write a rule that explains the ordered pairs:
(1,2/3), (2,4/9),(3,8/27),(4,16/81),(5,32/243)

The factorise form of the polynomials are

x² + 6x + 9 = (x+3)²

x² - 6x + 8 = (x-2)(x-4)

x² - 4x -32 = (x+4)(x-8)

x² + x -42 = (x + 7)(x - 6)

A number or other mathematical object is factorized or factored when it is written as the product of numerous factors, often smaller or simpler things of the same sort. For instance, factorizing the number 15 as 3*5

A number is swiftly factorized into smaller numbers or factors of the number using the factorization formula. A factor is a number that evenly divides the inputted number.

The subsequent stages aid in the polynomial factoring process. The steps to factorizing a polynomial are listed below.

The polynomials are

x² + 6x + 9 = x² + 3x + 3x + 9 = x(x+3) + 3(x+ 3) = (x+3)(x+3) = (x+3)²

x² - 6x + 8 = x² - 2x - 4x + 8 = x(x-2)-4(x -2) = (x-2)(x-4)

x² - 4x -32 = x² + 4x - 8x - 32 = x(x + 4) -8(x + 4) = (x+4)(x-8)

x² + x -42 = x² + 7x - 6x - 42 = x(x+7) - 6(x + 7) = (x + 7)(x - 6)

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The measure of the variability in the response variable that is not explained by the regression model is known as the residual sum of squares (RSS).

The residual sum of squares (RSS) is a measure of the variability in the response variable that is not explained by the regression model. It is calculated by summing the squared differences between the predicted values (from the regression model) and the observed values of the response variable. RSS is often used to measure the goodness of fit of a regression model and to compare different models. A lower RSS indicates a better fit. RSS can also be used to identify influential observations and outliers that may have a large impact on the regression results.

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During a trip, francine traveled x percent of the total distance at an average speed of 40 miles per hour and the rest of the distance at an average speed of 60 miles per hour. Francine's average speed for the entire trip is(300 - x) / 5

Suppose Francine first averages 40 mph.

Additionally, her second average speed was 60 mph.

Her overall average speed throughout the journey would then be determined as

x/100 * 40 + (1 - x/100) * 60

= 40/100 x + 60 - 60/100 x

= ( 60 - 20/100 x )

= 60 - 1/5 x

= (300 - x) / 5

Consequently, Francine's starting speed is 40 mph. She reaches a speed of 60 mph. She travels at a  (300 - x) / 5mph average speed for entire time.

your question is incomplete but most probably your full question was

During a trip, Francine traveled x percent of the total distance at an average speed of 40 miles per hour and the rest of the distance at an average speed of 60 miles per hour. In terms of x, what was Francine`s average speed for the entire trip?

A. (1800 - x) /2

B. (x + 60) /2

C. (300 - x ) / 5

D. 600 / (115 - x )

E. 12,000 / ( x + 200)

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The answers are a) 25 coaches, b) 24 coaches c) 26 people.

A division is a process of splitting a specific amount into equal parts.

Given that, there are 2546 people waiting for a train, each coach of the train holds 105 people.  

To find the number of coaches needed for 2546 people we will divide total by 105,

Therefore, 2546 / 105 = [tex]24\frac{26}{105}[/tex]

That mean, there are needed 25 coaches for 2546 people.

And, there will be 24 coaches which are completely filled and the last 25th coach, will have 26 people

Hence, the answers are a) 25 coaches, b) 24 coaches c) 26 people.

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According to the given triangle, the value of ∠F is  13.2°

The term triangle is known as the polygon with three sides.

Here we have given that the triangle FGH, f = 1. 2 inches, h = 2. 3 inches and H=26°.

Now, by using the law of sine, we have written the expression as,

=> sin 26°/ 2.3 = sin x°/1.2

where x refers the value of the angle F.

Now, we have to cross multiply the terms then we get,

=> 0.4384/2.3 = sin x°/1.2

=> 1.2(0.4384) = 2.3 sin x°

=> 0.5261/2.3 = sin x°

=> x° = sin⁻¹(0.2287)

=> x° =  13.2°

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Algebraic solutions that appear while we solve rational equations but do not fulfil the original equations are known as extraneous solutions. In other words, whereas unnecessary solutions appear to be ones, they are not.

Equations with variables in the denominators of rational expressions are referred to as rational equations.

In order to answer the rational equation we have to follow the rules:

(1) Rewrite the equation till the variable is removed from the denominators of the rational expressions.

