Factor the following examples of difference perfect squares for X to power of 2-9

to find a given term, substitute the corresponding value of n into the ninth term formula. For example, if the ninth term is 3n + 2, the 10th term of the sequence can be found by substituting n = 10 into the ninth term. 3 x 10 + 2 = 32 and so, the tenth term of the sequence is 32.

To find the nth term of an arithmetic sequence, use the following formula:

[tex]an = a + (n - 1)d[/tex]

an(nth term) = a(first term) + (n(term you are looking for) - 1) * d(common difference)

The answer is x4 = input.nextDouble() and double avgnumber = (x1 + x2 + x3 + x4) / 4.

Declare the double variables x1, x2, x3, and x4.
double x1, x2, x3, x4;
Read each variable from input in that order.
Scanner input = new Scanner(System.in);
System.out.println("Enter x1:");
x1 = input.nextDouble();
System.out.println("Enter x2:");
x2 = input.nextDouble();
System.out.println("Enter x3:");
x3 = input.nextDouble();
System.out.println("Enter x4:");
x4 = input.nextDouble();
To Find the average of x1, x2, x3, and x4 and assign the result to avgnumber.
double avgnumber = (x1 + x2 + x3 + x4) / 4;

//This code takes four double variables from input and calculates the average by adding the four numbers together and dividing by four. The result is stored in the double variable avgnumber.

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If a value of 48 was added, the median of the data-set would remain decay from 79.5 to 77.

The median of a data-set is the middle value of a data-set, the value of which 50% of the measures are less than and 50% of the measures are greater than.

The ordered data-set for this problem is given as follows:

57, 58, 61, 66, 71, 77, 82, 91, 95, 100, 102, 105.

The data-set has an even cardinality of 12, hence the median is the mean of the 6th and the 7th elements, as follows:

(77 + 82)/2 = 79.5.

A value of 48 would be lowest value of the data-set, the cardinality would be odd, and thus the middle value would be of 77.

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The length of BC is 10.

When two triangles have some common corresponding properties, they are said to be similar. But they are no congruent.

In the given question, comparing triangles ABC and DEC. We have;

DE/ AB = EC/ BC

But,

BC = 2BE

     = 2x

So that,

(x + 2)/ (4x - 6) = x/ 2x

(x + 2)/ (4x - 6) = 1/ 2

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

2x + 4 = 4x - 6

collect like terms

6 + 4 = 4x - 2

10 = 2x

x = 10/ 2

x = 5

Then,

BC = 2x

     = 2*5

BC = 10

The length of BC is 10.

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Answer:

  x = 30

Step-by-step explanation:

You are given an angle and the sum of that angle with another that is (3x-15)°, and you want the value of x.

The sum of the two angles is given as 100°.

  P +Q = 100°

  (3x -15)° +25° = 100° . . . . . . use the given values for angles and sum

  3x = 90 . . . . . . . . . . . . divide by ° and subtract 10

  x = 30 . . . . . . . . . divide by 3

The value of x is 30.

The value of X in the given system of matrix is,

[tex]X=\left[\begin{array}{ccc}\frac{-97}{145}&\frac{-45}{145} \\\\\frac{20}{29}&\frac{21}{29}\\\end{array}\right][/tex]

Matrices are one of the most powerful tools in mathematics. The evolution of the concept of matrices is the result of an attempt to obtain compact and simple methods of solving the system of linear equations.

We have 2 by 2 matrix in the form,

[tex]\left[\begin{array}{ccc}9&9\\-9&-9\\\end{array}\right] X+\left[\begin{array}{ccc}6&3\\7&9\\\end{array}\right] =\left[\begin{array}{ccc}-1&8\\-4&6\\\end{array}\right] X\\\\Assume, X=\left[\begin{array}{ccc}a&b\\c&d\\\end{array}\right] \\\\[/tex]

After multiplication,

[tex]9a+9c+6=-a+8c\\\\-9a-9c+7=-4a+6c\\\\9b+9d+3=-b+8d\\\\-9b-9d+9=-4b-6d\\\\[/tex]

After solving the given system of equations

[tex]a=\frac{-97}{145}\\\\b=-\frac{54}{145}\\\\c=\frac{20}{29}\\\\d={21}{29}\\\\Hence, \\X=\left[\begin{array}{ccc}\frac{-97}{145}&\frac{-45}{145} \\\\\frac{20}{29}&\frac{21}{29}\\\end{array}\right][/tex]

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The number of vitamins (in grams) for a price of x dollars. Then the correct option is B. The inverse function is P⁻¹(x) = (x - 6.4) / 0.50. And at x = 9.2, the value P⁻¹(x) will be 5.4 grams.

