Find an equation of the circle whose diameter has endpoints (2,2) and (-6,5) .

Answer: To find the directional vector, subtract the coordinates of the initial point from the coordinates of the terminal point.

Step-by-step explanation:

The solution to the given system of equations is x = 2, y = -1, and z = 1.

To solve the system of equations, we can use methods such as substitution or elimination. Here, we will use the method of elimination to find the values of x, y, and z.

First, let's eliminate the variable x by multiplying equation (1) by 2 and equation (3) by -1. This gives us:

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

-x + y - z = -4 (5)

Next, we can subtract equation (5) from equation (4) to eliminate the variable x:

5y - z = 2 (6)

Now, we have a system of two equations with two variables. Let's eliminate the variable z by multiplying equation (2) by 2 and equation (6) by 1. This gives us:

4x - 2y + 2z = 10 (7)

5y - z = 2 (8)

Adding equation (7) and equation (8), we can eliminate the variable z:

4x + 5y = 12 (9)

From equation (6), we can express z in terms of y:

z = 5y - 2 (10)

Now, we have a system of two equations with two variables again. Let's substitute equation (10) into equation (1):

x + 2y - (5y - 2) = -3

x - 3y + 2 = -3

x - 3y = -5 (11)

From equations (9) and (11), we can solve for x and y:

4x + 5y = 12 (9)

x - 3y = -5 (11)

By solving this system of equations, we find x = 2 and y = -1. Substituting these values into equation (10), we can solve for z:

z = 5(-1) - 2

z = -5 - 2

z = -7

Therefore, the solution to the given system of equations is x = 2, y = -1, and z = -7.

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Answer:

Step-by-step explanation:

the numerical coefficient of x2 here is 3.

Answer:

g(2) = 14

Step-by-step explanation:

g(x)=x^2+5x

Find the value of the function

Let x=2

g(2) = 2^2 +5(2)

      = 4 + 10

       = 14

According to the given data the non - degenerated closed interval in r is calculated as \(\int\limits^t_s\)f(t) - f(s).

Any set that only contains one real number is known as a degenerate interval (i.e., an interval of the form [a,a]).  an interval is measured in terms of numbers. An interval is any integer that falls between two specific numbers. This range encompasses all real numbers between those two. Real numbers can be any number anyone can think of. A degenerate interval is any set that contains only one real number (i.e., an interval of the form [a, a]). The empty set is included in this definition by some authors. A suitable interval is one that is either empty or degenerate and has an infinite number of elements.

f(x\(_r\)) - f(x\(_r\)₋₁)  = F' (e\(_r\))(x\(_r\) - x\(_r\)₋₁)

By summating the equation it becomes.

f(t) - f(s) \(\int\limits^t_s\) f < = f(t) - f(s) --------->

\(\int\limits^t_s\) ts < = f(t) - f(s)  ------------->2

From 1 and 2

\(\int\limits^t_-s < ={f(t) - f(s) < = \int\limits^t_d {f}\)

So, it finally becomes

\(\int\limits^t_s\)f < = f(t) - f(s)

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It can be evaluated using the limit comparison test or by integrating 1/\(x^3\) directly to get -1/2\(x^2\) evaluated from 1 to infinity, Therefore, the integral converges to 1/2.

The integral can be written as:

∫₁^∞ 1/x³ dx

To determine whether the integral converges or diverges, we can use the p-test for integrals. The p-test states that:

If p > 1, then the integral ∫₁^∞ 1/xᵖ dx converges.

If p ≤ 1, then the integral ∫₁^∞ 1/xᵖ dx diverges.

In this case, p = 3, which is greater than 1. Therefore, the integral converges.

To evaluate the integral, we can use the formula for the integral of xⁿ:

∫ xⁿ dx = x (n+1)/(n+1) + C

Using this formula, we get:

∫₁^∞ 1/x³ dx = lim┬(t→∞)⁡(∫₁^t 1/x³ dx)

             = lim┬(t→∞)⁡[ -1/(2x²) ] from 1 to t

             = lim┬(t→∞)⁡( -1/(2t²) + 1/2 )

             = 1/2

Therefore, the integral converges to 1/2.

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To determine if this integral converges or diverges, we can use the p-test. According to the p-test, if the integral of the form ∫1∞ 1/x^p dx is less than 1, then the integral converges. If the integral is equal to or greater than 1, then the integral diverges.

In this case, p=3, so we have ∫1∞ 1/x^3 dx = lim t→∞ ∫1t 1/x^3 dx.

Evaluating the integral, we get ∫1t 1/x^3 dx = [-1/(2x^2)]1t = -1/(2t^2) + 1/2.

Taking the limit as t approaches infinity, we get lim t→∞ [-1/(2t^2) + 1/2] = 1/2.