(2) Rearrange the equation and then solve the linear or quadratic one that results.

In order to look for extraneous solutions we have to follow rule:

(1) Resolve the rational equation.

(2) Replace the original equation with the solution(s). If a solution does not fulfil the initial equation, it is superfluous.

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On solving the provided question we can say that in the graph we have been provided with the equation y = 4x^2;  y = 0

Mathematicians use graphs to logically convey facts or values using visual representations or charts. A graph point will typically reflect a relationship between two or more things. Nodes, or vertices, and edges make form a graph, a non-linear data structure. Glue together the nodes, often referred to as vertices. This graph has vertices V=1, 2, 3, 5, and edges E=1, 2, 1, 3, 2, 4, and (2.5), (3.5). (4.5). Statistical charts (bar charts, pie charts, line charts, etc.) graphical representations of exponential growth. a logarithmic graph in the shape of a triangle

here,

in the graph we have been provided with the equation

y = 4x^2

and x = 0

so , y = 0

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245677654333322222

Step-by-step explanation:

44444444444444444

The monthly payment p when the amount borrowed , B is $175,000 is equals to the $1216.25.

We have provide the monthly payment p on a mortgage varies directly with the amount borrowed B. Mathematically, p B

=> p = k × B

where k is Proportionality constant.

First, we have to solve for "k" . If the monthly payment on a 30-year mortgage is $6.95 for every $1000 borrowed"

=> 6.95 = k × 1000

=> k = 6.95/1000 = 0.00695

-Now, we determine a linear function that relates the monthly payment p to the amount borrowed B for a mortgage with the same terms. For this plug the value of k in above equation

=> p = 0.00695× B

which is linear equation. Then calculate the monthly payment p by using above equation :

when the amount borrowed is $175,000

=> p = $175,000× 0.00695

=> p = $1216.25

Hence, required payment is $ 1216.25.

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A proportion is a statement of equality between two ratios. To determine whether two ratios form a proportion, you can use the cross-multiplication method.

This method involves multiplying the numerator of the first ratio by the denominator of the second ratio, then comparing it to the result of multiplying the denominator of the first ratio by the numerator of the second ratio. If the two results are equal, the two ratios form a proportion.

For example, let's look at the pair of ratios 7/9 and 28/36. To determine if they form a proportion, we can cross-multiply:

7/9 * 36 = 252 and 28/36 * 9 = 252

Since 252 = 252, the two ratios form a proportion. Similarly, we can use the cross-multiplication method to check the other pairs and confirm that all of them form a proportion.

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Right triangle ABC with altitude BD down to hypotenuse AC if AC = 25 and BC = 15, then the length of DC is 9.

What is the Pythagorean theorem?

Pythagoras theorem is: In a right angle triangle, the sum of squares of sides is equal to the square of the hypotenuse.

We can use the geometric properties of right triangles and the Pythagorean theorem to solve this problem.

Let's label the length of DC as x. We know that BD is an altitude of the right triangle ABC, which means that it is perpendicular to AC. Therefore, we can use the similar triangles formed by the right triangles ABD and CBD to find the length of x.

In triangle ABD, we have:

BD/AB = AB/AC

Simplifying, we get:

BD/15 = 15/25

Multiplying both sides by 15, we get:

BD = 9

Now, in triangle BCD, we have:

BD/BC = BC/DC

Substituting BD = 9 and BC = 15, we get:

9/15 = 15/x

Multiplying both sides by x, we get:

x = (15 * 9)/15 = 9

Therefore, the length of DC is 9.

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The short leg of a 30 60 90 triangle with hypotenuse of length c is equal to c*√3/2.

c*√3/2 = (hypotenuse length)*√3/2

If the hypotenuse is 10, then the short leg is

10*√3/2

= 10*1.732/2

= 8.66

In a 30 60 90 triangle, the angles are 30°, 60° and 90° and the length of the sides are in the ratio of 1 : √3 : 2. The hypotenuse is always twice the length of the shorter side, so the shorter side can be found by dividing the length of the hypotenuse by 2. The shorter side can also be found by multiplying the length of the hypotenuse by √3/2. For example, if the hypotenuse has a length of 10, then the shorter side has a length of 10*√3/2 = 8.66. So, the short leg of a 30 60 90 triangle with hypotenuse of length c is equal to c*√3/2.

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Using he formula of simple interest, the time it will take for a principal of $125 to grow to $1000 at a rate of 5.5% is 127.27 years

Simple interest is a method of calculating the interest charged on a loan or earned on an investment. It is based on the principle that interest is earned only on the original principal amount and not on any previously earned interest.

