For a, b, c, d € Z, prove that a - c|ab + cd if and only if a - cl ad + bc. 2. (a) What are the possible remainders when 12 + 16 + 20 is divided by 11? (b) Prove for every n € Z that 121 + n2 +

Answer:

Step-by-step explanation:

Remark

If x - 2 is a factor it means that the whole equation will return 0 when x = 2. That's because x - 2 will go to 0. It doesn't matter what the rest of the equation factors into. The x - 2 is enough to make it all go to 0.

Equation

y = x^4 - 3x^3 +2x - 8

Substitute and Solve

x = 2

y = 2^4 - 3*2^3 + 2(3) - 8

y = 16 - 24 + 6 - 8

y = - 8 - 2

y = - 10

Conclusion

x - 2 is not a factor of this equation.

Answer:

6 in. per triangle & 24 in total (white squares only)

Step-by-step explanation:

 So, one side is 12 inches and each side is made up of one blue and one white. With this you can just divide each side by 2, getting 6. There are 4 sides so,

4 sides X 6 in. per each square= 24

Therefore, she used 24 in. in total and 6 for each triangle.

Hoped this helped!

Let the each angle be x , 2x and 3x.

→ x + 2x + 3x = 5600

→ 8x = 5600

→ x = 5600/8

→ x = 700

the value of x is Rs.700.

Now, 2x = 2×700 = 1400

, 3x = 3×700 = 2100

Each one will get Rs.700 , Rs.1400 and Rs. 2100.

Answer:

Value of X=51.43

Step-by-step explanation:

the measure of the central angle of a regular heptagon is about 51.43 degrees which = X

if this helped please leave a rating and mark me brainliest

Answer:

72.8%

Step-by-step explanation:

Percentage residual value = (residual value / worth of the car) x 100

(44,999 / 61,815) X 100 = 72.8%

Answer:

J

Step-by-step explanation:

Given

5(y + 2) + 4 ← note 4 is outside the parenthesis

Each term in the parenthesis is multiplied by 5, that is

5 • y + 5 • 2 + 4 → J

Answer:

mDE⌢=129°, and mBC⌢=65°. Find m∠A

Step-by-step explanation:

a) The expected value of the probability distribution is 1.4

b) The standard deviation of the probability distribution is 1.07.

a) Expected Value:

The expected value, also known as the mean, is calculated by multiplying each value of x by its corresponding probability and then summing them up. Using the provided data:

x:     0    1    2    3

P(x): 0.25 0.3 0.25 0.2

Expected Value = 0(0.25) + 1(0.3) + 2(0.25) + 3(0.2)

              = 0 + 0.3 + 0.5 + 0.6

              = 1.4

Therefore, the expected value of the probability distribution is 1.4 (rounded to two decimal places).

b) Standard Deviation:

The standard deviation measures the dispersion or spread of the probability distribution. It is calculated using the formula:

Standard Deviation = √(∑(x - E(x))^2 * P(x)

where E(x) represents the expected value.

Using the provided data:

x:     0    1    2    3

P(x): 0.25 0.3 0.25 0.2

First, calculate the squared difference between each value of x and the expected value:

(0 - 1.4)^2 = 1.96

(1 - 1.4)^2 = 0.16

(2 - 1.4)^2 = 0.36

(3 - 1.4)^2 = 2.56

Next, multiply each squared difference by its corresponding probability:

1.96 * 0.25 = 0.49

0.16 * 0.3 = 0.048

0.36 * 0.25 = 0.09

2.56 * 0.2 = 0.512

Now, sum up the products:

0.49 + 0.048 + 0.09 + 0.512 = 1.14

Finally, take the square root of the sum to find the standard deviation.

Standard Deviation = √(1.14) ≈ 1.07

Therefore, the standard deviation of the probability distribution is approximately 1.07 (rounded to two decimal places).

To learn more about Standard Deviation: https://brainly.com/question/475676

#SPJ11

The given statement "If f(x) has roots over R, then f(x) is reducible over R" is a True statement.

The degree of f(x) is greater than one and it has roots over R, then we need to know about the basic theorem which is "If f(x) is a polynomial over a field K and f(a) = 0, then (x-a) divides f(x)".Hence, we can say that "If f(x) has degree greater than one and it has a root over a field R, then f(x) is reducible over R."

Hence, the given statement "If f(x) has roots over R, then f(x) is reducible over R" is a True statement.