Let the function f is given as

y = m(x + a) + c

Then the inverse function of the function f will be given by swapping x with y and y with x.

The function is given below.

P(n) = 0.50n + 6.4

The inverse of the function P(n) is given as,

x = 0.50P⁻¹(x) + 6.4

P⁻¹(x) = (x - 6.4) / 0.50

At x = 9.2, then we have

P⁻¹(9.2) = (9.2 - 6.4) / 0.50

P⁻¹(9.2) = 5.6 grams

The number of vitamins (in grams) for a price of x dollars.

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s3+5s2+8s+4

Step-by-step explanation:

Answer:

(1-e^(-2t))*u(t) - (1-e^(-t))*u(t)

Where u(t) is the step function

Step-by-step explanation:

use partial fraction decomposition. This involves expressing the rational function as the sum of simpler fractions, each with a pole at a different point in the complex plane. Once we have done this, we can use the formula for the inverse Laplace transform of a simple pole to find the inverse Laplace transform of the original function.

There are 94830 integers greater than 5400

At first, go it looks .like an infinite number but As digits are distinct

so a maximum 10 digits number is possible

but 2 & 7 can not be used so the maximum 8-digit number can be there

Total number = 4 digits numbers, 5 Digits numbers, 6 digits number, 7 digits numbers, 8 digits numbers

All the 5 - 8 digit numbers would  be > 5400

Available number of Digits = 8  ( 0, 1, 3, 4, 5, 6, 8, 9)

for numbers greater than 4 digits (5 - 8 Digits),  1st  digit can be  1, 3, 4, 5, 6, 8, 9 then from the 2nd digit onward 0 can also be a digit but the already used digit can not be used. and further one digit (already used) will keep reducing

5  Digits numbers = 7 * 7 * 6  * 5 * 4  = 5880

6 Digit Numbers =  7 * 7 * 6  * 5 * 4 *3 =  17640

7  Digits numbers = 7 * 7 * 6  * 5 * 4*2  = 35280

8 Digit Numbers =  7 * 7 * 6  * 5 * 4 *3*2*1 =  35280

Now in 4-digit numbers

Number starting with 6, 8, 9   > 5400   & number starting with 5

Number starting with 6 , 8 , 9 = 3 * 7 * 6 * 5 = 630

Number starting with 5, the second digit must be 4, 6, 8, 9

Number starting with 5 = 1 * 4* 6 * 5 = 120

Total integers greater than 5400

=5880 + 17640 + 35280 + 35280 + 630 + 120

= 94830

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For it to be parallel, the point must follow the translation from (2,7) to that point similar to (0, -3) to (-5, -5) which is left 5 and down 2. So left 5 and down 2 for (2, 7) makes it (-3, 5)

The area of the ΔABC is 98 cm²

In a triangle, we can use the sine formula to find the area of the triangle when we know one angle and the two side lengths opposite and adjacent to that angle.

Area of ΔABC = (1/2) bc sinA

Substitute b = 28 cm, c = 14 cm, and m∠A = 30° into the formula:

Area of ΔABC = (1/2) × 28cm × 14cm × sin 30°

Area of ΔABC = 98 cm²

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The angle θ of thread deflection in the extreme position is given by tan^−1(2).

The angle of thread deflection in the extreme position can be calculated by using the equation of motion of a simple pendulum.

The equation of motion for a simple pendulum is given by m g L sinθ = m a. Here, m is the mass of the ball, g is the gravitational acceleration, L is the length of the thread and θ is the angle of the thread.

From the given condition, the acceleration of the ball in the extreme and lowest positions are equal. This implies that the acceleration of the ball in the extreme position is equal to the acceleration due to gravity.

Therefore, the equation of motion reduces to g L sinθ = g. Solving for θ, we get sinθ = 1, which implies that θ = tan^−1(2).

Therefore, the angle θ of thread deflection in the extreme position is given by tan^−1(2).

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Answer:

y = -5x + 7

Step-by-step explanation:

Parallel lines on a graph have the same slopes/gradients.

m1=m2

First you want to rewrite the equation of the graph given. So put the 5x to the other side and you will have:

y = -5x -2

This means that the equation that we need must have the gradient -5 (bc it is m in y=mx+c)

The equation will be y = -5x + c

However we must still find c aka the y intercept.

Sub the point we are given (1,2) into the equation

We will have:

2 = -5(1) + c

2 = -5 + c

7 = c

Now that we know c, we know what the equation of the line is. Just sub it in (without 1 and 2)

y = -5x + 7

The outcome that are there when a six sided dice is rolled four times is 2

A sample space is a collection or a set of possible outcomes of a random experiment. The p space is represented using the symbol, “S”. The subset of possible outcomes of an experiment is called events. A sample space may contain a number of outcomes that depends on the experiment.