Since 1/2 is less than 1, we can conclude that the given improper integral converges.

Therefore, the value of the integral is ∫1∞ 1/x^3 dx = 1/2.
To determine whether the improper integral converges or diverges, we need to evaluate the integral and see if it results in a finite value. Here's the given integral:

∫(1 to ∞) (1/x^3) dx

1. First, let's set the limit to evaluate the improper integral:

lim (b→∞) ∫(1 to b) (1/x^3) dx

2. Next, find the antiderivative of 1/x^3:

The antiderivative of 1/x^3 is -1/2x^2.

3. Evaluate the antiderivative at the limits of integration:

[-1/2x^2] (1 to b)

4. Substitute the limits:

(-1/2b^2) - (-1/2(1)^2) = -1/2b^2 + 1/2

5. Evaluate the limit as b approaches infinity:

lim (b→∞) (-1/2b^2 + 1/2)

As b approaches infinity, the term -1/2b^2 approaches 0, since the denominator grows without bound. Therefore, the limit is:

0 + 1/2 = 1/2

Since the limit is a finite value (1/2), the improper integral converges. Thus, the integral evaluates to:

∫(1 to ∞) (1/x^3) dx = 1/2

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Answer:

x = 14

Step-by-step explanation:

45 = 3(x + 1)

Distribute the 3

3(x) = 3x

3(1) = 3

We now have 45 = 3x + 3

Subtract 3 from both sides

45 - 3 = 42

3 - 3 cancels out

We now have 42 = 3x

Divide both sides by 3

42/3 = 14

3x / 3 = x

We're left with x = 14

Answer:

x = 14

Step-by-step explanation:

45 = 3(x + 1)

Distribute

45 = 3x + 3

-3           -3

----------------

42 = 3x

----    ----

3       3

14   =  x

Answer:

389 hours and 23 minutes

Step-by-step explanation:

16x24=384

384+=5=389

and 23 minutes

The 99% confidence interval for the population proportion (p) is approximately 0.323 to 0.457, and the margin of error is approximately 0.067.

The margin of error and confidence interval can be calculated as follows:

First, we need to find the standard error of the proportion:

SE = sqrt[p(1-p)/n]

where:

p is the sample proportion (0.39 in this case)

n is the sample size (500 in this case)

Substituting the values, we get:

SE = sqrt[(0.39)(1-0.39)/500] ≈ 0.026

Next, we can find the margin of error (ME) using the formula:

ME = z*SE

where:

z is the critical value for the desired confidence level (99% in this case). From a standard normal distribution table or calculator, the z-value corresponding to the 99% confidence level is approximately 2.576.

Substituting the values, we get:

ME = 2.576 * 0.026 ≈ 0.067

This means that we can be 99% confident that the true population proportion falls within a range of 0.39 ± 0.067.

Finally, we can calculate the confidence interval by subtracting and adding the margin of error from the sample proportion:

CI = [p - ME, p + ME]

Substituting the values, we get:

CI = [0.39 - 0.067, 0.39 + 0.067] ≈ [0.323, 0.457]

Therefore, the 99% confidence interval for the population proportion (p) is approximately 0.323 to 0.457, and the margin of error is approximately 0.067.

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Answer: B, D, E (2^-1; subtract exponents)

Step-by-step explanation:

B > 1/2 = 2^-1

D > 2^-1 = 2^-1

E > Add exponents 2 + -5 = -1

For a rectangular prism, the

Answer:

100

Step-by-step explanation:

first we need to turn the feet into inches

20x12=240

30x12=360

now to get the area of the floor we need to do 360x240=

86,400

now the area of each tile is 24x36=864

now to find out how many tiles fit on the floor we need to do 86,400 divided by 864 which = 100

Answer:

135

Step-by-step explanation:

if you want to find w so it will be

\(w = 15 \times 9 = 135\)

Answer: (3,1) in point form x=3,y=1

Step-by-step explanation:

The function y = 2 superscript x baseline 5 belongs to an exponential family and is denoted as option C.

This is defined as a function whose value is a constant raised to the power of the argument and is denoted as e^{x}

In this case, the constant is denoted as 2 which is raised to the power of x thereby making it an exponential function.

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The given inequality is

First, we need to isolate y

To do that we want to move 2y from the right side to the left side, then

To do that subtract 2y from 3y and subtract 2y from (2y + 3)

Since 3y - 2y = 1y

Since 2y - 2y = 0

Since 0 + 3 = 3

Then the answer is

The answer is B

Answer:

X = -5

Step-by-step explanation:

See image for explanation

The quotient is 2x^2 + 4x +6.

The given polynomial is 2x^3 - 2x -12. As we can see that the given polynomial is a three-degree polynomial but the second degree term is missing, we can write the polynomial as 2x^3 + 0x^2 - 2x -12.

