Let X be the number of distinct birthdays among four persons selected uniformly at random. Assume that all years have 365 days and birthdays are randomly distributed throughout the year. Describe the random variable X.
(Hint: Rng(X) = {1, 2, 3, 4}. Here is what is meant by distinct birthdays with some examples:
"1 distinct birthday": Alice, Bob, Raul, and Yi-Fei were all born on January 1st
"2 distinct birthdays": Alice and Bob were born on Jan 1st, but Raul and Yi-Fei were born on July 23rd;
"2 distinct birthdays": Alice was born on Jan 1st, but Bob, Raul, and Yi-Fei were born on July 23rd;
"3 distinct birthdays": Alice and Bob were born on Jan 1st, Raul was born on July 3rd, and Yi-Fei was born on Dec 4th;
"4 distinct birthdays": All 4 were born on different days.

We determine that the square will fit inside the circle without touching the edge.

The relationship between the three sides of a right-angled triangle is described by the Pythagoras theorem, commonly known as the Pythagorean theorem. The Pythagorean theorem states that the hypotenuse square of a triangle equals the sum of the squares of the other two sides.

According to the Pythagoras' theorem, if a triangle has a right angle, the square of the hypotenuse equals the sum of the squares of the other two sides. Look at triangle ABC, where BC² = AB² + AC² is present. Thus, AB is the basis while AC is (height), and BC makes up the hypotenuse. It should be noted that the hypotenuse is the longest side in a right-angled triangle .

In light of the query,

Let BC be the square's diameter, which is 9 cm.

The side of the square should be AB = 5 cm.

Circle diameter DE = 9 cm

Using Pythagoras' Theorem: BC² = AB²+ AC²

AB = BC (square have equal sides)

BC² = 2AB² BC² = 2BC² = 2×5²  = 50cm

Therefore, 7.05 cm < 9 cm. As a result, the square will fit inside the circle without touching its edge.

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A decision maker has conditions of certainty when all the information needed to make the decision is available.

In decision making, there are three different conditions: certainty, risk, and uncertainty.

Certainty is when all the information needed to make a decision is available and the decision maker knows the outcome of each alternative.

Risk is when the decision maker has some information but does not know the outcome of each alternative with certainty.

Uncertainty is when the decision maker has little or no information and cannot predict the outcome of each alternative. In the case of the question, the decision maker has conditions of certainty because all the information needed to make the decision is available.

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The lowest score Heidi can get on the remaining quiz to have a final average of 90 is 94.

To determine the lowest score Heidi can get on the remaining quiz to have a final average of 90, we can use the formula for calculating the average

average = (sum of all scores) / (total number of scores)

We know Heidi's average so far is

90 = (87 + 86 + 96 + 87 + x) / 5

where x is the score on the remaining quiz.

To solve for x, we can start by multiplying both sides by 5

450 = 356 + x

Next, we can subtract 356 from both sides

x = 94

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Part a: The retirement plan Saving Plan #2 will give most money by age 65.

Part b: Difference in amount of money earned in each plans is $1195.21

Part a:  retirement plan will she earn the most money by age 65.

Saving Plan #1 :compounded annually

A = P[tex](1 + \frac{r}{n} )^{nt}[/tex]

Principal P = $2000

Time = 65 - 20 = 45 years.

Interest r = 2.8%.

A = 2000[tex](1 + \frac{0.028}{1} )^{1*45}[/tex]

A = $6929.79

Saving Plan #2 : simple interest

SI = PRT/100

Principal P = $2500

Time = 65 - 20 = 45 years.

Interest r = 5%.

SI = 2500*45*5/100

A  = SI + P

A = 2500 + 5625

A = $8125

The retirement plan Saving Plan #2 will give most money by age 65.

Part b: difference in the amount of money earned in both plans.

Difference = A(SI) - A(CI)

Difference = $8125 - $6929.79

Difference = $1195.21

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The transfοrmatiοn frοm the parent graph [tex]f(x) = 3^x[/tex]tο [tex]g(x) = -2(3)^x+5[/tex] can be described as a reflectiοn abοut the x-axis, fοllοwed by a vertical cοmpressiοn by a factοr οf 2, and finally, a vertical shift upward by 5 units.