The sample space of getting a 6 from a die is 1. A die has six sides and are labelled 1-6

The outcome of 4 times is is 4

Therefore for two rolls, it will be 4/2 = 2

Therefore the outcome to get 6 exactly two times is 2.

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The series discount of 20/10/10 means that there are three discounts given in sequence. The first discount is 20%, the second is 10%, and the third is 10%.

What does math's % mean?

In essence, percentages are fractions with a 100 as the denominator. We place the percent symbol (%) next to the number to indicate that the number is a percentage. For instance, you would have received a 75% grade if you answered 75 out of 100 questions correctly on a test (75/100).

Let's call the original price x.

x - (20/100x) = 0.8x

then

0.8x - (10/1000.8x) = 0.72x

and finally

0.72x - (10/100*0.72x) = 0.648x

So, the net cost of $453.60 is equal to 0.648x.

We can find the original price by dividing the net cost by 0.648:

x = $453.60 / 0.648 = $700

So, the list price of the PC was $700.

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This is a True statement that both the matrix equation and the augmented matrix translate into the same system of linear equations.

What are Linear equations?

An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation.

A rectangular matrix is a grouping of numbers into rows and columns. Systems of equations can be solved using matrices. But first, we need to understand how to use matrices to represent systems.

An augmented matrix can be used to express a set of equations. Each column in an augmented matrix represents a variable or the constant terms, and each row in an augmented matrix represents one equation in the system. As a result, it is clear that augmented matrices provide a convenient approach to express systems of equations.

Therefore it is true that the solution set of the equation's equation is the same as the solution set of the linear system whose augmented matrix is.

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Answer:

a)  Exponential growth function: 60%

b)  Exponential decay function: 20%

c)  Neither

d)  Exponential decay function: 45%

Step-by-step explanation:

[tex]\textsf{Exponential Growth}: \quad y=a(1+r)^x[/tex]

[tex]\textsf{Exponential Decay}: \quad y=a(1-r)^x[/tex]

where:

Given function:

[tex]f(x) = 0.3(1.6)^x[/tex]

The function is an exponential growth function and the growth rate is:

[tex]1+r=1.6 \implies r= 0.6 = 60\%[/tex]

Given function:

[tex]g(x) = 0.8^{0.5x} - 7[/tex]

The function is an exponential decay function and the decay rate is:

[tex]1-r=0.8 \implies r=0.2=20\%[/tex]

Given function:

[tex]h(x) = 3(-5)^x[/tex]

This is neither an exponential growth or decay function as exponential functions cannot have negative bases.

Natural base exponential function

[tex]y=ae^{rx}[/tex]

If a > 0 and r > 0, the function is an exponential growth function.

If a > 0 and r < 0, the function is an exponential decay function.

Given function:

[tex]f(x) = e^{-0.45x} + 4[/tex]

As a = 1 > 0 and r = -0.45 < 0, the function is exponential decay function and the decay rate is:

[tex]r=-0.45=45\%[/tex]

The domain of the function f(x) = √(x - 5) is x ≥ 5, thus, x = 3 is not in the domain.

Remember that for a function y = f(x), we define the domain as the set of the possible inputs.

Here we have the square root function:

f(x) = √(x - 5)

Remember that the argument of a square root needs to be zero or larger, then the domain of the given function is:

x - 5 ≥ 0

Solving for x:

x ≥ 5

The domain is the set of values equal to or larger than 5, thus, the value 3 is not in the domain.

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The theoretical probability is 25%, and the experimental probability is 27.5%.

Given is that There are 10 brown, 10 black, 10 green and 10 gold marbles in bag. A student pulled a marble, recorded the color, and placed the marble back in the bag. The table below lists the frequency of each color pulled during the experiment after 40 trials.

Thee given table is -

Outcome             Frequency

Brown                        13

Black                          9

Green                         7

Gold                           11

The probability of pulling out a gold ball will be -

P{gold} = 11/40 = 0.275 = 0.275 x 100 = 27.5%

P{gold} = 27.5%

Therefore, the theoretical probability is 25%, and the experimental probability is 27.5%.

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The formula for calculating the number of cards each player receives in Bridge is N/4, where N = number of cards in the deck.

For a standard deck of 52 cards, each player would receive 52/4 = 13 cards. This can be further simplified to 13.33, however, since cards cannot be divided, the result is rounded down to 13 cards. Therefore, each player in a Bridge game with a standard deck of 52 cards will receive 13 cards.