Simple interest can be calculated using the following formula:

Simple Interest = (Principal x Rate x Time) / 100

where:

Principal = the original amount of the loan or investment

Rate = the interest rate expressed as a decimal or percentage

Time = the length of time (in years or other time units) for which the interest is being calculated

In this problem, we can define our variables and substitute the values into the formula

S.I = P(1 + rt)

1000 = 125(1 + 0.05*t)

t = 127.27 years

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An expansion has a scale factor of x > 1 (greater than 1). A reduction is a scale factor that is 0 x 1 (higher than 0 but less than 1).

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The probability that at most three grafts fail is 0.98 and the probability that at least two grafts fail is 0.1.

To find the probability that at most three grafts fail, we need to find the sum of the probabilities for x = 0, 1, 2, and 3.

Using the given values of f(x), we get:

P(X <= 3) = f(0) + f(1) + f(2) + f(3)

= 0.7 + 0.2 + 0.05 + 0.03

= 0.98

So the probability that at most three grafts fail is 0.98.

To find the probability that at least two grafts fail, we need to find the sum of the probabilities for x = 2, 3, and 4 and subtract it from 1.

Using the given values of f(x), we get:

P(X >= 2) = 1 - (f(0) + f(1)) = 1 - (0.7 + 0.2) = 0.1

So the probability that at least two grafts fail is 0.1

--The question is incomplete, answering to the question below--

"Grafting the uniting of the stem of one plant with the stem or root of another; is widely used commercially to grow the stem of one variety that produces fine fruit on the root system of another variety with hardy root system: Most Florida sweet oranges grow on trees grafted to the root of sour orange variety. The density for X, the number of 'grafts that fail in series of five trials.

For the values of x = 0, 1, 2, 3, and 4 value of f(x) is 0.7, 0.2, 0.05, 0.03, and 0.01 respectively.

Use f(x) to find the probability that at most three grafts fail; that at least two grafts fail."

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Answer:

x = -3

hope you like it.

The factored form of the given equation is when calculated is found to be x( x - 12) + 4( x -12 ).

The given expression is

  x² - 8x - 48,

= x² -12x + 4x - 48

=x( x - 12) + 4( x -12 )

on further solving this factored form we will get the roots of the equation.

= ( x+4 )( x-12 )

Therefore , the roots of the given equation are ,

x= 12 and x = -4 .

The solution of a given algebraic expression is known as the roots of that equation.

The steps to get the factored form of an equation we can follow the steps, first we will write the factored form using integers in case any factor on the LHS of the equation is equal to  0, the entire expression will be equal to  0.

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Answer:

Step-by-step explanation:

We are given that AC = 22, AB = x + 22 and BC = x + 20, and we are trying to find the value of x.

Since we know that AB + BC = AC, we can use this equation to solve for x.

x + 22 + (x + 20) = 22

Simplifying the equation, we get

2x + 42 = 22

Subtracting 42 from both sides,

2x = -20

and finally,

x = -10

So the value of x is -10

We can check the solution by substituting x = -10 back into the original equation and see if they are true:

AB = x + 22 = -10 + 22 = 12

BC = x + 20 = -10 + 20 = 10

AB + BC = 12 + 10 = 22

So all the equation are true, therefore x = -10

Answer: $460

Step-by-step explanation:

plug in hours to equation

30(6)+25(4)+21(9)= 460 dollars

The probability that the 4 students all sit at least one seat apart from each other is 6÷126, or approximately 0.048.

There are 10 seats in a row and 4 students, so the total number of ways that the students can sit in the row is 10 x 4, or 210. However, we must subtract the number of ways that the students can sit in a row while sitting next to each other.

There are nine ways to choose the first student's seat, eight ways to choose the second student's seat (assuming the first two students are sitting next to each other), seven ways to choose the third student's seat, and six ways to choose the fourth student's seat.

This gives a total of 9876 ways for the 4 students to sit next to each other. Therefore, the probability that the 4 students all sit at least one seat apart from each other is (210–9876)÷210 or 6÷126 or approximately 0.048.

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A. True. On average, a person usually has between 15-30 acquaintances.

B. The exact number of acquaintances a person has can vary greatly, depending on the person’s lifestyle and social activities. Factors such as age, occupation, and geographic location can also play a role in the number of acquaintances one has.

Younger people tend to have more acquaintances than older people, since they are typically more active in their social circles. People who work in customer service and other occupations that involve direct contact with people often have a larger circle of acquaintances.

