20 are ±1, ±2, ±4, ±5, ±10, ±20

So the rational roots = (±1, ±2, ±3, ±4, ±6, ±12)/ (±1, ±2, ±4, ±5, ±10, ±20)

Solve for x when the given function is equal to zero

20x4 + x3 + 8x2 + x - 12 = 0

(4x - 3)(5x + 4)(x2 + 1) = 0

So we get:

4x - 3 = 0 or 5x + 4 = 0 or x2 + 1 = 0

x = 3/4, x = -4/5, x =1, x = -1

Hence, the rational roots are x = 3/4, x = -4/5.

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We have the given polynomial:

f(x) = 20x4 + x3 + 8x2 + x - 12

x = a/b

b is the factor of coefficient of leading term

-12 is the constant term and 20 is the coefficient of leading term

The possible factors of 20 are ±1, ±2, ±4, ±5, ±10, ±20

So the rational roots = (±1, ±2, ±3, ±4, ±6, ±12)/ (±1, ±2, ±4, ±5, ±10, ±20)

Solve for x when the given function is equal to zero

20x4 + x3 + 8x2 + x - 12 = 0

(4x - 3)(5x + 4)(x2 + 1) = 0

4x - 3 = 0 or 5x + 4 = 0 or x2 + 1 = 0

x = 3/4, x = -4/5, x =1, x = -1

The exact length of the curve for the function y = ln(1 - x²) is log(5/4) - 1/9

The general formula for the arc length of the curve y on the interval [a, b] is written as,

[tex]s=\int\limits^a_b {\sqrt{1+(\frac{dy}{dx})^2 } } \, dx[/tex]

Here we have given that the function is y = ln(1 - x²)

And the limit is 0 ≤ x ≤ 1/9

When we differentiate the function, then we get the value of y' as,

y' =  1/(1 - x²) × (-2x) = -2x/(1 - x²)

Now, we have to apply the values on the arc length formula, then we get,

[tex]s=\int\limits^{1/9}_0 {\sqrt{1+(\frac{-2x}{1-x^2} )^2 } } \, dx[/tex]

When we simplify this one then we get,

[tex]s=\int\limits^{1/9}_0 {\sqrt{\frac{1+x^4-2x^2+4x^2}{(1-x^2)^2} } } \, dx[/tex]

Now, we have to divide numerator by denominator and expressing using

the rule Dividend/Divisor = Quotient + (Remainder/Divisor)

Then we get the resulting equation as,

[tex]s=\int\limits^{1/9}_0 {-1 + \frac{2}{1-x^2} } \, dx[/tex]

When we apply the limit value, then we get

s = −1/9 + log∣10/8∣−log(1)

When we simplify this one then we get,

s = log(5/4) - 1/9

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Answer:

  (A)  $26

Step-by-step explanation:

You want to know the amount Byron received from the distribution to Alyah, Byron, and Cecil, given Cecil received $40.

Let x represent the amount being distributed, and a, b, c represent the amounts received by Alyah, Byron, and Cecil, respectively.

The given relations tell us ...

  a = 1 + 1/3(x -1)

  b = 6 + 1/3(x -a -6)

  c = x -a -b = 40

Substituting for b gives us ...

  40 = x - a - (6 +1/3(x -a -6)) = x -a -6 -1/3x +1/3a +2 = 2/3x -2/3a -4

  44 = 2/3(x -a) . . . . . . . add 4, factor out 2/3

  66 = x -a . . . . . . . . . multiply by 3/2

Substituting for a gives us ...

  66 = x -(1 +1/3(x -1)) = x -1 -1/3x +1/3 = 2/3x -2/3 = 2/3(x -1)

  99 = x -1 . . . . . . . multiply by 3/2

  100 = x . . . . . . add 1

Then ...

  a = 1 + 1/3(100 -1) = 1 + 99/3 = 34

  b = 6 + 1/3(100 -34 -6) = 6 + 1/3(60) = 26

Byron received $26.

__

Additional comment

Based on results, the "what is left" is the amount after the $1 or $6 distributions are made.

  Alyah: $34, Byron: $26, Cecil: $40, for a total of $100.

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Side-Side-Side (SSS) Theorem; Two triangles are congruent if three sides of one are equal respectively to three sides of the other (SSS=SSS).

