Use the method of completing the square to transform the equation 3x^2−12x+8=0. Which equation shows the transformed equation?
Is my answer correct?

The equation for adding "n" numbers in a row is [a + (a + 1) + (a + 2) +.... a + (n-1)]. As a result, (n/2) (first number + last number) is the sum of "n" consecutive numbers or "n" terms of AP (Arithmetic Progression). The formula for even consecutive numbers is 2n, 2n+2, 2n+4, 2n+6, and so on.

The next two odd consecutive integers are (2n + 3) and (2n + 5) if 2n + 1 is an odd number. For illustration, assume that 2n + 1 is the odd number 7. Its successive numbers are identified as (7 + 2) and (7 + 4), or 9 and 11. Consecutive odd numbers are odd integers that are separated by 2 and come after one another. If the number x is odd, then the numbers x + 2, x + 4, and x + 6 are also odd.

Any collection of consecutive odd numbers starting with 1 has a sum that is always equal to the square of the total number of digits. If the numbers 1, 3, 5, 7, 9, 11,..., and (2n-1) are odd, then the sum of the first odd number is 1. First two odd numbers added together equal 1 + 3 = 4 (4 = 2 x 2). Two successive odd numbers added together are always divisible by 4.

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The polynomial p(x) must have at least two zeros.

A polynomial p(x) can have a maximum, minimum, or neither at any given point. The number of zeros of p(x) is equal to the number of positive and negative changes in the sign of the coefficients of the polynomial.

Since p(1) has a relative maximum at (-20), a relative minimum at (13) and a relative maximum at (57), there must be at least two changes in the sign of the coefficients. Therefore, the polynomial p(x) must have at least two zeros.

To determine how many zeros the polynomial has, we will need to calculate the sign of the coefficients at each point. For example, if the coefficient of x2 is positive at x = -20, but negative at x = 13, then we know that the polynomial has one zero between -20 and 13. We can use this method to determine the number of zeros of p(x).

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Answer:

  ₹1400

Step-by-step explanation:

You want to know the monthly installment when a refrigerator costing ₹34500 is paid for with ₹6500 down and 24 payments that include 10% simple interest.

The amount remaining after the ₹6500 down payment is ...

  ₹34500 -6500 = ₹28000

The amount to be repaid in installments will be this amount with 2 years' finance charge:

  ₹28000 × (1 +rt) = ₹28000 × (1 +0.10·2) = ₹28000×1.20

  = ₹33600

When that is divided into 24 equal payments, each monthly installment is ...

  ₹33600/24 = ₹1400

Each monthly installment is ₹1400.

The average savings per year in the last five years is 29,814.40 Option D

Generally, Average savings refers to the amount of money that a person or household has saved over a particular period of time, divided by the number of months or years in that period.

It is a measure of the average amount of money that is saved each month or year. The average savings rate can vary widely depending on a person's income, expenses, and financial goals. Some people may have very high average savings rates, while others may have very low average savings rates.

To estimate the average savings per year in the last five years, you need to add up the amounts saved in those years and divide by the number of years.

The amounts saved in the last five years are $70,453, $87,977, $54,718, $40,684, and $28,270, for a total of $291,182.

Dividing this by 5 gives an average of $58,236.40 per year, so the answer is 29,814.40 Option D

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  Answer: [tex]9x^{2} -6x^{2} y+y^{2}[/tex]

  Step-by-step explanation:

Applying the perfect square formula:[tex](a-b)^{2} = a^{2}- 2ab+ b^{2}[/tex]

[tex](3x^2- y)^2= (3x^2)^2- 2*3x^2*y+ y^2[/tex]

Simplifying this further, we get:

[tex]9x^2- 6x^2y+y^2[/tex]

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Answer:

Step-by-step explanation:(t-by)(4t+3by)

The first term in the first bracket is multiplied by the last bracket

t(4t+3by)=4t^2+3bty

The second term in the first bracket is multiplied by the last bracket

-by(4t+3by)=-4bty-3b^2y^2

Add the results together and simplify where possible

4t^2+3bty-4bty-3b^2y^2=4t^2-bty-3b^2y^2

Step-by-step explanation:

To find this algebraic phrase, we need to use the rules of algebra to express the given statement in mathematical notation. The given statement says that the sum of three times the opposite of a number and -7 is some unknown value.

We can start by expressing the opposite of a number in mathematical notation. The opposite of a number is equal to the number multiplied by -1. So, we can write the opposite of a number as -x.

Next, we can express the fact that the opposite of a number is being multiplied by 3. To do this, we can simply write 3(-x) to represent three times the opposite of a number.

Finally, we can express the fact that -7 is being added to the result. To do this, we can simply write 3(-x) - 7 to represent the sum of three times the opposite of a number and -7.

