4 Which trinomial is equivalent to
3(x-2)²-2(x-1)?
1) 3x²-2x-10
2)
3x² - 2x - 14
3)
3x² - 14x+10
4)
3x²-14x+14

The formula for the entries of [tex]M^{n}[/tex], where n is a positive integer is [tex]=\left[\begin{array}{cc}2 \times 9^n-7^n & 7^n-9^n \\2\left(9^n-7^n\right) & 2 \times 7^n-9^n\end{array}\right][/tex]  for M = [tex]\left[\begin{array}{cc}11 & -2 \\4 & 5\end{array}\right][/tex] .

Let us find the formula for entries of [tex]M^{n}[/tex], where n is a positive integer.

Let M be a 2 x 2 matrix  [tex]\left[\begin{array}{cc}11 & -2 \\4 & 5\end{array}\right][/tex]

we get the eigenvalues and their associated eigenvectors as follows-

Eigenvalue : 9λ , multiplicity : 1λ, eigenvector : [ 1, 1]

Eigenvalue : 7λ , multiplicity : 1λ, eigenvector : [ 0.5, 1]

now, we have

[tex]{\left[\begin{array}{ll}9 & 0 \\0 & 7\end{array}\right] }[/tex] = [tex]\left[\begin{array}{cc}1 & \frac{1}{2} \\1 & 1\end{array}\right]^{-1}[/tex] [tex]\left[\begin{array}{cc}11 & -2 \\4 & 5\end{array}\right][/tex]  [tex]\left[\begin{array}{cc}1 & \frac{1}{2} \\1 & 1\end{array}\right][/tex]

              = [tex]\left[\begin{array}{cc}2 & -1 \\-2 & 2\end{array}\right][/tex]  [tex]\left[\begin{array}{cc}11 & -2 \\4 & 5\end{array}\right][/tex]  [tex]\left[\begin{array}{cc}1 & \frac{1}{2} \\1 & 1\end{array}\right][/tex]

hence, [tex]\left[\begin{array}{cc}11 & -2 \\4 & 5\end{array}\right][/tex] = [tex]\left[\begin{array}{cc}1 & \frac{1}{2} \\1 & 1\end{array}\right][/tex]  [tex]\left[\begin{array}{cc}9 & 0 \\0 & 7\end{array}\right][/tex]  [tex]\left[\begin{array}{cc}2 & -1 \\-2 & 2\end{array}\right][/tex]

So,

[tex]{\left[\begin{array}{cc}11 & -2 \\4 & 5\end{array}\right]^n } & =\left[\begin{array}{ll}1 & \frac{1}{2} \\1 & 1\end{array}\right]\left[\begin{array}{ll}9 & 0 \\0 & 7\end{array}\right]^n\left[\begin{array}{cc}2 & -1 \\-2 & 2\end{array}\right][/tex]

                    [tex]= \left[\begin{array}{ll}1 & \frac{1}{2} \\1 & 1\end{array}\right]\left[\begin{array}{cc}9^n & 0 \\0 & 7^n\end{array}\right]\left[\begin{array}{cc}2 & -1 \\-2 & 2\end{array}\right][/tex]

                    [tex]=\left[\begin{array}{cc}2 \times 9^n-7^n & 7^n-9^n \\2\left(9^n-7^n\right) & 2 \times 7^n-9^n\end{array}\right][/tex]

Thus, the formula for the entries of [tex]M^{n}[/tex], where n is a positive integer is [tex]=\left[\begin{array}{cc}2 \times 9^n-7^n & 7^n-9^n \\2\left(9^n-7^n\right) & 2 \times 7^n-9^n\end{array}\right][/tex] for M = [tex]\left[\begin{array}{cc}11 & -2 \\4 & 5\end{array}\right][/tex] .

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Noah is using the 50/30/20 budgeting money management strategy

What is money management?

Money management in mathematics is the application of mathematical principles and techniques to the management of personal or corporate money. It entails the use of mathematical tools like equations, graphs, and statistics to analyse financial data and make educated decisions about budgeting, saving, investing, and spending. Mathematicians also use probability and risk analysis to manage money by estimating the likelihood of different financial events and making decisions based on the benefits and dangers of various financial options. Overall, mathematicians' understanding of money management enables people and organisations to better manage their financial resources and reach their financial objectives.

Noah is using the 50/30/20 budgeting money management strategy because he is using 50% of his income for his basic needs, 30% for entertainment, and 20% for savings and debt repayment.