Side-Side-Side or SSS is a kind of triangle congruence rule where it states that if all three sides of one triangle are equal to all three corresponding sides of another triangle, the two triangles are considered to be congruent. Two or more triangles are said to be congruent when the measurements of the corresponding sides and the corresponding angles are equal. Let us learn more about the SSS congruence rule, SSS theorem, the formula, and solve a few examples.

The SSS postulate applies to triangles that have the same measurements for corresponding sides. An example would be a triangle that has side lengths 3, 4, and 5 and a triangle that has side lengths 4, 3, and 5

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Thus, total amount of children tickets bought =30 tickets

equation, a declaration of equivalence between two expressions with variable- and/or number-filled expressions. In essence, equations are questions, and efforts to discover a method for answering them have fueled the growth of mathematics.

Here,

The total adults and children ticket bought  = 50

The cost of one children ticket= 10$

The cost of one  adult ticket= 20$

The total spent amount = 700$

let adult be y and children be x

Thus,

equation => x+y=50 and 10x+20y=700

=>x=50-y

=>10(50-y)+20y=700

=>500 -10y +20y =700

=>500+10y =700

=>10y=500-700

=>y=200/10

=>y=20

=>x=50-20=30

=>x=30

Thus, total amount of children tickets bought =30 tickets

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The mean of the data 6 ,7 ,10 ,12, 13, 4, 8 ,12 is 9.

Mean is the average of the given numbers and is calculated by dividing the sum of given numbers by the total number of numbers.

The basic formula to calculate the mean is calculated based on the given data set. Each term in the data set is considered while evaluating the mean. The general formula for mean is given by the ratio of the sum of all the terms and the total number of terms. Hence, we can say;

Mean = Sum of the Given Data/Total number of Data

Mean= 6 +7+ 10+ 12+ 13+ 4+ 8 +12 /  8 = 72/8 = 9

Hence, The mean of the data 6 ,7 ,10 ,12, 13, 4, 8 ,12 is 9.

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Answer:

B, D

Step-by-step explanation:

To change a fraction to a decimal, divide the numerator (number on top) by the denominator (number on the bottom).

To change a decimal number to a percent, multiply the number by 100%.

A. 40/1000 = 0.04 = 4%

No

B. 6/5 = 1.2 = 120%

Yes

C. 50/33 = 1.5151... = 151.51...%
No

D. 1/8 = 0.125 = 12.5%

Yes

E. 1/3 = 0.333... = 33.333...%

No

Answer: B, D

Answer:

6138

Step-by-step explanation:

First, we have to find the population of the city in 2015

6% = 0.06

193,000 times 0.06 = 11580 people increase

We know it is increasing, so we have to add them

193,000 + 11580 = 204580 people in 2015

Now let's find the 3% decrease

3% = 0.03

204580 times 0.03 = 6137.4

So, about 6138 people decrease from 2015 to 2020

The solution of the given system of equations 6x + 2y = 4 , 9x -3 y = 12 is equal to x =1 and y = -1.

As given in the question,

Given system of equations are :

6x + 2y = 4     ____(1)

 9x -3 y = 12   _____(2)

Multiply (1) by 3 and (2) by 2 and add equation (1) and  (2) to eliminate y variable and get the value of variable x ,

18x + 6y = 12

18x - 6y = 24

36x      = 36

⇒x = 36 / 36

⇒ x = 1

Substitute value of x = 1 in the given equation (1) to get the value of variable y,

6(1) + 2y = 4

⇒ 6 + 2y = 4

⇒ 2y = 4 - 6

⇒ y = -1

Therefore, given system of equations 6x + 2y = 4 , 9x -3 y = 12 solution is equal to x = 1 and y = - 1.

The above question is incomplete, the complete question is:

What is the solution of the system of equations 6x + 2y = 4 , 9x -3 y = 12?

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Answer:

7/20

0.35

35%

Step-by-step explanation:

12 year olds: 40%

12 year olds: 25%

11 year olds: 100% - 40% - 25% = 35%

35% = 35/100 = 7/20

35% = 0.35

35% = 35%

The range of the function f(x) = x² - 6x with domain of (-7, -2, 1) is calculated to be (91, 16, -5)

The domain is controlled by the input values. considering the points (-7, -2, 1)

The range is solved using the given function

f(x) = x^2 - 6x

substituting for x in the function

for x = 7

= 7² - 6 * -7 = 91

for x = -2

= -2² - 6 * -2 = 16

for x = 1

= 1² - 6 * 1 = -5

The range is (91, 16, -5)

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The quotient (x3 - 3x2 + 5x - 3) ÷ (x - 1) is x2 - 2x + 3 and remainder becomes zero

What means quotient in math?