Therefore, the algebraic phrase for the sum of three times the opposite of a number and -7 is 3(-x) - 7.

The combinations of partial quotients that can be used to find the quotient of 84÷4 are given as follows:

What is the partial quotient method?

when a division is done applying the partial quotient method, consecutive subtractions are done with n groups of the divisor. Each partial quotient is the number of groups of each term and the final quotient is the sum of the partial quotients.

The final quotient of 84÷4 as follows:

84÷4 =21

hence the sum of quotients is 21.

The possible combinations are only two.

The other combinations are incorrect.

The sum of the two linear expressions with only terms will be zero when the equations are x + y = a and x - y = -a.

A set of variables called an equation is one in which two mathematical expressions are equivalent to one another.

Let two linear equations are,

x + y = a

and x - y = b

The sum of the equations,

x + y + x - y = a + b

2x = a + b

x = (a + b)/2

The value of the x should be 0,

(a + b)/2 = 0

a + b = 0

a = - b

To get the sum of linear expressions with only x term, be zero, the coefficient of the linear equations should be equal and with negative sign.

The required linear equations are,

x + y = a

and x - y = -a

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Answer:

d = 18

Step-by-step explanation:

d = square root (x2 -  x1)^2 + (y2 - y1)^2

Point A ( -1,2) Point B (1,-2)

Now let's put the number in

d = square root ( 1 -(-1)^2 + (-2 - 2)^2

Now let's get rid of the square root, and we have

(1-(-1) + (-2 -2)^2

2 + (-4)^2

2 + 16

18

So, the distance AB = 18

Answer:

[tex]AB = 4.5[/tex]

Step-by-step explanation:

⭐To find the distance between two points, you can use the distance formula: [tex]d = \sqrt{(x_2-x_1)^2 +(y_2 - y_1)^2}[/tex], where:

First, identify the coordinates you need to find the distance between, and label one coordinate as [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex].

Next, substitute [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] into the distance formula.

[tex]d = \sqrt{(1-(-1))^2+(-2-2)^2}[/tex]

[tex]d = \sqrt{(1+1)^2+(-4)^2}[/tex]

[tex]d = \sqrt{2^2+(-4)^2}[/tex]

[tex]d = \sqrt{4+16}[/tex]

[tex]d = \sqrt{20}[/tex]

∴ d ≈ 4.5

The given data is 24,26,23,26,22,25,26,28

There are the following values as shown in the given data.

To find the mode first we have to assign each value that how many times it appears.

1. 24-1 the number 24 appears only 1 time.

2. 26-3 the number 26 appears three times.

3. 23-1 the number 23 appears only one time.

4. 22-1 the number 22 appears only one time.

5. 25-1 the number 25 appears only one time.

6. 28-1 the number 28 appears only one time.

So, the mode of the given data is 26 as it appears the most number of times.

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The Median of 10 and 24 is 17.

The middle value in a sorted, ascending or descending list of numbers is known as the median, and it has the potential to describe a data collection more accurately than the average does. It reflects the midway of the data since it is the point above and below which half (50%) of the observed data falls.

The mean and mode are the other two primary trends in addition to the median. The ratio of the total number of observations to the sum of all observations is known as the mean. The value that appears most frequently in the given data collection is called the mode.

Given,

First Number=10

Second Number=24

We know, Median=Average of two numbers

⇒ Median= [tex]\frac{10+24}{2}[/tex]= 34/2= 17

Therefore, The Median of 10 and 24 is 17.

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First Number=10

Second Number=24

We know, Median=Average of two numbers

⇒ Median = 34/2= 17

Therefore, The Median of 10 and 24 is 17.

Answer:

[tex]b=\dfrac{2V}{ah}-c[/tex]

Step-by-step explanation:

Given equation:

[tex]V=\dfrac{1}{2}a(b+c)h[/tex]

Multiply both sides of the equation by 2:

[tex]\implies 2 \cdot V=2 \cdot \dfrac{1}{2}a(b+c)h[/tex]

[tex]\implies 2V=a(b+c)h[/tex]

Divide both sides by ah:

[tex]\implies \dfrac{2V}{ah}=\dfrac{a(b+c)h}{ah}[/tex]

[tex]\implies \dfrac{2V}{ah}=b+c[/tex]

Subtract c from both sides:

[tex]\implies \dfrac{2V}{ah}-c=b+c-c[/tex]

[tex]\implies \dfrac{2V}{ah}-c=b[/tex]

Therefore:

[tex]\implies b=\dfrac{2V}{ah}-c[/tex]

Answer:

x = 3 and JL = 18

Step-by-step explanation:

JN and NL are equal to each other so set both equations equal to each other
15 - 2x = 4x - 3

solve for x by moving terms to other side

x = 3

plug in 3 for x in JN's equation

JN = 15 - 2(3)

JN = 9

Since JN and NL are equal to each other, JL is just the sum of those two lengths combined

so all you have to do is double JN

9 x 2

is 18

so JL is 18

The relationship between a parallelogram's area, base, and height:

Area = Base x height

A parallelogram is just a flat shape having four parallel, straight sides that are congruent with one another.