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Therefore the value of the z score comes out to be Z = 1.1261

Simply expressed, a z-score (sometimes called a standard score) gives you a sense of how distant from the mean a data point is. Technically, however, it's a calculation of how far a raw score deviates from or exceeds the population mean.

The range of Z-scores ranges from -3 standard deviations (which would be on the far left of the normal distribution curve) to +3 standard deviation. The mean and population standard deviation must be known in order to use a z-score.

Here,

In a World Atlas study, 10% of people have blue eye color. Lane decided to observe 44 people and she concluded 7 people had blue eyes. Calculating the z-score

Given that :

Sample size (n) = 44

Number of people with blue eyes (x) = 7

Proportion (p) = 10% = 0.1

Using the relation :

Z = (p" - p) / [tex]\sqrt{\frac{pq}{n} }[/tex]

Since : q = 1 - p = 1 - 0.1 = 0.9

p" = x / n = 7/ 44

p"= 0.15909

pq = 0.1 * 0.9 = 0.09

Hence,

Z = (0.15909- 0.1) / [tex]\sqrt{\frac{0.09}{44} }[/tex]

Z = 0.0509 / 0.0452

Z = 1.1261

Therefore the value of the z score comes out to be

Z = 1.1261

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The standard error of the estimate is like a standard deviation for all error scores in a regression.

The standard deviation of the sample distribution is referred to as the standard error in statistics. In most cases, the sample mean of a data set differs from the actual population mean. SE is used to denote it. It is used to gauge how well a sample of a population represents that population.

The measure of the sample mean of the population is expressed as the standard deviation of the measure of the standard error of the mean, also known as the standard deviation of the mean. It is referred to as SEM. For instance, the sample mean typically serves as an estimator of the population mean. However, if we take yet another sample from the same population, it can yield a different result.

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x =3 and y = 4 , these two perpendicular bisectors will come together. These are the triangle's circumcenter's coordinates.

What is perpendicular in triangle?

The sides of a triangle are divided into two equal portions by the perpendicular, which is parallel to the sides drawn from the opposing vertices.

The circumcenter of a triangle is the location where the three perpendicular bisectors of the triangle meet.

A(0, 0), B(0, 8), C(6, 0)

Circumcenter , P(x,y)

AP = BP = CP

AP² = BP²

(x - 0 )² + ( y - 8 )² = ( x- 0)² + ( y - 0 )²

x² + y² + 64 - 16y = x² + y²

 64 - 16y = 0

 16y = 64

     y = 4

BP = CP

BP² = CP²

(x - 0)² + ( y- 0 )² = ( x- 6)² + ( y - 0)²

x² + y² = x² 36 - 12x + y²

       36 - 12x = 0

         12x = 36

           x = 3

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As the standard deviation for Sample Values and Population are different. The sample Standard Deviation is 5.196

The standard deviation is a statistic that expresses how much variance or dispersion there is in a group of numbers.

Formula for standard deviation calculation is:

[tex]\sigma = \sqrt {\sum \frac {(X - \mu) ^ {2}}{N}}[/tex] (Population Standard Deviation)

[tex]s = \sqrt {\sum \frac {(X - \bar x) ^ {2}}{n-1}}[/tex] (Sample Standard Deviation)

[tex]\bar x= 19.1[/tex]

[tex]\sum {(X - \bar x) ^ {2}} = 162[/tex]

[tex]n-1 = 6[/tex]

[tex]s = \sqrt {\sum \frac {(X - \bar x) ^ {2}}{n-1}} = \sqrt {\frac {162}{6}}[/tex]

[tex]s= \sqrt 27[/tex]

[tex]s= 5.196[/tex]

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The number of pieces of blue chalk is 6.

Expression in mathematics is combination of variables with the use of operations and given rules. It can be in the form of equation, numbers etc.

Let x be the number of blue chalk and y be the number of yellow chalk.

Given that, the ratio of yellow chalk and blue chalk is 1:2.

And there are 18 pieces of chalk.

That means the expression x + y = 18

And according to condition,

x/y = 1/2
Using cross multiplication,

2x = y

And we have the expression ,

x + y = 18

substituting 2x = y,

x + 2x = 18

3x = 18

x = 6

Therefore the number of pieces of blue chalk is 6.

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The value of the equation after the evaluation is 35

The operation on numbers that are available in brackets can be distributed for each number outside the bracket, according to the distributive property. It is one of the mathematical properties that is used the most. Commutative and associative qualities are the other two important features.

The distributive property is straightforward to recall. Numerous mathematical features allow us to make algebraic expressions as well as arithmetic calculations simpler.

