Given that p and q are 2 distinct real roots

20c2 + 10c = {c | c ≠ 0}

The sets for these two rational expressions are as follows:


22x + 11 x2 – 3x – 10 = {x | x ≠ 1/2}


1 – 2c = {c | c ≠ 1/2}


20c2 + 10c = {c | c ≠ 0}


To simplify the expressions, use the following steps:


1. Factor out the greatest common factor (GCF) if one exists.


2. Simplify the numerator and denominator separately.


3. Combine the numerator and denominator.

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The polynomial P(x) must have a degree of 4.

This is because a polynomial with real coefficients must have complex zeros in conjugate pairs. This means that if 1+i is a zero of the polynomial, then its conjugate, 1-i, must also be a zero. Similarly, if 2-i is a zero, then its conjugate, 2+i, must also be a zero. Therefore, the polynomial P(x) must have zeros at 1, 1+i, 1-i, 2-i, and 2+i. Since a polynomial's degree is equal to the number of its zeros, the polynomial must have a degree of 4.

In summary, a polynomial with real coefficients and zeros at 1, 1+i, and 2-i must have a degree of 4.

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You ask your neighbor to water a sickly plant while you are on vacation. Without water it will die with probability 90%: with water it will die with probability 20%. You are 80% certain that your neighbor will remember to water the plant. The probability that the plant will die when you return  is 34%. If the plant is dead, the probability that the neighbor forgot to water it is approximately 52.94%.

1. The probability that the plant will die when you return can be calculated using the law of total probability. We need to consider both scenarios, where the neighbor remembers to water the plant and where they forget to water the plant.

P(plant dies) = P(plant dies | neighbor remembers) * P(neighbor remembers) + P(plant dies | neighbor forgets) * P(neighbor forgets)

= (0.20 * 0.80) + (0.90 * 0.20)

= 0.16 + 0.18

= 0.34

So the probability that the plant will die when you return is 34%.

2. If the plant is dead, we need to calculate the probability that the neighbor forgot to water it using Bayes' theorem.

P(neighbor forgets | plant dies) = P(plant dies | neighbor forgets) * P(neighbor forgets) / P(plant dies)

= (0.90 * 0.20) / 0.34

= 0.5294

So if the plant is dead, the probability that the neighbor forgot to water it is approximately 52.94%.

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Answer:

I don't know dude...............

Therefore, ∑F(i) = F(n+2) - 1 is true for the disk transportation problem.

The disk transportation problem described in the question is a classic example of the Tower of Hanoi puzzle. The goal of the puzzle is to move all the disks from peg A to peg C while following the rules mentioned in the question. The recurrence relation for computing the total number of moves required to transfer the n disks from peg A to peg C can be written as follows:

F(n) = 2F(n-1) + 1

This recurrence relation can be derived by considering the fact that to move n disks from peg A to peg C, we first need to move the top n-1 disks from peg A to peg B using peg C as an intermediate peg. This requires F(n-1) moves. Next, we need to move the largest disk from peg A to peg C, which requires 1 move. Finally, we need to move the n-1 disks from peg B to peg C using peg A as an intermediate peg, which again requires F(n-1) moves. Therefore, the total number of moves required to transfer the n disks from peg A to peg C is F(n) = 2F(n-1) + 1.

Now, to show that ∑F(i) = F(n+2) - 1, we can use the recurrence relation F(n) = 2F(n-1) + 1 and the fact that F(1) = 1. By substituting n = 1, 2, 3, ..., n-1, n in the recurrence relation and adding all the equations, we get:

∑F(i) = 2∑F(i-1) + n

Using the fact that F(1) = 1 and rearranging the terms, we get:

∑F(i) = F(n+1) - 1

Therefore, ∑F(i) = F(n+2) - 1 is true for the disk transportation problem.

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The minimum value of the objective function is -15, which occurs at the corner point (0, 5).

The corner points of a linear programming problem are the points where the constraints intersect. These points can be found by solving the system of inequalities for each pair of constraints.

For this problem, we can find the corner points by solving the system of inequalities for each pair of constraints:

3x – y >= 2 and x + y <= 5:
- Add y to both sides of the first inequality: 3x >= 2 + y
- Subtract 2 from both sides of the first inequality: 3x - 2 >= y
- Substitute 3x - 2 for y in the second inequality: x + (3x - 2) <= 5
- Simplify: 4x <= 7
- Divide by 4: x <= 7/4
- Substitute 7/4 for x in the first inequality: 3(7/4) - 2 >= y
- Simplify: 5/4 >= y

The first corner point is (7/4, 5/4).