The functiοn g(x) is οbtained by transfοrming the parent graph οf [tex]f(x) = 3^x[/tex]in the fοllοwing way:

Therefοre, the transfοrmatiοn frοm the parent graph [tex]f(x) = 3^x[/tex] tο[tex]g(x) = -2(3)^x+5[/tex] can be described as a reflectiοn abοut the x-axis, fοllοwed by a vertical cοmpressiοn by a factοr οf 2, and finally, a vertical shift upward by 5 units.

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The appropriate test for this investigation of the mean amount of purchases for random sample of 56 orders with standard deviation of $5.30 is option (a). a one-sample t-test for a population mean,

The reason to test whether the population mean amount of purchases is greater than $100 based on a sample of 56 orders.

A one-sample t-test for a population mean is used

When a sample and we want to test a hypothesis about the population mean, and the population standard deviation is not known.

Here, a sample mean and sample standard deviation, and to test whether the population mean is greater than a given value ($100).

A one-sample t-test for a sample mean, is not appropriate,

As we are not testing the sample mean itself, but rather using it to make an inference about the population mean.

A one-sample z-test for a population proportion, is not appropriate because we are not testing a proportion, but rather a mean.

A two-sample t-test for a difference between population means, is not appropriate because we only have one sample, not two.

A matched-pairs t-test for a mean difference, is not appropriate

As we do not have paired observations, but rather a single sample of 56 orders.

Therefore, appropriate test for investigation with given standard deviation is option a. A one-sample t-test for a population mean.

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Answer:

so with this problem it would be rhombus because there are four sides right but they are slanted and rohmbus are slanted

The sum of a number and its opposite, or additive inverse, is always zero. Therefore, 23 added to its additive inverse, -23, equals zero.

When two numbers are added together, the result is their sum. In this case, we are adding 23 and -23.

The number 23 is a positive integer, and its opposite or additive inverse is the negative of 23, which is -23. When added to the original number, results in a sum of zero, because of the additive inverse of a number property.

So, when we add 23 to -23, we get:

23 + (-23) = 0

This is because adding a number and its additive inverse always results in a sum of zero.

In general, when we add any number to its additive inverse, we get a sum of zero. This is a fundamental property of addition in mathematics and is known as the additive inverse property.

For example, if we add 10 to its additive inverse, -10, we get:

10 + (-10) = 0

Likewise, if we add -7 to its additive inverse, 7, we get:

-7 + 7 = 0

In fact, we can add any number to its additive inverse and get a sum of zero. This property is used in many mathematical applications, such as solving equations and balancing chemical reactions.

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The second cylinder has the greater volume, as it has a greater radius and a greater height than the first cylinder. The volume of the second cylinder is 740π cubic inches, which is 145.75π cubic inches greater than the volume of the first cylinder.

The volume of the two cylinders can be calculated using the formula for the volume of a cylinder, which is V = πr2h, where r is the radius and h is the height of the cylinder.

For the first cylinder, the radius of the cylinder is [tex]8.5/2 = 4.25[/tex] inches, and the height is 11 inches. Therefore, the volume of the first cylinder is V = π(4.25)2 x 11 = 594.25π cubic inches.

For the second cylinder, the radius of the cylinder is 11/2 = 5.5 inches, and the height is 8.5 inches. Therefore, the volume of the second cylinder is V = π(5.5)2 x 8.5 = 740π cubic inches.

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We have to find the values of a, b, and c from the above equation. So the value of scalars (a, b, c) will be = (a, b, 2a-3b)/2 or (-2b-2c, b, c)