Definition of Quotient

The number we obtain when we divide one number by another is the quotient. For example, in 8 ÷ 4 = 2; here, the result of the division is 2, so it is the quotient. 8 is the dividend and 4 is the divisor.

x^3 - 3x^2 +5x -3 / x-1 = x^2 -2x +3

x^3 -+ x^2

------------

0   2x^2 +5x

     2x^2 +2x

  ----------------

       0      3x +3

               3x +3

              ---------

               0    0

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A triangle's area is 1/2(b*h), where b is the base and h is the height. A triangle's base can be any of its sides, and its height is the length of the altitude from the opposite vertex to that base.

The area is the region defined by an object's form. The area of a form is the space covered by a figure or any two-dimensional geometric shape in a plane. The quantity area indicates the extent of a region on a planar or curved surface. Surface area refers to the area of an open surface or the border of a three-dimensional object, whereas area of a plane region or plane area refers to the area of a form or planar lamina.

Here,

The area of a triangle is 1/2(b*h), where b is the base and h is the height. A triangle's base is any one of its sides, and its height is the length of the altitude from the opposite vertex to that base.

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Sales is a term used to describe the activities that lead to the selling of goods or services.

Let x represent the number of eggs that she uses for one batch of brownies.

Let y represent the number of eggs that she uses for one batch of cookies.

Last month, she made 2 batches of brownies and 3 batches of cookies. This means that

2x + 3y = 16 - - - - - - - - - -1

The month before, she baked 1 batch of brownies and 1 batch of cookies, which required a total of 6 eggs. This means that

x + y = 6 - - - - - - - - - - - - - 2

Multiplying equation 1 by 1 and equation 2 by 2, it becomes

2x + 3y = 16

2x + 2y = 12

Subtracting, it becomes

y = 4

Substituting y = 4 into equation 2, it becomes

x + 4 = 6

x = 6 - 4 = 2

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5 (21 – 7) + 7 × 2 and (d) 5 are the expressions with numbers only since they have only numerical constants and the other expressions given involve variables.

What equation contains an expression?

The equal to sign (=) is the best indicator of whether a given problem is an equation or an expression because it indicates that the problem is an equation.

                It is only an expression if there isn't an equal to (=) sign present. It contains data that is used to demonstrate value, such as numbers, variables, and operators.

5 (21 – 7) + 7 × 2 and (d) 5 are the expressions with numbers only since they have only numerical constants and the other expressions given involve variables.

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The true inequality is 4π > 12.

Inequalities are mathematical expressions involving the symbols >, <, ≥ and ≤. Therefore, let's solve the inequalities that is true.

Hence,

[tex]\frac{2\pi }{2} < 3[/tex]

π < 3 (This is false because 3.14 is greater than 3)

4π > 12

divide both sides by 4

π > 3 (This is true.)

π + 6 < 9

subtract 6 form both sides

π < 3 (This is false)

3π - 1 < 8

3π < 9

π < 3 (This is false)

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The candle has burned down  [tex]3 \frac{3}{4}[/tex]  inches after 6.5 hours.

To calculate this, we first need to determine the rate at which the candle burns by dividing the total burn time (11 hours) by the total length of the candle ( [tex]5 \frac{1}{2}[/tex]  inches). This gives us a burn rate of 2 hours per inch.

Next, we can multiply the burn rate by the time the candle has been burning (6.5 hours) to determine how far the candle has burned. This gives us a result of 13 inches, which is equal to [tex]3 \frac{3}{4}[/tex] inches in standard units. Therefore, the candle has burned down  [tex]3 \frac{3}{4}[/tex]  inches after 6.5 hours.

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Answer:

x=4

y= 5

Step-by-step explanation:

6x+y=29

3x-y=7

Let's add them together

9x = 36

x= 4

Then put 4 back in the equation for x

6(4) + y =29

24 + y = 29

y= 5

Answer:

x-intercept: (-21/2,0)

y-intercept : (0,-21)

The parent function of a parabola is y = x².

A function is said to be a parent function if it is expressed in the simplest form and satisfies the definition of a particular type of function.

The simplest function that satisfies the definition of a parabola is given by y = x². It is also called quadratic function.

Its graph passes through the origin (0,0) and lies in first and second quadrant.