Using the distributive property we can rewrite this expression as:

[tex]15(2\frac{1}{3} )= (15*2)+(15*\frac{1}{3} )[/tex]→[tex]30[/tex]→[tex]\frac{15}{3}[/tex]→[tex]30+5[/tex]→[tex]35[/tex]

Evaluating the equation:

[tex]15(2\frac{1}{3} )=15*(\frac{7}{3} )=35[/tex]

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Answer:

Look below

Step-by-step explanation:

There are several methods for solving a system of nonlinear equations, which are a set of equations that cannot be solved using linear methods. Some of these methods include:

Graphical methods: These involve plotting the equations on a graph and finding the points where they intersect, which represent the solutions to the system.

Substitution method: This involves solving one of the equations for one variable in terms of the other, and substituting this expression into the other equation. The resulting equation is then solved for the remaining variable.

Elimination method: This involves adding or subtracting the equations in such a way as to eliminate one of the variables. The resulting equation is then solved for the remaining variable.

Newton's method: This is an iterative method that involves starting with an initial guess for the solution and then using an iterative process to improve the guess until it converges to the true solution.

Broyden's method: This is a variant of Newton's method that involves using a Jacobian matrix to calculate the updates to the solution at each iteration.

To find the composition of two functions f(g(x)) and g(f(x)), you need to apply the outer function to the result of the inner function. For example, if f(x) = x^2 and g(x) = x + 1, then the composition f(g(x)) would be equal to f(x+1) = (x+1)^2, and the composition g(f(x)) would be equal to g(x^2) = x^2 + 1.

To determine if a function is invertible, you need to check if it is one-to-one. A function is one-to-one if every element in the range corresponds to exactly one element in the domain. If a function is one-to-one, it has an inverse function, which is denoted by f^(-1)(x). To find the inverse function, you can solve the original function for the variable in the range and express the variable in the domain in terms of the range. For example, if f(x) = x^2 + 1, then f^(-1)(x) would be the inverse function, which can be found by solving f(x) for x to get x = sqrt(x-1).

The difference quotient is a mathematical concept that is used to approximate the slope of a curve at a particular point. It is defined as the difference between the y-values of two points on the curve, divided by the difference between the x-values of those points. The difference quotient can be written as:

(f(x + h) - f(x))/h

where f is the function, x is the x-value of the point at which the slope is being approximated, and h is a small value that is used to calculate the approximation. To calculate the difference quotient, you can plug the values of f, x, and h into the formula and perform the calculations.

Answer:

Step-by-step explanation:

Hello...

y=x-8

2x+y=-5 -> y=-2x-5

subsitution

-2x-5=x-8

3x=3

x=1

y=x-8

y=1-8

y=-7

(1,-7)

The probability of having two hearts in a randomly drawn hand of 5 cards is 0.2637

Number of cards are drawn from a standard deck = 5

The favorable outcomes = 2 hearts

The probability is the ratio of the number of favorable outcomes to the total number of outcomes

The probability = Number of favorable outcomes / Total number of outcomes

Total number of cards = 52

Number of heart cards = 13

Number of remaining cards = 52 - 13

= 39

Then the probability of two hearts in five card hand = (5/2) × (13/52)^2 × (39/52)^3

= (5/2) × 1/16 × 27/64

= 0.2637

Therefore, the probability is 0.2637

I have solved the question in general, as the given question is incomplete

The complete question is:

What is the probability of having two hearts in a randomly drawn hand of 5 cards?

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A single value that is used to approximate a population parameter is a point estimate (D).

In conclusion, the answer is D.

Meanwhile, the margin of error is part of the confidence interval. It is calculated by multiplying the critical value by the sample proportion's standard deviation. Then, a confidence interval in the population denotes a range within which the point estimate value is expected to decrease by a specific percentage. Last, the critical value is contrasted to the acquired statistical test in hypothesis testing to decide whether or not the null hypothesis must be rejected.

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On factorizing 2v² + 4v = 6 the obtained solutions of the quadratic equation are v = 1 and v = -3.

What is factorization by splitting middle term?

The method of Splitting the Middle Term by factorization is where you divide the middle term into two factors. We know that composite numbers can be expressed as the product of prime numbers.

Rule to factorize trinomial expression where coefficients are real numbers, is to split b (the coefficient of x) into two real numbers such that the algebraic sum of these two numbers is b and their product is c, then factorize by grouping method.