For the given problem, let's assume that,  $a \begin{bmatrix} 0& 1& -1& 1\\1& 0& 2& 1\end{bmatrix} + b \begin{bmatrix} 1& 1& 1& 1\\0& 1& 1& 0\end{bmatrix} + c \begin{bmatrix} 2& 0& 1& 2\\-1& 2& 1& 1\end{bmatrix} = 0$$\begin{bmatrix} 0& a& -a& a\\a& 0& 2a& a\end{bmatrix} + \begin{bmatrix} b& b& b& b\\0& b& b& 0\end{bmatrix} + \begin{bmatrix} 2c& 0& c& 2c\\-c& 2c& c& c\end{bmatrix} = \begin{bmatrix} 0& 0& 0& 0\\0& 0& 0& 0\end{bmatrix}$Simplifying this, we get,$$\begin{bmatrix} b+2c& a& b-c& a+2c\\a+b& b+2c& 3c& a+c\end{bmatrix} = \begin{bmatrix} 0& 0& 0& 0\\0& 0& 0& 0\end{bmatrix}$$As we see the matrix of the system, we see that both rows are linearly dependent. In order to get non-zero scalars, the determinant of the matrix needs to be zero.$$\begin{vmatrix} b+2c& a& b-c& a+2c\\a+b& b+2c& 3c& a+c\end{vmatrix} = 0$$$$\begin{aligned} &\begin{vmatrix} b+2c& a& b-c\\a+b& b+2c& 3c\end{vmatrix} + \begin{vmatrix} b+2c& a& a+2c\\a+b& b+2c& a+c\end{vmatrix} = 0 \\ &c(-2a^{2} + 2b^{2} + 6ab - 6ac + 4bc) = 0\end{aligned}$$Now we have two possibilities, either the determinant is zero, or c=0. If c=0, we can find that the matrix equation will give us two linearly independent equations, which will not have any solution. So the determinant of the matrix should be zero. Therefore, $-2a^{2} + 2b^{2} + 6ab - 6ac + 4bc = 0$Dividing the equation with $-2$, we get,$$a^{2} - 3ab + 3ac - 2b^{2} - 2bc = 0$$We have to find non-zero scalars a, b, and c such that the above equation holds true. Therefore, we have to find the values of a, b, and c from the above equation. So the value of scalars (a, b, c) will be = (a, b, 2a-3b)/2 or (-2b-2c, b, c). Answer: (a, b, 2a-3b)/2 or (-2b-2c, b, c)

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Snowballing payments according to the highest interest rate is likely to save the most money in the long run.

Option (A) is correct.

What is the interest rate?

An interest rate is the amount charged, expressed as a percentage of principal, by a lender to a borrower for the use of assets, such as money or property. It is typically calculated as an annual percentage of the principal amount, and represents the cost of borrowing or the reward for saving.

Snowballing payments according to the highest interest rate is likely to save the most money in the long run.

This method involves paying off the credit card with the highest interest rate first, while continuing to make minimum payments on the other cards. Once the card with the highest interest rate is paid off, the next highest interest rate card is tackled, and so on.

By prioritizing the highest interest rate cards, the overall amount of interest paid will be lower than if the payments were made based on the lowest balance or a fixed payment each month. Additionally, paying only the minimum balance each month will result in much higher interest charges and a longer payoff period.

While the snowball method of paying off the lowest balance may provide psychological benefits by creating a sense of progress and momentum, it may not always be the most cost-effective way to pay off debt.

Hence, Snowballing payments according to the highest interest rate is likely to save the most money in the long run.

Option (A) is correct.

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The equation of the circle is: [tex](x - 7)^2 + (y + 7)^2 = 32[/tex]. The general equation of a circle with center (h, k) and radius r is:

[tex](x - h)^2 + (y - k)^2 = r^2[/tex]

We are given that the center of the circle is (7, -7) and that it contains the point (11, -3).

Using the formula for the equation of a circle, we can substitute the values of h and k:

[tex](x - 7)^2 + (y + 7)^2 = r^2[/tex]

To find the value of [tex]r^2[/tex], we can substitute the coordinates of the point (11, -3) into the equation and solve for[tex]r^2[/tex]:

[tex](11 - 7)^2 + (-3 + 7)^2 = r^2[/tex]

[tex]4^2 + 4^2 = r^2[/tex]

[tex]16 + 16 = r^2[/tex]

[tex]32 = r^2[/tex]

Therefore, the equation of the circle is: [tex](x - 7)^2 + (y + 7)^2 = 32[/tex]

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The total number of positive integers with exactly four decimal digits that are divisible by 5 and by 7 is 255

There are a total of 12 positive integers with exactly four decimal digits that are divisible by 5 and by 7.
To find these numbers, we can start by finding the smallest and largest four-digit numbers that are divisible by 5 and 7. The smallest four-digit number that is divisible by 5 and 7 is 1050 (5 * 7 * 30) and the largest is 9945 (5 * 7 * 283).
Next, we can find how many multiples of 35 (5 * 7) are between 1050 and 9945. To do this, we can subtract the smallest multiple (1050) from the largest (9945) and divide by 35:
(9945 - 1050) / 35 = 8895 / 35 = 254
This means there are 254 multiples of 35 between 1050 and 9945. However, we need to add 1 to this number to include the smallest multiple (1050), so the total number of positive integers with exactly four decimal digits that are divisible by 5 and by 7 is 254 + 1 = 255.