3x – y >= 2 and x >= 0:
- Set x = 0 and solve for y: 3(0) - y >= 2, y <= -2
- Set y = 0 and solve for x: 3x - 0 >= 2, x >= 2/3

The second corner point is (2/3, 0).

x + y <= 5 and x >= 0:
- Set x = 0 and solve for y: 0 + y <= 5, y <= 5
- Set y = 0 and solve for x: x + 0 <= 5, x <= 5

The third corner point is (0, 5).

x + y <= 5 and y >= 0:
- Set x = 0 and solve for y: 0 + y <= 5, y <= 5
- Set y = 0 and solve for x: x + 0 <= 5, x <= 5

The fourth corner point is (5, 0).

Now we can plug each corner point into the objective function to find the minimum value:

C = 3x – 3y

C = 3(7/4) - 3(5/4) = 3
C = 3(2/3) - 3(0) = 2
C = 3(0) - 3(5) = -15
C = 3(5) - 3(0) = 15

Therefore, the solution to the linear programming problem is (0, 5).

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Answer:

c

Step-by-step explanation:

it makes sense

Answer:

#1 No

#2 Yes

#3 No

#4 No

Hope this helps!

Answer:

The quotient of (2x³ + x² - x - 4) ÷ (x + 4) is 2x^2 - 7x + 17, and the remainder is 27x - 4.

Step-by-step explanation:

     2x^2 - 7x + 17

x + 4 | 2x^3 + x^2 - x - 4

- (2x^3 + 8x^2)

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

-7x^2 - x

+ (-7x^2 - 28x)

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

27x - 4

Therefore, the quotient of (2x³ + x² - x - 4) ÷ (x + 4) is 2x^2 - 7x + 17, and the remainder is 27x - 4.

As the variance/mean ratio is significantly greater than 1, the population is found to be a clumped distribution.

A clumped distribution, also known as an aggregated distribution, is a pattern of dispersion or arrangement of individuals within a population where they are found in groups or clusters. This means that individuals within a population are more likely to be found in certain areas, while other areas may have few or no individuals.

From the table in the attached image, it can be seen that

the variance= sum of (x -  0.6)^2/ sum of frequency

= 362.88/288

= 1.26

Variance/mean = 1.26/0.6 = 2.1 which is greater than 1

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Answer: B

Step-by-step explanation:

Answer:

x=10

Step-by-step explanation:

solve for x: 1/2x+4=9

First, you need to get the variable x to be on a side of the equation, by itself. That is your goal throughout the problem. The easiest way to start this is by removing 4 from the left side of the equation. We know that before the number 4 is a plus sign. In order to remove 4 from the left side of the equation, we must do the opposite of the plus sign. The plus sign represents addition, and the opposite of addition is subtraction. This means we need to subtract 4 from the left side. Remember, that whatever we do to one side, we must do to the other side! This means we must subtract 4 on BOTH sides of the equation.

On the left side of the equation, we have 4 and we subtract it by 4.

4-4=0

Since the answer is 0 we can forget about the number, because it does not hold any value.

Next, on the right side of the equation we have 9, and we subtract it by 4, as well because whatever we do to one side, we must do to the other side.

9-4=5

Our new equation should be: 1/2x=5

Our last step is to continue our goal from the beginning of the problem; to get x alone on one side of the equation. In order to complete that goal, we must remove 1/2 from the left side of the equation. Remember when we subtracted 4 one each side, we took the opposite of the sign. In this equation, we don't necessarily see a sign like before. However, whenever x is directly beside another number, that means that it is being multiplied by that number. Just like how the opposite of addition is subtraction, the opposite of multiplication is division. We need to divide 1/2 on both sides.

On the left side, we divide 1/2x by 1/2.

1/2 divided by 1/2 is 10

One isn't necessary to keep in the equation ONLY if it is next to x, like in this case.

Lastly, whatever we do to one side, we must do to the other. We finish the problem by dividing 5 by 1/2.

5 divided by .5 is 10

We are left with x=10.

The answer is 10.

A solution of the equation is an ordered pair where the y-value is equal to the equation when the x-value is plugged in. An example of a solution for the equation y = 3x + 5 is the ordered pair (2, 11), because when 2 is plugged in for x, the y-value is 11 (3 * 2 + 5 = 11).