The divisor is (x-2).

First we choose a term to multiply with the first term of the divisor such that we get the first term of the polynomial:

(x) (2x^2) = 2x^3

Thus, we multiply the divisor (x-2) by 2x^2 which gives 2x^3 - 4x^2

Now we subtract this from the polynomial which gives 4x^2 -2x -12.

Repeating the same we multiply the divisor by 4x which gives 4x^2 - 8x. Subtracting the same from 4x^2 -2x -12, we get 6x - 12.

Now we multiply the divisor with 6 to get 6x - 12. Subtracting it from the remaining polynomial 6x -12 leaves the remainder 0.

Thus, we get the quotient as  2x^2 + 4x +6.

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Answer:

(8*5) * 2 = 80

Step-by-step explanation:

So first you want to find how many windows are on the side he sees and then you want to multiply that by 2 to get how many are on the train in total because we are assuming that each side has the same amount of windows so your answer is (8*5) * 2 = 80

Answer:40

Step-by-step explanation:

Well 8x5= 40

Answer:

Length: 20, Width: 14

Step-by-step explanation:

(x-12)(x-18)

x^2-30x+216=280

x^2-30x-64=0

x=32,-2

Plug 32 into x, and see if it equals 280

The linear program is as follows:

T - M ≤ -20,000

P - T ≤ -5,000

N - T ≤ -5,000

S - T ≤ -5,000

G - T - P ≤ 0

L - G ≤ -200

N + S - 2T - 2P ≤ 0

B - P ≤ 0

B - S ≤ 0

B + P ≤ 60,000

L - B - T ≤ 0

Let's define decision variables for each employee's salary as follows:

Let T, P, N, S, G, L, and B represent the salaries of Tom, Peter, Nina, Samir, Gary, Linda, and Bob, respectively.

Our objective is to minimize the salary of the highest paid employee. We can achieve this by introducing another variable, M, that represents the maximum salary among all employees. Therefore, our objective is to minimize M.

Minimize: M

Subject to:

T ≥ 20,000

P ≥ T + 5,000

N ≥ T + 5,000

S ≥ T + 5,000

G ≥ T + P

L ≥ G + 200

N + S ≥ 2(T + P)

B ≥ max(P, S)

B + P ≥ 60,000

L ≤ B + T

Now, we can write the linear program in standard form by moving all variables to the left-hand side of the constraints and adding slack variables:

Minimize: M

Subject to:

T - M ≤ -20,000

P - T ≤ -5,000

N - T ≤ -5,000

S - T ≤ -5,000

G - T - P ≤ 0

L - G ≤ -200

N + S - 2T - 2P ≤ 0

B - P ≤ 0

B - S ≤ 0

B + P ≤ 60,000

L - B - T ≤ 0

All variables are non-negative.

This linear program can be solved using a linear programming solver to find the minimum value of M that satisfies all the constraints. Once we have the optimal solution, we can retrieve the salaries of each employee from the linear program solution.

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Answer:

(-4,5)

Step-by-step explanation:

Answer:

y=4/3x+4

Step-by-step explanation:

Answer:

  0.57 inches

Step-by-step explanation:

To find the quantity, multiply the rate by the time.

  (0.057 in/min) × (10 min) = 0.57 in

At the given rate, 0.57 inches fell in 10 minutes.

Answer:

Step-by-step explanation:

We can defined the amplitude of a wave as the height of it, because it's the distance from the maxium point to the minimum point. In other words, it's the longest vertical displacement along the wave.

Additionally, amplitude represents power, when we apply waves to real phenomenons like the sound. So, greater grade of amplitude would represent louder sounds.

Therefore, the increase of amplitude would increase distance between the maximum and minimun point of the wave.

Answer:

i believe it's 6.76×10^2

Answer:

3,000 meters

Step-by-step explanation:

10*60=600/4=150*20=3000 meters (I highly doubt a turtle can swim three kilometers in 10 min... especially if it's a box turtle).

The point for maximum growth are (1.386, 14.99).

We have a logistic function in the form

f(x) = 30/ (1+ 2 \(e^{-0.5x\))

Now, to find the x coordinate we can write

30/2 = 30/ (1+ 2 \(e^{-0.5x\))

As, the numerators of both sides are equal

1/2 = 1/ (1+ 2 \(e^{-0.5x\))

2 = 1+ 2 \(e^{-0.5x\)

2 \(e^{-0.5x\) = 2-1

2 \(e^{-0.5x\) = 1

\(e^{-0.5x\) = 1/2

Taking log on both side we get

x= ln(2)/ 0.5

x= 1.386

Now, y= 30/ ( 1 + 2 (0.50007))

y= 30/ 2.00014

y= 14.99

Thus, the point for maximum growth are (1.386, 14.99).

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