Therefore, the answer is 255.

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To convert 93 inches to yards, we can use the conversion factor:

1 yard = 36 inches

So, we have:

93 inches = (93/36) yards

To convert this to fraction form, we can simplify the fraction:

93/36 = 31/12

Therefore, 93 inches is equal to 31/12 yards in fraction form.

Answer: 93 inch to yd is 2.58 which rounds to 2.6. 2.6 as a fraction is 13/5.

Step-by-step explanation:

there 36 inches in one yard. in order to make a decimal  place the decimal number over its place value.

The final term is 4/5√5*√(1+5x)+C.

To evaluate the integral ∫dx/√(5x(1+5x)), we can use substitution. Let's let u=1+5x. Then, du=5dx and dx=du/5. Now we can substitute these values into the integral and simplify:

∫dx/√(5x(1+5x))=∫(du/5)/√(5x(u))=∫du/(5√(5xu))=∫du/(5√(5x(1+5x)))

Now we can substitute back in for u and dx:

∫du/(5√(5x(1+5x)))=∫(du/5)/√(5x(u))=∫(du/5)/√(5x(1+5x))=∫dx/√(5x(1+5x))

Now we can integrate:

∫dx/√(5x(1+5x))=2/5√5∫du/√u=2/5√5*2√u+C=4/5√5*√(1+5x)+C

So the final term is 4/5√5*√(1+5x)+C.

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Answer:

Brainly is already free

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The inverse of f(x) = (8x+11)/(15x-3) is = 11 + 3x / 15x-8

With relation to the original function f, the inverse function is denoted by the symbol f-1, and both the original function's domain and its range are transformed into the inverse function's domain and range, respectively.

Swapping (x, y) with (y, x) with reference to the line y = x yields the graph of the inverse function.

A function's inverse, indicated by the symbol f-1, only exists when the function is both a one-one and an onto function.

Keep in mind that f-1 is NOT f's inverse.

The domain value of x is determined by the combination of the function f and the reciprocal function f-1.

f(x) = (8x+11)/(15x-3)

swapping(x,y)

11 + 3x / 15x-8

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The distance between pοints P and Q is 10 units.

Distance refers tο an οbject's οverall mοtiοn, regardless οf directiοn. Regardless οf an οbject's starting οr ending cοοrdinates, distance can be defined as the amοunt οf grοund cοvered.

In οrder tο sοlve this riddle, the Pythagοrean theοrem, which asserts that the square οf the hypοtenuse in a right triangle equals the sum οf the squares οf the legs, must be used. Using the cοοrdinates οf these pοints, we can determine that the hypοtenuse in this situatiοn is the separatiοn between pοints P and Q.

The distance fοrmula, a fοrmula fοr calculating the separatiοn between twο lοcatiοns in a cοοrdinate plane, can be used. The fοrmula fοr distance is:

d = √[(x2 - x1)² + (y2 - y1)²]

where (x1, y1) and (d, the distance between the twο spοts) (x2, y2).

Using the cοοrdinates οf pοints P and Q, we can determine what fοllοws:

d = √[(6 - (-2))² + (-1 - 5)²]

d = √[8² + (-6)²]

d = √(64 + 36)

d = √100\sd = 10

As a result, there are 10 units between pοints P and Q.

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The only value of a that makes |A| = 0 is a = 0. there is only one value that satisfies the condition, our answer is: 0.

Here's how to approach it:Given the matrix A, we need to find all values of a that make the determinant of A (denoted |A|) equal to 0. To do this, we will first calculate |A| by multiplying the elements of A in a particular way:|A| = a(2a + 1) - (2a)(a + 3) = 2a² + a - 2a² - 6a = -5aNow, we know that |A| = 0 when -5a = 0, which occurs only when a = 0.

Therefore, the only value of a that makes |A| = 0 is a = 0.

The requested answer is in the form of a comma-separated list. Since there is only one value that satisfies the condition, our answer is: 0.