Learn more about degree of f(x) at https://brainly.com/question/12305423

#SPJ11

Answer:

Simplifying

an = 8n + -7

Reorder the terms:

an = -7 + 8n

Solving

an = -7 + 8n

Solving for variable 'a'.

Move all terms containing a to the left, all other terms to the right.

Divide each side by 'n'.

a = -7n-1 + 8

Simplifying

a = -7n-1 + 8

Reorder the terms:

a = 8 + -7n-1

Step-by-step explanation: Tenth is always the first decimal point so 1 rounds down, making it 628.3.

Answer:

628.3

Step-by-step explanation:

A Tenth is the number after the dot. It rounds down 3, therefore, the answer is 628.3.

The second derivative of the function r(t) = (118,5t, cos t),

is determine as r''(t) = (0, 0, - cos t).

The second derivative of the function is calculated by applying the following method.

The given function;

r(t) = (118, 5t, cos t)

The first derivative of the function is calculated as;

derivative of 118 = 0

derivative of 5t = 5

derivative of cos t = - sin t

Add the individual derivatives together;

r'(t) = (0, 5, - sin t)

The second derivative of the function is calculated as follows;

derivative of 0 = 0

derivative of 5 = 0

derivative of - sin t = - cos t

Adding all the derivatives together;

r''(t) = (0, 0, - cos t)

Thus, the second derivative of the function is determine as  r''(t) = (0, 0, - cos t).

Learn more about derivative here: https://brainly.com/question/28376218

#SPJ4

Answer:

28.14

Step-by-step explanation:

The solution to a system of the type x2=A+f(t) must be 22 and is given in:

(a) Eigenvalues: λ = -2, 11. Eigenvectors: (1, 1), (-1, 1).

(b) Particular solution: [tex]\begin{equation}x = -\frac{1}{13}e^{-2t} + \frac{1}{13}e^{11t} + f(t)[/tex]

(c) General solution: [tex]\begin{equation}x = c_1e^{-2t} + c_2e^{11t} - \frac{1}{13}e^{-2t} + \frac{1}{13}e^{11t}[/tex]

(d) Second linearly independent solution: x = 22t - 23.

Here is the explanation :

(a) The system is of the form x' = Ax + f(t), where A is a 2x2 matrix and f(t) is a 2x1 vector-valued function. The characteristic equation of A is |A - λI| = 0, which in this case gives us λ² + λ - 22 = 0. The eigenvalues are λ = -2 and λ = 11. The eigenvectors corresponding to these eigenvalues are (1, 1) and (-1, 1), respectively.

(b) The particular solution to the system in (a) is given by [tex]\begin{equation}x = c_1e^{-2t} + c_2e^{11t} + f(t)[/tex].

The function f(t) must satisfy the initial conditions x(0) = (1, -6) and x'(0) = (-2, 1). Using these initial conditions, we can find [tex]c_1[/tex] and [tex]c_2[/tex] as follows:

[tex]\begin{equation}c_1 = \frac{1 - 6}{-2 - 11} = -\frac{1}{13}[/tex]

[tex]\begin{equation}c_2 = \frac{-2 + 1}{-2 - 11} = \frac{1}{13}[/tex]

Therefore, the particular solution to the system is

[tex]\begin{equation}x = -\frac{1}{13}e^{-2t} + \frac{1}{13}e^{11t} + f(t)[/tex]

(c) The general solution to the system is given by [tex]\begin{equation}x = c_1e^{-2t} + c_2e^{11t} + u[/tex], where u is a particular solution to the system. In this case, we have already found [tex]\begin{equation}u = -\frac{1}{13}e^{-2t} + \frac{1}{13}e^{11t}[/tex].

Therefore, the general solution to the system is [tex]\begin{equation}x = c_1e^{-2t} + c_2e^{11t} - \frac{1}{13}e^{-2t} + \frac{1}{13}e^{11t}[/tex].

(d) The system has a repeated eigenvalue of -1, and Fire is one solution to the system. The second linearly independent solution can be found using the method of variation of parameters. In this method, we assume that the second solution is of the form x = vt + w, where v and w are constants to be determined. Substituting this into the system gives us the following equations:

-2v + w = -21

v + 11w = -1

Solving these equations gives us v = 22 and w = -23. Therefore, the second linearly independent solution is x = 22t - 23.