A solution of the equation y = 3x + 5 is an ordered pair of values that satisfies the equation. In other words, when the x-value of the ordered pair is plugged into the equation, the resulting y-value should be the same as the y-value of the ordered pair. For example, the ordered pair (2, 11) is a solution of the equation because when 2 is plugged into the equation, the result is 11 (3 * 2 + 5 = 11). This is true for any ordered pair that satisfies the equation, as the y-value of the ordered pair should always be equal to the result of the equation when the x-value is plugged in. Solutions of equations can be found by solving for the x-value and then plugging it into the equation to find the corresponding y-value. This is the same for any equation, not just y = 3x + 5.

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a. The polyhedron that can be constructed using the net made of squares is a cube.

b. The polyhedron that can be constructed using the net made of squares is also a cube.

c. The polyhedron that can be constructed using the net made of a regular hexagon and isosceles triangles is a hexagonal pyramid.

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The number of students who voted for each mascot is given as follows:

Then the difference is given as follows:

nT - nC.

The difference between the two amounts is obtained applying the proportions in the context of the problem.

The circle graph gives the percentage of each type of vote.

Hence the amounts relative to each type of vote are given as follows:

In which:

The problem is incomplete, hence the general procedure is given to solve the problem.

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The height of a right cone is 42 units.

The area or volume occupied by a right circular cone is referred to as the right circular cone's volume. A three-dimensional solid object called a right circular cone has a pointed end on one side and a circle on the other. The vertex of the cone is another name for the sharp end. A cone with a right circular shape is one whose axis is parallel to the base plane.

Here, we have

Given: The volume of a right cone is 2016\piπ units^3. If its diameter measures 24 units

Height of the cone = Volume of a cone ÷ 1/3(πr²)

Where:

π = 22/7

r = radius = diameter / 2 = 24 / 2 = 12 units

h = height

2016π÷ (1/3 x π x 12²) = 42 units

Hence, the height of a right cone is 42 units.

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When 1 is put in the box, it generates an equation that is equal to 2 - 5. The expressions |-3 -2|, |2-(-3)|, |-3 + (-2)|, |-3 - (-2)|, etc., represent the distance between the two points  integers on number line.

A number line is used to display integers. A number line is a graphic representation of a straight line of numbers. It consists of positive and negative integers such as 1, 2, and so forth, as well as a zero that is neither positive nor negative.

Part A:

2 - 5 = -3

2 + 1 = 3

The absolute value of a number is the distance on the number line between that number and 0.

That distance is always positive.

b. The absolute value symbol is " | | ".

Part B: |-3 -2| = 1

On the number line, this point represents the distance of one unit from -3 to -2.

|2-(-3)| = 5

On the number line, this point represents the distance of 5 units between 2 and -3.

|-3 + (-2)| = 5

The 5 units at this point on the number line reflect the distance from -3 to -2.

|-3 - (-2)| = 1

On the number line, this point represents the distance of one unit between -3 and -2.

It's a good idea to have a backup plan in place in case something goes wrong. The expressions |-3 -2|, |2-(-3)|, |-3 + (-2)|, |-3 - (-2)|, etc., represent the distance between the two points on the number line.

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Answer: 256

Step-by-step explanation: This is a rectangular prism and shows the length, width, and height, so we need to use the formula length times width times height. So 8 * 8 * 4 equals 256.

f(x) is 5/2 times larger than g(x) for large positive or negative values of x, except at the two values x = 3 ± √7 where the expression is undefined.

A relation is a function if it has only One y-value for each x-value.

To find out how many times larger f(x) is than g(x), we need to divide the value of f(x) by the value of g(x).

Then we simplified the expression and found that it is always larger than g(x) except at two values of x where it is undefined.

To determine how much larger f(x) is than g(x), we looked at their leading coefficients and found that f(x) is always larger than g(x) for large positive or negative values of x.

Finally, we took the limit of f(x) / g(x) as x approaches infinity or negative infinity and found that it approaches -5/2.

Hence,  f(x) is 5/2 times larger than g(x) for large positive or negative values of x, except at the two values x = 3 ± √7 where the expression is undefined.

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The interest earned each year is $25 and the total amount at the end of each year would be $525, $550, $575, $600, and $625 respectively.

What is simple interest?

Simple interest is a method of calculating interest on a loan or investment where the interest is calculated only on the principal amount. It is based on a fixed percentage of the principal amount and does not take into account any interest earned on previous interest payments.

The formula for calculating simple interest is I = PRT, where I is the interest, P is the principal amount, R is the annual interest rate, and T is the time period in years.

Using the simple interest formula:

I = P * r * t

where I is the interest earned, P is the principal or initial deposit, r is the annual interest rate, and t is the time in years.