People who live in larger, more populous cities tend to have more acquaintances than those who live in rural areas. Acquaintances are also gained through activities such as volunteering, attending social gatherings, or joining clubs or organizations.

The more activities a person participates in, the more likely they are to gain more acquaintances. Acquaintances may also form from casual interactions with people, such as neighbors or store clerks. Acquaintances are typically not close friends, but people that the individual knows enough about to recognize them and exchange pleasantries.

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Complete question:

The average person usually has between 15 - 30 acquaintances.True or False.

The mystery number is satisfying the above mentioned conditons is 283.

The mystery number is a three-digit number made up of the digits 2, 8, and 3. The 3 and the 8 are not next to each other in the number and the 2 comes before the 3. From the given information, we know that the only possible arrangement of the digits is 283. Therefore, the mystery number is 283. It's important to note that there could be other possibilities if more information was provided about the mystery number. But given the information provided, 283 is the only possible answer.

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The above statement indicates that the linear inequality -5>-7 is true.

Many straightforward inequalities may be resolved by adding, taking away, multiplying, or splitting both sides until the variable is all that remains. However, these factors will shift the direction of inequality: Using a negative number to multiply or divide both sides. switching the left and right sides. Ax + by > c or ax + by c are the two possible solutions to the two-variable system of linear inequalities. According to the provided collection of disparities, the signals of inequality can change.

Differences (interval notation: (-∞,∞)) -5>-7

The inequality -5>-7 is valid as a result.

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Answer:

312

Step-by-step explanation:

120x0.4=48

48x3=144

120x0.7=84

84x2=168

168+144=312

Where is the problem?

Step-by-step explanation:

I don't see it

For a given non-zero vector v in r3 there is a unique unit vector parallel to it the correct answer is 'True'.

How about a value vector which is a non-zero vector, this one? What connection does this have to a unit vector?

I'm given the following justification: "Remember that two vectors a and b are parallel if

If and only if two vectors A and B are scalar multiples of one another, they are said to be parallel. k is a constant that does not equal zero. The cross-product of the two vectors can be determined.

Let u

be a non-unit vector. Set n=u/|u|

Then n is a unit vector and u is parallel to n since u=|u|n.

a⃗ =λb⃗

for a certain scalar λ

Keep in mind that|  λa⃗ |=|λ||a⃗ |

Therefore, given a vector a is λ, the value will result in a vector λ =λa⃗ with magnitude 1.

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Divide the numerator by the denominator to create a mixed number from an incorrect fraction. The mixed number is created after the division in such a way that the achieved quotient becomes the whole number, the leftover becomes the new numerator, and the denominator stays the same.

A mixed number is one that combines both a proper fraction and a full number. Mixed fractions are another name for mixed numbers.

A fraction that has the numerator higher than or equal to the denominator is said to be inappropriate. "Top-heavy" fractions are sometimes used to describe improper fractions.

Follow these procedures to convert a mixed number to an incorrect fraction:

1. Divide the entire number by the numerator.

2. Increase the numerator by that sum.

3. Add that total to the denominator from the previous step.

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This means that the polynomial does not have any rational roots and must have irrational roots.

The Rational Root Theorem states that any rational roots of a polynomial equation must take the form p/q, where p is a constant term factor and q is a leading coefficient factor.

In this case, the constant term is 22 and the leading coefficient is 4. Therefore, the possible rational roots are

+1/-1, +2/-2, +11/-11, +22/-22.

None of these possible rational roots are actual roots of the equation, so the polynomial does not have any rational roots and must have irrational roots.

None of the possible rational roots are actual roots, so the polynomial must have irrational roots.

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If the side DG ∥ EF , then the additional information that is required to prove DEFG is an isosceles triangle is (a) DE ≅ GF .

What is an Isosceles Trapezoid ?

An isosceles trapezoid is a trapezoid in which the non parallel sides are congruent .

From the figure , we can see that , in trapezoid DEFG the sides , DG║ EF,

the sides, DG and EF are the parallel sides,

the sides, DE and GF are the non parallel sides,

According to the definition of the Isosceles trapezoid , the given trapezoid DEFG will be isosceles only if side DE and GF are congruent.

That means , side DE ≅ GF .

The given question is incomplete , the complete question is

In the diagram, DG ∥ EF. What additional information would prove that DEFG is an isosceles trapezoid?

(a) DE ≅ GF

(b) DE ≅ DG

(c) EF ≅ DG

(d) EF ≅ GF

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Answer: A

Step-by-step explanation: I got it right