To know more about the eigenvalues refer here :

https://brainly.com/question/29861415#

#SPJ11

Answer:

Step-by-step explanation:

Answer:

Answer is linked

Step-by-step explanation:

The equation is in slope-intercept form, which is y = mx + b.

To graph the line, first we have to find the slope, m, and the y- intercept, b.

So, the slope is 2 and the y- intercept is 1.

We can graph this, beginning with the y- intercept, 1. The y- intercept is always on the y axis, so the (x) value will always be zero.

Plot a point at (0, 1).

Next, add more points using the slope. The slope is 2, or [tex]\frac{2}{1}[/tex]. Start at the point we have made on the y axis. The slope equals the [tex]\frac{rise}{run}[/tex]. We can rise 2 units, then run one more unit to the right. If the slope is negative, the run goes to the left. However, in this case, the slope is positive, to it slants to the right.

We end on point (1, 3). We can continue this path infinitely, some other points on the graph could be (2, 5), (3, 7), (4, 9) and (5, 11).

Connect these points to make a line.

The finished line is linked below as well.

I hope this helps :] Good luck ^^

The functions are differentiable at all the z-plane is f'(z) = 2x when function is f(z) = x² + y² + i2xy.

Given that,

The function is f(z) = x² + y² + i2xy

We have to determine if the functions are differentiable throughout the z-plane or only a portion of it, and then we must assess any derivatives that may exist.

We know that,

Take the function,

f(z) = x² + y² + i2xy

f(x + iy)  = x² + y² + i2xy

f(x + iy)  = u + iv

We can say, u =x² + y², v= 2xy

Differentiate u with respect to x

uₓ = 2x

Differentiate v with respect to y

[tex]v_y[/tex] = 2x

So,

uₓ = 2x = [tex]v_y[/tex]

uₓ = [tex]v_y[/tex]

Differentiate u with respect to y

[tex]u_y[/tex] = 2y

Differentiate v with respect to x

[tex]v_x[/tex] = 2y

So,

[tex]u_y[/tex] = -[tex]v_x[/tex] = -2y ⇒ y = 0

Let D = {z : x | x, y∈R}

f is differentiable on D.

The derivative is f'(z) = [tex]u_x + iv_x[/tex] = 2x

Therefore, the functions are differentiable at all the z-plane is f'(z) = 2x.

To know more about function visit:

https://brainly.com/question/18962394

#SPJ4

The solution to f(x) = g(x) can be found by looking at the point where the graphs of the two functions intersect.

The given functions are: f(x) = 73x - 3g(x) = 2x - 4. To find the solution, we need to set f(x) = g(x) and solve for x.73x - 3 = 2x - 4. Simplifying the above expression, we get: 71x = 1x = 1/71.Therefore, the solution to f(x) = g(x) is x = 1/71. Now let's look at the given graph: From the graph, we can see that the solution x = 1/71 is not listed as one of the answer choices.

However, we can see that the point of intersection of the two lines is at approximately x = 0.02. Therefore, the correct answers are: 0 (since x = 0.02 is rounded to the nearest whole number, which is 0) and2 (since the point of intersection has an x-coordinate of approximately 0.02, which is between 0 and 3).Therefore, the correct answers are:0 and 2.

To know more about point of intersection refer to:

https://brainly.com/question/29185601

#SPJ11

To find all real values of x for which f(x) equals zero, we need to solve the equation f(x) = 0. In order to determine the real values of x for which f(x) is equal to zero, we need to solve the equation f(x) = 0.

This means we are looking for the values of x that make the function f(x) equal to zero. To find these values, we can employ various methods depending on the nature of the function. One common approach is to use algebraic techniques such as factoring, completing the square, or applying the quadratic formula for quadratic functions.

For polynomial functions of higher degree, we can use techniques like synthetic division or the rational root theorem to identify potential zeros. Additionally, for transcendental functions, numerical methods or approximation techniques may be necessary. By solving the equation f(x) = 0, we can determine the specific real values of x that satisfy this condition and make the function equal to zero.

Learn more about quadratic formula here: https://brainly.com/question/22364785

#SPJ11

Answer:

Locate the ordered pair (0, –6). From that point on the graph, move up 2, right 1 to locate the next ordered pair on the line. Draw a line through the two points.