Accordingly, a parallelogram is a closed shape, a flat figure, and a quadrilateral.

Therefore, each parallelogram is:

In such a parallelogram, the length among one side is referred to as the "base," and the length of the perpendicular segment connecting that side to the opposing side is referred to as the "height."

Area = base x height

Thus, a parallelogram's base can be any of its sides. A given parallelogram always has two base-height pairs.

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it is always important to carefully evaluate the assumptions of the model and confirm that it is an appropriate fit for the data.

What is Explanatory Variables?

A researcher-manipulated variable is an explanatory variable when it comes to an experiment. It serves as a measurement of the change brought about in the response variable. A predictor variable or an independent variable are terms that are frequently used to describe an explanatory variable.

It is not possible to determine whether a Poisson regression model would be a good choice for any of the explanatory variables without further information.

To determine whether a Poisson regression model is a good fit for the data, you will need to consider the following:

The relationship between the response variable (i.e., the observed species counts) and the explanatory variables should be modeled using a linear relationship. This can be visually assessed by creating scatterplots of the logged response variable against each of the explanatory variables and examining the pattern of the points. If the points form a roughly linear pattern, then a Poisson regression model may be appropriate.

The response variable should follow a Poisson distribution. This can be assessed by examining the distribution of the logged response variable using a histogram or a Q-Q plot. If the distribution is approximately symmetrical and has a single peak, then a Poisson regression model may be appropriate.

The residuals (i.e., the difference between the observed and predicted values) of the model should be approximately normally distributed with a mean of zero. This can be assessed by creating a plot of the residuals against the fitted values and examining the pattern of the points. If the points form a roughly random pattern centered around zero, then the model is likely to be a good fit.

If all of these conditions are met, then a Poisson regression model may be a good choice for modeling the relationship between the response variable and the explanatory variables.

However, it is always important to carefully evaluate the assumptions of the model and confirm that it is an appropriate fit for the data.

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Answer:

1/3

Step-by-step explanation:

There are 12 students in total and 4 liked Midsummer Night's Dream

Therefore 4 out of the 12 students like the play the best which can be represented in a fraction

4/12 - When you represent this as a fraction, it is also the probality, when randomly selected, a Shakespeare student likes the play the best.

This probability can then be simplified by dividing the denominator and numerator by 4

4/4 = 1 and 12/4 = 3

So, the answer is 1/3

In Euclidean geometry, parallel lines (lines that never intersect) are equidistant in the sense that the distance of any point on one line from the nearest point on the other line is the same for all points.

In geometry, parallel lines can be defined as two lines in the same plane that are at equal distance from each other and never meet. They can be both horizontal and vertical. We can see parallel lines examples in our daily life like a zebra crossing, the lines of notebooks, and on railway tracks around us.

There are 3 main rules:

Corresponding angles are equal. A line cutting across two parallel lines creates four pairs of equal corresponding angles, as in the diagram below.

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The probability that the ticket holds the winning numbers is given as follows:

1/29,322,216.

A probability is calculated by the division of the number of desired outcomes by the number of total outcomes.

For the Megaball, we have that you pick one from a set of 27, hence the probability is given as follows:

p = 1/27.

For the Winnerball, you must pick the correct combination of 5 numbers from a set of 44.

Applying the combination formula, the number of combinations of 5 numbers from a set of 44 is given as follows:

C(44,5) = 44!/(5! x 39!) = 1,086,008.

Then the probability of getting the correct combination is given as follows:

p = 1/1,086,008

The probability of a ticket holding the winning numbers is given as follows:

p = 1/27 x 1/1,086,008 = 1/29,322,216.

The complete problem is given as follows:

The lottery in our state consists of two drawings. First, a MegaBall is picked from among 27 numbered balls. Second, five WinnerBalls are picked from among 44 numbered balls. To win the lottery, you must pick the MegaBall number correctly and also pick the numbers on the five WinnerBalls (but you don't need to get the order right for the WinnerBalls). What is the probability that the ticket I hold has the winning numbers?

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Preview how to add two-digit numbers to refresh our memory before we look at how to add two numbers with four or more digits.

One result, known as the sum, is produced when two or more integers are added together. It is advisable to arrange two or more integers vertically while adding them, making sure that the digits with the same place value are in the same column. Every one of the ones should be in its own column, followed by every ten in its own column, and so on.

here ,

As you align the place value columns, write the numbers directly above one another.