For an initial deposit of $500 at an annual interest rate of 5%, the interest earned each year and the total amount at the end of each year would be:

Year 1:

I = 500 * 0.05 * 1 = $25

Total = 500 + 25 = $525

Year 2:

I = 500 * 0.05 * 1 = $25

Total = 525 + 25 = $550

Year 3:

I = 500 * 0.05 * 1 = $25

Total = 550 + 25 = $575

Year 4:

I = 500 * 0.05 * 1 = $25

Total = 575 + 25 = $600

Year 5:

I = 500 * 0.05 * 1 = $25

Total = 600 + 25 = $625

Therefore, the interest earned each year is $25 and the total amount at the end of each year would be $525, $550, $575, $600, and $625 respectively.

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Answer: C

Step-by-step explanation:

replace n=1 with f(n)= 5n-2 we have

f(1)=3 => remove answers B and D

f(n)= 5n-2 so f(n-1)= 5(n-1) -2=5n-7

Try with answers C and D to see if it satisfies this

f(n)= f(n-1)+5= 5n - 7+5=5n-2 => C is correct

Answer: 55

Step-by-step explanation: 13 -7 = 16. 16/2 = 8. 8 + 7 = 15. 8 X 5 = 40

The measures of the angles in the figure are DBE = 64 degrees, CBE = 26 degrees. Others are shown below

Figure 7

The angle DBC is right angled

So, we have

17x + 13 + 32 - 2x = 90

This gives

15x + 45 = 90

So, we have

x = 3

Solving for the other angles, we have

DBE = 17 * 3 + 13 = 64

CBE = 32 - 2 * 3 = 26

Figure 8

Here, we have

5x + 29 = 9x - 15 -- alternate angles

So, we have

4x = 44

Divide

x = 11

Solving for the other angles, we have

WVZ = 9 * 4 - 15 = 21

CBE = 90 - 21 = 69

Figure 9

Here, we have

8x - 17 = 5x + 13 -- alternate angles

So, we have

3x = 30

Divide

x = 10

Solving for the other angles, we have

RTS = 5 * 10 + 13 = 63

PTQ = 90 - 63 = 27

Figure 10

Here, we have

6x + 25 + 2x + 23 = 180 -- angles on a straight line

So, we have

8x = 132

Divide

x = 16.5

Solving for the other angles, we have

EFG = 6 * 16.5 + 25 = 124

IFH = 180 - 124 = 56

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The volume of the parallelepiped determined by the vectors u, v, and w is 20.

To calculate the volume of the parallelepiped determined by the vectors u, v, and w, we need to use the scalar triple product. The scalar triple product of three vectors is defined as the dot product of one vector with the cross product of the other two vectors. In this case, the volume of the parallelepiped is given by:

Volume = |u . (v x w)|

Where "." represents the dot product and "x" represents the cross product.

First, let's calculate the cross product of v and w:

v x w = (2i + k) x (4j) = 8k - 4i

Next, let's take the dot product of u and the result of the cross product:

u . (v x w) = (i - 2j + 3k) . (8k - 4i) = -4 + 24 = 20

Finally, we take the absolute value of the result to get the volume of the parallelepiped:

Volume = |20| = 20

Therefore, the volume of the parallelepiped determined by the vectors u, v, and w is 20.

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The answer is correct. The division of polynomials is a straight forward process. To divide one polynomial by another, we need to divide each term in the numerator (the top part of the fraction) by the denominator (the bottom part of the fraction). Let's use long division to solve this equation.

Step 1: Divide the leading coefficient (the first number) of the numerator by the leading coefficient of the denominator.  [tex]16y3 ÷ (y+3) = 16y2.[/tex]

Step 2: Multiply the result of step 1 by the denominator and subtract it from the numerator. 16y2 (y+3) - 16y3 = -3y2.

Step 3: Bring down the next coefficient from the numerator, y4, and repeat the process.

Step 4: Divide the leading coefficient of the new numerator, -3y2, by the leading coefficient of the denominator, [tex]y+3. -3y2 ÷ (y+3) = -3y.[/tex]

Step 5: Multiply the result of step 4 by the denominator and subtract it from the numerator. -3y (y+3) - (-3y2) = 0.

Step 6: Since the numerator is now 0, the division is complete. The final answer is: [tex]16y2 - 3y + (93 + 61y + 49y2) ÷ (y+3).[/tex]

To check your answer, multiply the divisor (y+3) and the result of the division. If the product is equal to the numerator, then the answer is correct.