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a.The system can be expressed as an augmented matrix as follows:

| 1+2 -2  3 | 0 |
| -2  1-1 6 | 23|
| 0   2  1 | 0 |

The matrix in echelon form:

| 1+2 -2  3 | 0 |
| 0   1  0 | 4.6|
| 0   0  1 | -9.2|

b. there are no nontrivial solutions for this system.

(a) The following is how the system can be represented as an augmented matrix:

| 1+2 -2  3 | 0 |
| -2  1-1 6 | 23|
| 0   2  1 | 0 |

Next, we can use Gaussian elimination to get the matrix into echelon form. The steps are as follows:

1. Subtract 2 times the first row from the second row:

| 1+2 -2  3 | 0 |
| 0   5  0 | 23|
| 0   2  1 | 0 |

2. Subtract 2/5 times the second row from the third row:

| 1+2 -2  3 | 0 |
| 0   5  0 | 23|
| 0   0  1 | -9.2|

3. Divide the second row by 5:

| 1+2 -2  3 | 0 |
| 0   1  0 | 4.6|
| 0   0  1 | -9.2|

The matrix is now in echelon form.

(b) To find all values of 1 for which the system has nontrivial solutions, we need to find the values of 1 that make the determinant of the matrix equal to zero. The determinant of the matrix is (1+2)(1)(1) - (-2)(0)(1) + (3)(0)(0) = 3. So, the only value of 1 that makes the determinant equal to zero is 1 = 0. Therefore, there are no nontrivial solutions for this system.

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The required length of the rectangle is l = 5 units

Let's assume that the length of the rectangle is represented by the variable l (in units).

Then, the width of the rectangle can be expressed in terms of l as l - 2 (in units).

The area of the rectangle is given as 15 square units. We know that the area of a rectangle is the product of its length and width. So we can write:

l(l-2) = 15

Expanding the left-hand side, we get:

[tex]$$l^2 - 2l = 15$$[/tex]

Bringing all the terms to one side, we get a quadratic equation:

[tex]$$l^2 - 2l - 15 = 0$$[/tex]

We can factor this equation as:

(l - 5)(l + 3) = 0

So the possible values for l are l=5 and l=-3. Since length can't be negative, we discard the negative value.

Therefore, the length of the rectangle is l = 5 units

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The scuba driver is 466.71 feet far from the sea turtle. The solution has been obtained by using trigonometry.

What is trigonometry?

In the area of mathematics known as trigonometry, right-angled triangles, including their sides, angles, and connections, are studied.

We are given that the angle of their eyesight is 40° below sea level and the turtle is 300 ft under the surface of the water.

We know that, in trigonometry, sin θ is the ratio of opposite side to its hypotenuse.

Here, θ = 40° and the measure of opposite side is 300 ft.

So, from this we get,

⇒ Sin 40° = [tex]\frac{300}{x}[/tex]

⇒ x = [tex]\frac{300}{sin 40}[/tex]

⇒ x = [tex]\frac{300}{0.6428}[/tex]

⇒ x = 466.71 feet

Hence, the scuba driver is 466.71 feet far from the sea turtle.

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Answer:

A

Step-by-step explanation:

For obvious reasons...........

Answer:

207892838088

I hope that's right. <3

The average power absorbed by capacitor is zero. The power in the capacitor is the average power that the capacitor consumes. Since the capacitor only stores charge, it does not dissipate energy.

As a result, the average power absorbed by a capacitor is zero. The instantaneous power absorbed by the capacitor is given by: P=V × I, Where V is the voltage across the capacitor and I is the current flowing through it.

Since there is no current flowing through the capacitor in the steady state, the instantaneous power absorbed by the capacitor is zero. The energy stored in the capacitor is given by: U=1/2C V², Where C is the capacitance of the capacitor and V is the voltage across it.

The capacitor stores energy when it is being charged, and this energy is returned to the circuit when it is discharged. As a result, the average power absorbed by a capacitor is zero.

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The average velocity of the given following intervals is :

a) 16 m/s

b) 12 m/s

c) 8 m/s

d) (24+16h)/h m/s

The average velocity of an object over a given interval is equal to the change in position (Δs) over the change in time (Δt).