The total number of cards in the deck is 52, so each player will get 13 cards. This can be expressed mathematically using the formula P = 52/4, where P is the number of cards per player. Therefore, P = 13. We can also use the formula to calculate the number of players if we know the total number of cards. For example, if we have 156 cards, the number of players can be calculated using the formula P = 156/4, which gives us P = 39. Therefore, there will be 39 players in the game.

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The correct statement about quantitative research is:

It uses formal questions and predetermined response options in questionnaires administered to large numbers of respondents.

We know that the quantitative research is nothing but the process of collecting and analyzing numerical data.

It is used to find the patterns, make predictions, test the relationships, and generalize results to given populations.

Whereas the qualitative research involves collecting and analyzing non-numerical data.

Quantitative research is mostly used in the natural sciences and social sciences.

It collects data using sampling methods, or by sending out online surveys/ polls, and questionnaires.

It uses formal questions and predetermined response options in questionnaires administered to large numbers of respondents.

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The complete question is:

Which of the following is true of quantitative research?

1)    It enables researchers and clients to get closer to their customers and potential customers than does qualitative research.

2)    It uses formal questions and predetermined response options in questionnaires administered to large numbers of respondents.

3)    It is most often used with exploratory research designs.

4)    It usually involves collecting detailed data from relatively small samples by asking questions or observing behavior.

5)    It is superior for studying topics that involve complex psychological motivations not easily reduced to survey formats and quantitative analyses.

The probability that 8 or more of these students were classed at professional level is given as follows:

0%.

The mass probability formula, giving the probability of x successes, is of:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are given by:

The values of the parameters for this problem are given as follows:

n = 10, p = 0.05.

Hence the probability of 8 or more of these students were classed at professional level is given as follows:

P(X >= 8) = P(X = 8) + P(X = 9) + P(X = 10)

In which:

Hence the probability is of 0%.

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The formula used to explain this statement is known as Modus Tollens, which is a form of logical inference.

Modus Tollens states that if the antecedent (A) of a conditional statement is false, then the consequent (B) must also be false. This is expressed mathematically as ¬A ⟹ ¬B. The formula used to explain this statement is known as Modus Tollens, which is a form of logical inference.

In this particular example, A is the statement that Lewis is a famous author, and B is the statement that Lewis knows how to write. Since the statement A is false, the statement B must also be false. This can be represented mathematically as:

¬A ⟹ ¬B

¬(Lewis is a famous author) ⟹ ¬(Lewis knows how to write)

False ⟹ False

Therefore, Lewis does not know how to write.

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what are you up for now and what time do you think you'll have time for

The row form of the system is 5x = 2 and y – y = 0.

Column form:

3x + y = 5

2x – y = –3

Row form:

3x + 2x = 5 – 3

y – y = 0

The row form of this system is 3x + 2x = 5 – 3 and y – y = 0. To convert from column form to row form, the first step is to eliminate the y terms in the equations. To do this, we need to add the two equations together. This gives us:

3x + y = 5

2x – y = –3

3x + 2x = 5 + (–3)

y – y = 0

5x = 2

y – y = 0

Finally, we can solve for x and y.

5x = 2  ⇒  x = 2/5

y – y = 0  ⇒  y = 0

Therefore, the row form of the system is 5x = 2 and y – y = 0.

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Answer:

50h(5h - 2)

Step-by-step explanation:

Open up all the parenthesis on each answer

only the first one is correct

Answer:

50h(5h-2)

Step-by-step explanation:

Solution given

250h² - 100h

50*5*h*h-50*2*h

taking common

50*h(5*h-2)

50h(5h-2)

here taking common and keeping remaining on bracket

50h(5h-2)

The solution of the system of linear equations has infinitely many solutions.

Linear equation is defined as an algebraic equation of the form y=mx + b. involving only a constant and a first-order term, where m is the slope and b is the y-intercept.

Here we have given that the following linear equations are given then are listed as follows:

x + y = 4

y + z = 4

x + z = 4

ax + by + cz = 0

Here we have know that the  sub-system consisting of 3 first equations has a unique solution x = y = z = 2.

While we add the fourth equation, then it becomes look like as follows:

=> 2a + 2b + 2c = 0

When we simplify this one then we get,

=> a + b + c = 0.

Which means that if  a + b + c = 0,   then the system of 4 equations has a unique solution otherwise it is IMPOSSIBLE to this system to have infinitely many solutions.

Complete Question:

Try to find values of a, b, and c (if possible) such that the system of linear equations has a unique solution, no solution, and infinitely many solutions. (If not possible, enter IMPOSSIBLE.)

x + y = 4

y + z = 4

x + z = 4

ax + by + cz = 0

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Answer:

where is the table?

Step-by-step explanation:

repost it with a picture of the table so we can answer it or tell the details and I'll answer in the comments?