Let's check: (y+3)(16y2 - 3y + (93 + 61y + 49y2)) = 16y3 + y4 + 93 + 61y + 49y2, which is the numerator of the original equation.

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Answer: 8

Step-by-step explanation: (9-7)^3= 8

Answer: ? = 8

Step-by-step explanation: 2 x 2 x 2 = 8

a) f(0) = 3(0)^2 + 3(0) - 3 = -3
b) f(3) = 3(3)^2 + 3(3) - 3 = 33
c) f(−3) = 3(-3)^2 + 3(-3) - 3 = 15
d) f(−x) = 3(-x)^2 + 3(-x) - 3 = 3x^2 - 3x - 3
e)−f(x) = -(3x^2 + 3x - 3) = -3x^2 - 3x + 3
f) f(x+2) = 3(x+2)^2 + 3(x+2) - 3 = 3x^2 + 12x + 15
g) f(3x) = 3(3x)^2 + 3(3x) - 3 = 27x^2 + 9x - 3
h) f(x+h) = 3(x+h)^2 + 3(x+h) - 3 = 3x^2 + 6xh + 3h^2 + 3x + 3h - 3

We are asked to find the following for the function f(x)=3x^2+3x−3: (a) f(0) (b) f(3) (c) f(−3) (d) f(−x) (e) −f(x) (f) f(x+2) (g) f(3x) (h) f(x+h)

(a) f(0) = 3(0)^2 + 3(0) - 3 = -3
(b) f(3) = 3(3)^2 + 3(3) - 3 = 33
(c) f(−3) = 3(-3)^2 + 3(-3) - 3 = 15
(d) f(−x) = 3(-x)^2 + 3(-x) - 3 = 3x^2 - 3x - 3
(e) −f(x) = -(3x^2 + 3x - 3) = -3x^2 - 3x + 3
(f) f(x+2) = 3(x+2)^2 + 3(x+2) - 3 = 3x^2 + 12x + 15
(g) f(3x) = 3(3x)^2 + 3(3x) - 3 = 27x^2 + 9x - 3
(h) f(x+h) = 3(x+h)^2 + 3(x+h) - 3 = 3x^2 + 6xh + 3h^2 + 3x + 3h - 3

I hope this helps! Let me know if you have any further questions.

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Answer: i think -22/3 and 6/17

Step-by-step explanation:

So, the value of the car after 2 years, rounded to the nearest dollar, is $8450.

To determine the value of the car after 2 years, we need to plug in x=2 into the exponential function y=20000*(13000/20000)^x.

y=20000*(13000/20000)^2

y=20000*(0.65)^2

y=20000*0.4225

y=8450

Therefore, the value of the car after 2 years is $8450.

To round to the nearest dollar, we can look at the decimal part of the number. Since the decimal part is less than 0.5, we can round down to the nearest whole number.

So, the value of the car after 2 years, rounded to the nearest dollar, is $8450.

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The matrix B such that BA gives the matrix resulting from A after the given row operations are performed.3R3​+R1​⇒R1​−7R2​⇒R2​​B= is B = [[1, 0, 3], [0, -7, 0], [0, 0, 1]].

Assuming that A is a matrix with three rows, we can find the matrix B such that BA gives the matrix resulting from A after the given row operations are performed.3R3​+R1​⇒R1​−7R2​⇒R2​​B= by following these steps:

1. Start with the identity matrix, I, which is a matrix with ones along the main diagonal and zeros everywhere else:
I = [[1, 0, 0], [0, 1, 0], [0, 0, 1]]

2. Apply the first row operation, 3R3​+R1​⇒R1​, to the identity matrix by adding three times the third row to the first row:
I = [[1+3(0), 0+3(0), 0+3(1)], [0, 1, 0], [0, 0, 1]]
I = [[1, 0, 3], [0, 1, 0], [0, 0, 1]]

3. Apply the second row operation, −7R2​⇒R2​, to the identity matrix by multiplying the second row by -7:
I = [[1, 0, 3], [0*(-7), 1*(-7), 0*(-7)], [0, 0, 1]]
I = [[1, 0, 3], [0, -7, 0], [0, 0, 1]]

4. The resulting matrix, I, is the matrix B that we are looking for:
B = [[1, 0, 3], [0, -7, 0], [0, 0, 1]]

Therefore, the matrix B such that BA gives the matrix resulting from A after the given row operations are performed.3R3​+R1​⇒R1​−7R2​⇒R2​​B= is B = [[1, 0, 3], [0, -7, 0], [0, 0, 1]].

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