Step-by-step explanation:

(0, -6) is the y-intercept, as x = 0.  Moving up 2, and right 1 represents the slope of the function. Going up is positive in the y direction, and going right is positive in the x direction.  

Drawing a line through the 2 points gives a sneak peak on the full function to be graphed

PRO GAMER MOVE: function is y = 2x - 6

Answer:

It's A. (Locate the ordered pair (0, –6). From that point on the graph, move up 2, right 1 to locate the next ordered pair on the line. Draw a line through the two points.)

Answer:

8 + (-43) - 1152 =  -1187

Step-by-step explanation:

With 90% confidence, the lower confidence limit (LCL) for the mean winnings is approximately $34,955.09 and the upper confidence limit (UCL) is approximately $40,485.31.

The mean winnings for all the show's players with a 90% confidence level, we can use the formula for a confidence interval for the population mean.

The sample of winnings:

30,692, 43,231, 48,269, 28,592, 28,453, 36,309, 45,318, 36,362, 42,871, 39,592, 35,456, 40,775, 36,466, 36,287, 38,956

We can calculate the sample mean (x(bar)) and the sample standard deviation (s) from the given data.

Sample mean

(x(bar)) = (30,692 + 43,231 + 48,269 + 28,592 + 28,453 + 36,309 + 45,318 + 36,362 + 42,871 + 39,592 + 35,456 + 40,775 + 36,466 + 36,287 + 38,956) / 15

≈ 37,720.2

Sample standard deviation

s = √[((30,692 - 37,720.2)² + (43,231 - 37,720.2)² + ... + (38,956 - 37,720.2)²) / (15 - 1)]

≈ 6,522.45

The standard error (SE) of the mean is calculated as SE = s /√n, where n is the sample size.

Standard error (SE) = 6,522.45 / √15 ≈ 1,682.12

To calculate the confidence interval, we need to find the critical value corresponding to a 90% confidence level. For a 90% confidence level, the critical value is approximately 1.645.

Margin of error = Critical value × Standard error

= 1.645 × 1,682.12

≈ 2,765.11

Lower confidence limit (LCL) = Sample mean - Margin of error

= 37,720.2 - 2,765.11

≈ 34,955.09

Upper confidence limit (UCL) = Sample mean + Margin of error

= 37,720.2 + 2,765.11

≈ 40,485.31

Therefore, with 90% confidence, the lower confidence limit (LCL) for the mean winnings is approximately $34,955.09 and the upper confidence limit (UCL) is approximately $40,485.31.

To know more about confidence click here :

https://brainly.com/question/29680703

#SPJ4

The question is incomplete the complete question is :

How much money do winners go home with from the television quiz show Jeopardy? To determine an answer, a random sample of winners was drawn and the amount of money each won was recorded and listed below. Estimate with 90% confidence the mean winning's for all the show's players. 30692 43231 48269 28592 28453 36309 45318 36362 42871 39592 35456 40775 36466 36287 38956 Lower confidence level (LCL) = ? Upper confidence level (UCL) = ?

Answer:

volume of cylinder=pi×r²×h

volume of cylinder =3.14×(11ft)²×10ft

volume of cylinder=3799.4ft³

Answer:

20 people chosen to March

Step-by-step explanation:

The sample can be explained as a random subset of the population. It is a given number of draws or selection made usually at Random from the entire or larger population set. The sample is usually smaller Than the population and if done randomly will be representative of the population set. The entire spectator attending the baseball game is the population of interest while the 20 selected from the entire pool to March in the victory parade is the sample data obtained from the population set.

Answer:

158.35

Step-by-step explanation:

Step-by-step explanation:

[tex]1250 - 8 \times 82 = \\ = 1250 - 656 = \\ = 594[/tex]

Answer:

$594

Step-by-step explanation:

since it doesn't seem to be accounting for interest

not going to worry about it

you would start with the initial amount that she had and then subtract 82x

x=8

so 1250-82x or 82(8)

so 1250-656

594

and if your teachers a stickler make sure that you add the dollar sign because they might count it off by half if you do not

Answer:

2/12

Step-by-step explanation:

since there are six sides, rolling twice will give you a total of 12 possibilities, each time, you have 1 chance out of 6 each time to roll 3

1/6 + 1/6 = 2/12

If you want to, or need to reduce 2/12, divide both the numerator and denominator by two, and you will get 1/6 again.

You dont deserve answers if ur gonna do that to other people.