According to the given question:

Factorizing 2v² + 4v = 6 by Splitting the Middle Term method

2v² + 4v = 6

2v² + 4v - 6 = 0

2v² + 6v - 2v - 6 = 0

2v(v+3) - 2(v+3) = 0

(2v-2)(v+3) = 0

Therefore the solutions are

2v - 2 = 0                                      v +3 = 0

v = 1                                                   v = -3

Hence on factorizing 2v² + 4v = 6 the obtained solutions of the quadratic equation are v = 1 and v = -3

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This statement best describes the coefficient, 3,700 is "the amount of the initial deposit". which is the correct answer would be option (C).

An exponential function is defined as a function whose value is a constant raised to the power of an argument is called an exponential function.

The exponential function is given in the question as:

3700(1.05)^4t

This expression is for the amount that will be in the account, in dollars, after t years.

As per the question,

The coefficient, 3,700 represents the amount of the initial deposit in the given exponential function

Thus, the correct answer would be an option (C).

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Answer: A. No, she would spend $26.

Step-by-step explanation:

Let y be the total cost and x be the number of minutes

So the equation is

y = 1.6x + 2

Now put 15 in for x

y= 1.6(15) + 2

y= $26

So the answer is A. No, she would spend $26.

The value of x is [tex]\frac{37 - b}{a}[/tex] by taking a and b as non-zero constant . It is solved by using simple arithmetic calculations .

What are arithmetic calculations?

Arithmetic is the branch of mathematics that deals with the study of numbers using various operations on them. Basic operations of math are addition, subtraction, multiplication and division. These operations are denoted by the given symbols.,

Addition : (+)

The addition is the process of taking two or more numbers and adding them together. In other words, it is the total sum of all the numbers.

Subtraction : (-)

Subtraction is the process in which we remove objects from the original group.

Multiplication : (×)

Multiplication is adding the same number to itself a certain number of times.

Division : (÷)

The division is breaking a large object or group into smaller parts or groups.

Here ,

given equation: ax + b = 37

To calculate value of x :

ax  = 37 - b

As, it is given that a is non-zero constant then,

x = (37 - b)/a

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From the quadrilateral proof seen below we can prove that;

∠C + ∠D = 2∠AOB

The bisection of an angle simply means to divide an angle into two equal parts.

The sum of the interior angles of a quadrilateral is 360 degrees. Thus;

∠A + ∠B + ∠C + ∠D = 360°     ------(1)

In △AOB,

∠AOB + ∠A/2 + ∠B/2 = 180°

Multiply through by 2 to get;

2∠AOB + ∠A + ∠B = 360°

Thus;

∠A + ∠B = 360° - 2∠AOB

Put 360° - 2∠AOB for ∠A + ∠B in eq 1 to get;

360° - 2∠AOB + ∠C + ∠D = 360°

This simplifies to;

∠C + ∠D = 2∠AOB

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Complete question is;

Bisectors of two adjacent angles of angles A and B of quadrilateral ABCD intersect at a point O. Prove that 2∠AOB = ∠C + ∠D

Answer Reformatting the input :

Changes made to your input should not affect the solution:

(1): "y4"   was replaced by   "y^4".  2 more similar replacement(s).

STEP

1

:

Equation at the end of step 1

 0-(((4•(x3))•(y2))•7xy4)

STEP

2

:

Equation at the end of step

2

:

 0 -  ((22x3 • y2) • 7xy4)

STEP

3

:

Final result :

 ( -22•7x4y6)

Sakura spoke 2 minutes in Hungarian and (5 - 2) = 3 minutes in Polish.

Given that, Sakura gave instructions for 5 minutes. We consider, Sakura gave instructions in Hungarian for [tex]x[/tex] minutes and in Polish for (5 - [tex]x[/tex]) minutes.

Sakura speaks 150 words per minute in Hungarian so in [tex]x[/tex] minutes, total words to be spoken is 150[tex]x[/tex]

Sakura speaks 190 words per minute in Polish so in (5 - [tex]x[/tex]) minutes, total words to be spoken in 190(5 - [tex]x[/tex])

By the given condition we have the equation,

Words spoken in Polish = Words spoken in Hungarian + 270

⇒ 190 (5 - [tex]x[/tex]) = 150[tex]x[/tex] + 270

⇒ 950 - 190[tex]x[/tex]= 150[tex]x[/tex] + 270

⇒ 150[tex]x[/tex] + 190[tex]x[/tex] = 950 - 270

⇒ 340[tex]x[/tex] = 680

⇒ [tex]x[/tex] = 2

Sakura spoke 2 minutes in Hungarian and (5 - 2) = 3 minutes in Polish.