From the right to the left, add the numbers in each column.

Fill in the space provided beneath each column of digits with the solution to each addition.

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As per the system of equation, a. 3y = -12x + 6 l y= -4x+ 2 has infinite number of solutions.

The rule to identify the number of solutions to the system of equation is written as,

In the given equation (a1/a2) ≠ (b1/b2), then there will be a unique solution.

Where as If (a1/a2) = (b1/b2) = (c1/c2), then there will be infinitely many solutions.

Finally If (a1/a2) = (b1/b2) ≠ (c1/c2), then there will be no solution.

Here we have given that pair of equations to show if the system has no solution, one solution, or infinitely many solutions.

Here we have to take the first equation

a. 3y = -12x + 6 l y= -4x+ 2

Now, we have to write it in the standard form, then we get,

=> 12x + 3y = 6, 4x + y = 2

Here the values of a1 = 12, b1 = 3, c1 = 6 and the values of a2 = 4, b2 = 1 and c2 = 2.

When we take the rule of system of equation we have identified that

=> 12/4 = 3/1 = 6/2

=> 3/1 = 3/1 = 3/1

Therefore, this one has the infinite number of solution.

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From the conditions provided and solving the equation using the variables of the question, The number of chicken wings is 6 and mozzarella sticks is 8.

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions.

The methods used for solving equations are:

x= number of chicken wings

x+2 = number of mozzarella sticks

60x+ 90(x+2) = 1080

150x+180=1080

150x=1080-180

x=900/150

x=6

x+2 = 8

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Answer:

so to mu calculation I prideict your answer is 10

The minimum number of neckless needed to sell to make a profit is 18 thus option (A) is correct.

A difference between two values indicates whether one is smaller, larger, or basically not similar to the other.

In other words, inequality is just the opposite of equality for example 2 =2 then it is equal but if I say 3 =6 then it is wrong the correct expression is 3 < 6.

As per the given,

12n > 135 + 4.50n

In order to make a profit and solve inequality,

12n - 4.50n > 135

7.5n > 135

n > 18

Thus, it needed to sell more than 18 to make a profit.

Hence "The bare minimum of necklaces that must be sold in order to turn a profit is 18".

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(a) When r = 12, then the value of M would be M = 504.

(b) When M = 224, then the value of r would be r = 64.

What is a direct variation?

The relationship between two values where their ratio equals a constant number is known as a direct proportion or direct variation.

In the given question, M is directly proportional to r²

M ∝ r²

M = kr²

Now When r = 2, M = 14,

k = 14/(2)²

k = 7/2

(a) When r = 12,

   M = (7/2)(12)² = (7/2)*144 = 72 * 7

  M = 504

(b)When M = 224,

  224 = (7/2)r² = (224*2)/7 = 32 * 2

  M = 64

Hence,

(a) When r = 12, then the value of M would be M = 504.

(b) When M = 224, then the value of r would be r = 64.

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The number of rides that it would take for the quickpass to be less expensive would be 28 rides.

The monthly quikpass would cost $ 55 and give a person unlimited rides. The single ride on the other hand, would cost $ 2 per ride.

The number of rides till the monthly quikpass is cheaper, can be found by the formula:

= Cost of monthly quikpass / Cost of single rides

= 55 / 2

= 27.5 rides

= 28 rides

In conclusion, if a person takes 28 rides then the monthly quikpass would be less expensive.

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As the data are given in the question [tex]x^{2}+7[/tex],

It is a quadratic equation because it has a degree of 2.

The standard form of a quadratic equation is expressed as, ax² + bx + c = 0, where

x represents an unknown (variable)

a, b, and c represent known numbers, where a ≠ 0

The values of x that satisfy the equation are called solutions of the equation, and roots or zeros of the expression on its left-hand side.

The given equation has a = 1, b = 0, and c = 7. Therefore, all the values are there in the form of the standard equation, so it is a quadratic equation.

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Question - How is [tex]x^2+7[/tex] a quadratic equation?

A. From the Limit Comparison Test, the series converges conditionally.

The Limit Comparison Test can be used to determine whether a given series converges or diverges. In this case, the given series is sigma^infinity_k = 0 9(-1)^k/k^4 + 2.

To use the Limit Comparison Test, we need to compare the given series to a known series. For example, we can compare it to the series sigma^infinity_k = 1/k^4.

We can then calculate the ratio of the two series:

sigma^infinity_k = 0 9(-1)^k/k^4 + 2

sigma^infinity_k = 1/k^4

Ratio: sigma^infinity_k = 0 9(-1)^k / (1/k^4)

Since the limit of the ratio of two series is a finite number, the given series converges. However, since the ratio is not 1, it converges conditionally, not absolutely.

Therefore, the answer is A - From the Limit Comparison Test, the series converges conditionally.

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