One or more parabolas can be easily obtained by transforming the parent function of the parabola.

Therefore, the parent function of parabola is given by y = x².

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The Median for the following data 3 445 712 767 will be 578.5.

One measure of central tendency is the median. The median of a set of numbers is its midway value. It splits a sample of given data into the upper and lower halves. A minimum of half of the observations are above the median and a minimum of half are below it.

When there are exactly even numbers of observations in a data collection, the median can be calculated as follows:

sorting of the sample data in ascending or descending order.

If there are an even number of observations (let's say n), identify the (n/2)nd and [(n/2) + 1] th observations.

The average of the top two observations is the same as the median of the data given (as determined in step 2).

Here n = 4, So [4/2 + (4/2)+1}/2, So the median will be 578.5.

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Answer:

15-11=4ans

123-23=100ans

Answer:

7

Step-by-step explanation:

index of root = 2

exponent = 2

divide both by 2

2:2 = 1 (the root expires)

2:2 = 1 (the exponent expires)

7

There are 19 such integers with 4 as a digit between 1 and 100, including 4, 14, 24, 34, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 54, 64, 74, 84, and 94.

An integer, pronounced "IN-tuh-jer," is a whole number that can be positive, negative, or zero and is not a fraction. Integer examples include: -5, 1, 5, 8, 97, and 3,043. 3.14 and 1*(1/2) are two examples of numbers that are not integers. The collection of whole numbers and their antipodes is known as the integers. The set of integers does not include fractions or decimals. Integers include, for instance, 2,5,0,12,244,15, and 8.

4-digit numbers are ones with only four digits, the first of which must be one or higher and the remaining three of which may be any number between zero and nine. Four-digit numerals include 5693, 1023, and 9825 as examples. The INTEGER data-type stores whole numbers with a precision of 9 or 10 digits, ranging from -2,147,483,647 to 2,147,483,647. Because it is a reserved value, the number 2,147,483,648 cannot be utilized. The INTEGER value is generally used to store counts, amounts, and other data since it is stored as a signed binary integer.

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The two important first steps in data analysis are data cleaning and exploring it, so, option A is correct.

A measure of the relationship between two variables is a correlation. Variables can be related in a number of ways, including linearly, non-linearly, and in other ways. Variables can also have varying degrees of association with one another. The most popular linear coefficient used to determine how closely two variables correlate is called Pearson's correlation coefficient, or PCC.

The steps of data analysis are shown below,

First, define the question. Identifying your purpose is the first stage in any data analysis procedure.

Gathering the data is the second step.

Third step: data cleaning.

The fourth step is data analysis.

Five: Present your findings.

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The value of 4 to the 3rd power =64

According to the power rule of exponents,

am = m times a x a x a

Thus, 43 can be written as 4 × 4 × 4 = 64.

Thus, the value of 4 to the 3rd power i.e., 4^3 is 64

Exponent is the process of representing huge numbers as powers, according to the definition. Exponent, then, is the number of times a number has been multiplied by itself. Using 6 as an example, multiply it by itself four times, or 6 6 6 6. You can write this as 64. In this case, the exponent is 4 and the base is 6.

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The cartesian equation for x = t² and y = 2 + 3t is x = (1/9)y² - (4/9)y + (4/9).

Where the value of A, B, and C are 1/9, - 4/9, and 4/9.

The parameter t that we have

The cartesian equation x = (1/9)y² - (4/9)y + (4/9)

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The third step in sketching the graph of a rational function is "Finding the function's zeros and vertical asymptotes and plotting them on a number line".

What is vertical asymptotes?

A graph's vertical asymptote is a vertical line with the equation x = a, where the graph tends to positive or negative infinity as the inputs get closer to the value of a. A graph's horizontal asymptote is a horizontal line with the equation y = b, where the graph approaches the line as the inputs go closer to ∞ or –∞.

The steps to sketch a graph of rational function:

1. Ensure that the function's denominator and numerator are listed in decreasing order of power.

2. Discover the domain

3. Completely factor the numerator and denominator. Any shared factors between the numerator and denominator should be eliminated. (Once factors have been cancelled, the reduced function is what remains. For all subsequent actions, employ the reduced function.) Skip Step 4 if there are no common factors.

4. Look for any holes

5. Search for any vertical asymptotes.

6. Find the Horizontal Asymptote.

7. Look for any x- and y-intercepts.

8. Locate test points

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