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The result after subtracting w2 from w1 is -3i+2

Given that,

w1=-3i

w2=-2

So,

w1 -w2= -3i-(-2)

         =-3i+2

Here w1 is a complex number and w2 is a normal number. And we know that we can add or subtract a complex number only with a complex number only. And a normal number with a normal one only.

Therefore, the result after subtracting  w2 from w1 is -3i+2.

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Answer:

For $10.50, you can buy 1 pound of shrimp

Step-by-step explanation:

We know that "c" is the total cost and "p" is the number of pounds of shrimp. The number 10.50 is considered to rate for every pound of shrimp because, if we replace "p" with 1 pound, we will get the answer of $10.50. Thus, it costs $10.50 for every pound of shrimp.

Answer:

62.625

Step-by-step explanation:

First, we divide 33.4 by 4 to see what ONE gallon weighs.
33.4/4=8.35

8.35*7=58.45+(8.35*(1/2))= 62.625

Therefore, your answer is 62.625

I hope you understand my explanation. I pride myself on making my answers, short, descriptive, yet easy to read.

please give brainliest! Thanks! Hope this helped.

Answer:

62.625 lb

Step-by-step explanation:

Define the variable:

Set up a ratio of weight to number of gallons:

[tex]\implies x:7.5=33.4 :4[/tex]

Solve for x:

[tex]\implies \dfrac{x}{7.5 }=\dfrac{33.4}{4}[/tex]

Cross multiply:

[tex]\implies 4x=33.4 \cdot 7.5[/tex]

[tex]\implies 4x=250.5[/tex]

Divide both sides by 4:

[tex]\implies \dfrac{4x}{4}=\dfrac{250.5}{4}[/tex]

[tex]\implies x=62.625[/tex]

Therefore, the weight of 7.5 gallons of water is 62.625 lb.

The 21st term of the given arithmetic sequence is 83. The nth term of an arithmetic sequence is applied to find the required value where n = 21.

The nth term of an arithmetic sequence is calculated by the formula

aₙ = a + (n - 1) · d

Here the first term is 'a' and the common difference is 'd'.

The given sequence is an arithmetic sequence.

3, 7, 11, 15, 19, ....

So, the first term in the sequence is a = 3 and the common difference between the terms of the given sequence is d = 7 - 3 = 4.

Thus, the required 21st term in the sequence is

a₂₁ = 3 + (21 - 1) × 4

⇒ a₂₁ = 3 + 20 × 4

⇒ a₂₁  = 3 + 80

∴ a₂₁  = 83

So, the 21st term in the given arithmetic sequence is 83.

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To write its equation in the form y is a(xh)2+k and then determine the value of the coefficient a.

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c)  It will have less variation.

Decreasing the sample size will generally result in more variation in the distribution of sample means. This is because with a smaller sample size, there is less information available to estimate the population mean, which means that the sample mean will be less precise and will vary more from one sample to the next.

For example, if you take a sample of 10 individuals from a population and calculate the mean of their heights, the sample mean will likely be a good estimate of the population mean height. However, if you take a sample of just 2 individuals and calculate the mean of their heights, the sample mean will be less precise and will be a less reliable estimate of the population mean height. This is because the sample of 2 individuals may not be representative of the overall population, and the sample mean will be more influenced by extreme values or outliers.

In general, as the sample size decreases, the distribution of sample means will become more spread out and will have more variation. This is because with a smaller sample size, there is more uncertainty about the population mean, and the sample means will be more likely to deviate from the true population mean.

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Answer:

(-41, 30)

Step-by-step explanation:

The midpoint of a segment lies on the segment.

x: (-88 + 6)/2 = -41

y: (61 + (-1)) = 30

Answer: (-41, 30)

The pizza is 6.5 feet tall in height

From the question, we have the following parameters that can be used in our computation:

Volume = 195 cubic feet

Length = 6 feet

Width = 5 feet

The height of the pizza can be calculate using

Height = Volume/(Length * Width)

Substitute the known values in the above equation, so, we have the following representation

Height = 195/(6 * 5)

Evaluate

Height = 6.5

Hence, the height is 6.5 feet

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To solve this expression, you can first simplify the fractions:

5/11 * -11/6 = (-5/6) * (-6/5)

Then, you can multiply the fractions:

(-5/6) * (-6/5) = (-30/30) = -1

So, the result of the expression is -1.

The area of the square is 25ft² and the perimeter is 20ft.

It's important to note that the area of a square is calculated as:

= Side ²

The perimeter is calculated as:

= 4 × Side

From the information given, the side is 5ft. The area will be:.

= 5 × 5

= 25ft²

The perimeter will be:

= 4 × Sode

= 4 × 5ft.

= 20 feet

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