For part (a) of the question, the interval is [1,4] and the change in position is s(4)-s(1). The change in time is 4-1.
Therefore, the average velocity over the interval [1,4] is (s(4)-s(1))/(4-1).
Plugging in the equation given, this is (-8×4×2+24×4)-(-8×1×2+24×1))/(4-1).
The average velocity over the interval [1,4] is 16 m/s.

For part (b) of the question, the interval is [1,3] and the change in position is s(3)-s(1). The change in time is 3-1.
Therefore, the average velocity over the interval [1,3] is (s(3)-s(1))/(3-1).
Plugging in the equation given, this is (-8×3×2+24×3)-(-8×1×2+24×1))/(3-1).
The average velocity over the interval [1,3] is 12 m/s.

For part (c) of the question, the interval is [1,2] and the change in position is s(2)-s(1). The change in time is 2-1.
Therefore, the average velocity over the interval [1,2] is (s(2)-s(1))/(2-1).
Plugging in the equation given, this is (-8×2×2+24×2)-(-8×1×2+24×1))/(2-1).
The average velocity over the interval [1,2] is 8 m/s.

For part (d) of the question, the interval is [1,1+h] and the change in position is s(1+h)-s(1). The change in time is (1+h)-1.
Therefore, the average velocity over the interval [1,1+h] is (s(1+h)-s(1))/((1+h)-1).
Plugging in the equation given, this is (-8×(1+h)2+24×(1+h))-(-8×12+24×1))/((1+h)-1).

The average velocity over the interval [1,1+h] is (24+16h)/h m/s.

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The statement that is true is 7/2 is an extraneous solution. So correct option is 1.

Algebraic form: this is the most common form of an equation, which involves using symbols and algebraic operations, such as addition, subtraction, multiplication, division, exponents, and roots. For example, 2x + 3 = 7 is an algebraic equation that can be solved for x.

Geometric form: this form of an equation represents the relationship between the geometric properties of shapes, such as the area, perimeter, or angle measures. For example, the equation A = lw represents the area of a rectangle, where A is the area, l is the length, and w is the width.

To solve the equation, we need to first find the least common denominator, which is x(x - 2). We can then multiply both sides by this denominator to eliminate the fractions.

Multiplying both sides by x(x - 2), we get:

2x(x - 2) - 11(x - 2) = 8/(x - 2)

Expanding and simplifying, we get:

2x² - 4x - 11x + 22 = 8/(x - 2)

2x² - 15x + 22 = 8/(x - 2)

Multiplying both sides by (x - 2), we get:

2x² - 15x + 22(x - 2) = 8

2x² - 15x + 22x - 44 = 8

2x² + 7x - 52 = 0

To solve for x, we can use the quadratic formula:

x = (-b ± √(b² - 4ac)) / 2a

where a = 2, b = 7, and c = -52.

Plugging in these values, we get:

x = (-7 ± √(7² - 4(2)(-52))) / (2(2))

x = (-7 ± √(329)) / 4

Therefore, the solutions to the equation are:

x = (-7 + √(329)) / 4 and x = (-7 - √(329)) / 4

To check for extraneous solutions, we need to plug in each solution back into the original equation and make sure that it does not result in a denominator of 0.

For x = (-7 + √(329)) / 4, the denominator of the second term in the original equation is:

x - 2 = (-7 + √(329)) / 4 - 2 = (-1 + √(329)) / 4

Since this is not equal to 0, the solution x = (-7 + √(329)) / 4 is not extraneous.

For x = (-7 - √(329)) / 4, the denominator of the first term in the original equation is:

x - 2 = (-7 - √(329)) / 4 - 2 = (-9 - √(329)) / 4

Since this is equal to 0, we cannot use this solution because it would result in a division by 0 in the original equation. Therefore, the extraneous solution is:

x = (-7 - √(329)) / 4

The statement that is true is:

7/2 is an extraneous solution.

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Answer:

If a line has an undefined slope, it means it is a vertical line. A vertical line passing through the point (12, -20) would have all points on the line with an x-coordinate of 12. Therefore, the equation of the line would be:

x = 12

So, any point of the form (12, y) would be on this line, where y can be any real number.

Answer:

x=12

Step-by-step explanation:

since 12 is the x coordinate, and an undefined slope is vertical that means x has to equal to 12

Step-by-step explanation:

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

Answer: 1.889

Step-by-step explanation:

Answer: g(x)=32

Step-by-step explanation: