NEED HELP ASAP

What are the restrictions of:
(n^2 -6) / (n^2 -2)

5 and 2
+/- SQRT5 and +/- SQRT2
5 and -2

The simplified form of i^13 is -i.

The simplified form of i^13 is -i.

To find the simplified form, remember that i^4 = 1, so i^13 = i^(4*3+1) = i^(4*3) * i = (i^4)^3 * i = 1^3 * i = i.

Therefore, the simplified form of i^13 is -i.

Answer:

D). Y'= [tex]4x^{5}-12x^{4}+6x[/tex] and y'= [tex]5x^{3}-2x[/tex]

Step-by-step explanation:

We are given the equation [tex]4x^{5}-12x^{4}+6x=5x^{3}-2x[/tex].

On simplifying this equation, we get [tex]4x^{5}-12x^{4}-5x^{3}+8x=0[/tex]

i.e. Let, Y'= [tex]4x^{5}-12x^{4}+6x[/tex] and y'= [tex]5x^{3}-2x[/tex]

Now, according to the options,

A) Y =  [tex]-4x^{5}+12x^{4}-6x[/tex] = -Y' , that means the graph will be inverse of the required graph.

B) As the coefficient of 'x' in our given equation and the equation of option B are different, both will have different graphs.

C) As y =  [tex]-5x^{3}+2x[/tex] = -y', this means that the graph will be inverse of the required graph.

Hence, all above options are discarded and so option D is correct.

To find the shortest distance from Robert's home to his office, we use the Pythagorean theorem with the distances traveled north and east to calculate the length of the hypotenuse, which is approximately 7.2 kilometers.

Robert leaves his home and drives 6 km due north and then 4 km due east. To determine the shortest distance from Robert's home to his office, we can use the Pythagorean theorem. This scenario forms a right-angled triangle where the two sides are the north-bound and east-bound legs of his journey, and the hypotenuse is the shortest distance.

Step 1: Label the lengths of the two sides adjacent to the right angle as 'a' and 'b', where 'a' is the 6 km north-bound leg and 'b' is the 4 km east-bound leg.

Step 2: Apply the Pythagorean theorem, which states that the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides:

c² = a² + b²

Step 3: Substitute the known values into the theorem:

c² = 6² + 4²

Step 4: Calculate the squares of the sides and sum them:

c² = 36 + 16

Step 5: Sum the squares gives us:

c² = 52

Step 6: Take the square root of both sides to find 'c':

c = √52

Step 7: Calculate the square root which approximately equals:

c = 7.2 km

Therefore, the shortest distance from Robert's home to his office is approximately 7.2 kilometers.

Answer:

B

Step-by-step explanation:

TT two tails/no heads

TH one tail/one head

HT

HH two heads/no tails

The number of possible outcomes if two quarters are tossed and the total numbers of heads and tails are counted is 8.

Probability refers to a possibility that deals with the occurrence of random events.

The probability of all the events occurring need to be 1.

Since there are number of possibility as;

TT two tails/no heads

TH one tail/one head

HTand HH two heads/no tails

Each quarter will come up heads or tails which is 2 possibilities.

Thus for three tosses the number of outcomes is 2 x 2 x 2 = 8.

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The situation can be represented as three inequalities: g + p < 120, g < 45, p > 30, where g is the time spent in the gym and p is the time spent in the pool.

The situation you described can be represented as a system of inequalities. Let's denote gym time as g and pool time as p. Then, the system of inequalities would be the following:

These inequalities represent the constraints on how you can divide your time between the gym and the pool. Any solution to this system would be a pair of numbers (g, p) that satisfy all three inequalities, meaning it's a valid way for you to divide your time.

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The correct system of inequalities is Option 1: x + y < 120 (representing the total time constraint), x < 45 (reflecting the condition of spending less time in the gym), and y > 30 (representing the condition of spending more time in the pool). This corresponds to Option 1 in the given systems of inequalities.

The correct system of inequalities that represents your time allocation between the gym and the pool is Option 1. Let's define x as the time you spend in the gym and y as the time you spend in the pool. According to the given conditions and constraints, the total time, which is the sum of x and y, should be less than 120 minutes (x + y < 120). Furthermore, you want to spend less than 45 minutes in the gym (x < 45) and more than 30 minutes in the pool (y > 30). These three inequalities jointly form a system that accurately represents your situation at the gym and pool.

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The complete question is given below:

You have less than 120 minutes to spend in the gym and in the pool. You want to spend less than 45 minutes in the gym and more than 30 minutes in the pool. Which system represents the situation?

Option 1:

x + y < 120

x < 45

y > 30

Option 2:

x + y = 120

x = 45

y = 30

Option 3:

x + y <= 120

x < 45

y > 30

Option 4:

x + y < 120

x <= 45

y >= 30

To find x, we need to solve the quadratic equation 5x^2 - 100 = 0 using the quadratic formula.

To find x, we need to solve the quadratic equation 5x^2 - 100 = 0 using the quadratic formula. The formula is x = (-b ± √(b^2 - 4ac)) / (2a), where a, b, and c are the coefficients of the quadratic equation.

In this case, a = 5, b = 0, and c = -100. Plugging these values into the quadratic formula, we get:

x = (-0 ± √(0^2 - 4 * 5 * -100)) / (2 * 5)

Simplifying further, we have:

x = (√2000) / 10

Therefore, x equals approximately ±14.14.

The value of x is 2 and value of y is 3 in the system of equation.

Two or more expressions with an Equal sign is called as Equation.

The system of equations are 4x+5y=7

y=3x+9

We have to find the value of x and y by substitution method in system of equation

Substitute the value of y in first equation

4x+5(3x+9)=7

4x+15x+45=7

Add the like terms

19x+45=7

Subtract 45 on both sides

19x=7-45

19x=-38

Divide both sides by 19

x=-2

Now plug in x value

y=3(-2)+9

y=3

Hence, the value of x is 2 and value of y is 3 in the system of equation.

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First step to solve this is to convert this mixed fraction into improper fraction. To convert this, you need to multiply the denominator to the whole number then add the numerator. The result would be the numerator of the improper fraction. The denominator is the same:

(25 x 3) + 16 = 91

Therefore, the improper fraction is 91/25. To change this to percentage, you need to divide the numerator with the denominator and multiply by 100.

91/25 = 3.64 x 100 = 364%

Answer:

11.25 cm2 would be your answer.

Answer with explanation:

In the given right triangle

 [tex]\sin 60^{\circ}=\frac{\text{Perpendicular}}{\text{Hypotenuse}}\\\\ \frac{\sqrt{3}}{2}=\frac{\text{Perpendicular}}{2\sqrt{3}}\\\\ \text{Perpendicular}}=2\sqrt{3} \times\frac{\sqrt{3}}{2}\\\\\text{Perpendicular}}=\sqrt{3} \times\sqrt{3} \\\\\text{Perpendicular}}=3[/tex]

→Side opposite to 60° angle = 3 units

Option C : 3 Units

Answer:

8*6*6

Step-by-step explanation:

vote me

Answer:

Angela needed to multiply [tex]\frac{1}{2}[/tex] by each of the terms inside the parentheses.

Her product when multiplying [tex]\frac{1}{2} X 2[/tex] is incorrect.

Step-by-step explanation:

For simplifying the expression [tex]\frac{1}{2}(3x+2)[/tex], we need to multiply [tex]\frac{1}{2}[/tex] by each of the terms inside the parentheses.

So,

Upon multiplying [tex]\frac{1}{2}[/tex] by 6X we get 3X.

Upon multiplying [tex]\frac{1}{2}[/tex] by 2 we get 1.

Thus the final simplified expression must be 3x+1

So we can say,

Angela needed to multiply [tex]\frac{1}{2}[/tex] by each of the terms inside the parentheses.

Her product when multiplying [tex]\frac{1}{2} X 2[/tex] is incorrect.

Angela attempted to use the distributive property to simplify the expression 1/2 (6X + 2), but while she correctly simplified 1/2 * 6X to 3X, she incorrectly simplified 1/2 * 2 as 2, instead of 1. Therefore, her method was correct, but the computation was incorrect.

In mathematics, the Distributive Property is used to simplify expressions like the one Angela has used - 1/2 (6X + 2). In order to distribute correctly, Angela should perform the operation of multiplication for each term inside the parentheses by the 1/2 outside the parentheses. Therefore, it should look like this: (1/2 * 6X) + (1/2 * 2). This will simplify to 3X + 1. The issue with Angela's work was that, while she correctly simplified 1/2 * 6X to 3X, she incorrectly simplified 1/2 * 2 as 2, instead of the correct 1 value. Therefore, the correct statement about Angela's work is "Her product when multiplying is incorrect".

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By definition we have to:

Natural resources are all the material goods and services provided by nature without alteration by human beings; and that they are valuable for human societies because they contribute directly to their well-being and development (raw materials, minerals, food) or indirectly (essential ecological services for the continuity of life on the planet).

Therefore, the depletion of natural resources is considered an environmental cost because without these resources, life on planet Earth is difficult as we know it today.

Answer:

C. Resource depletion

Calvin and Alvin together take approximately 1.875 hours, or 1 hour and 52.5 minutes, to wax a car.

To find out how long it takes Calvin and Alvin to wax a car together, we can use the formula for working together:

[tex]\[\frac{1}{T} = \frac{1}{T_1} + \frac{1}{T_2}\][/tex]

Where:

-[tex]\( T \)[/tex] is the time taken when working together,

- [tex]\( T_1 \)[/tex] is the time taken by Calvin alone, and

- [tex]\( T_2 \)[/tex] is the time taken by Alvin alone.

Given:

- Calvin takes 3 hours to wax a car alone, so [tex]\( T_1 = 3 \)[/tex] hours,

- Alvin takes 5 hours to wax a car alone, so [tex]\( T_2 = 5 \)[/tex] hours.

Substitute the values into the formula:

[tex]\[\frac{1}{T} = \frac{1}{3} + \frac{1}{5}\][/tex]

To solve for T, first find a common denominator:

[tex]\[\frac{1}{T} = \frac{5}{15} + \frac{3}{15} = \frac{8}{15}\][/tex]

Now, invert both sides of the equation to isolate T:

[tex]\[T = \frac{15}{8} \text{ hours} \approx 1.875 \text{ hours}\][/tex]

So, it takes Calvin and Alvin approximately 1.875 hours, or 1 hour and 52.5 minutes, to wax a car together.

The Correct Question is :

Suppose that it takes Calvin 3 hours to wax a car if he works alone and it takes Alvin 5 hours to wax a car if he works alone.

How long does it take them to wax a car if they work together? Write an equation and solve for the unknown.

Show your work.

Answer:

the length of the hypotenuse = 32.45 centimeters

Step-by-step explanation:

A right triangle has legs that are 18 centimeters and 27 centimeters long

In a right angle triangle , to find hypotenuse we use Pythagorean theorem

[tex]c^2= a^2+b^2[/tex]

where a  and b are the length of two legs

Given a= 18  and b = 27

Lets find out C , plug in all the value in the formula

[tex]c^2= 18^2+27^2[/tex]

[tex]c^2=324 +729= 1053[/tex]

c^2 = 1053

now take square root on both sides

c= 32.45

So the length of the hypotenuse = 32.45 centimeters

For the given set of parallel lines l and m, the value of x is equal to 4.

According to the question,

l ║ m

As per the theorem pertaining to transversal and parallel lines,

∠1 and ∠2 are supplementary if and only if they are interior angles.

m∠1 + m∠2 = 180°                    _____(1)

Here, ∠1 = 20x + 5

∠2 = 24x - 1

Substitute the value ∠1 and ∠2 in (1), we get

20x + 5 +24x - 1 = 180°

44x + 4 = 180°

44x = 176

x = 4

Hence, for the given set of parallel lines l and m, the value of x = 4.

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Answer:  The other endpoint of the segment is (-1, -11).

Step-by-step explanation:  Given that the midpoint of a line segment is (6, -6) and one endpoint is (13, -1).

We are to find the co-ordinates of the other endpoint.

Let (a, b) be the co-ordinates of the other end-point.

Then, according to the given information, we have

[tex]\left(\dfrac{a+13}{2},\dfrac{b+(-1)}{2}\right)=(6,-6)\\\\\\\Rightarrow \left(\dfrac{a+13}{2},\dfrac{b-1}{2}\right)=(6,-6).[/tex]

Equating the x and y co-ordinates on both sides of the above, we get

[tex]\dfrac{a+13}{2}=6\\\\\\\Rightarrow a+13=12\\\\\Rightarrow a=12-13\\\\\Rightarrow a=-1[/tex]

and

[tex]\dfrac{b-1}{2}=-6\\\\\\\Rightarrow b-1=-12\\\\\Rightarrow b=-12+1\\\\\Righatrrow b=-11.[/tex]

Thus, the other endpoint of the segment is (-1, -11).

The probability of rolling exactly three 2s in five rolls of a six-sided die is 32.15%, calculated using the binomial probability formula. The correct answer from the provided options is C) 32.15%.

The student is asking about the probability of achieving a specific number of successes in a series of independent events, which is a problem that can be solved using the binomial probability formula. In this case, a success is defined as rolling a 2 on a six-sided die. The probability of rolling a 2 (success) on a single roll is \(\frac{1}{6}\), and the probability of not rolling a 2 (failure) is \(\frac{5}{6}\).

Therefore, the probability of rolling exactly three 2s in five rolls can be calculated by the formula:

\(P(X=k) = \binom{n}{k} \cdot p^k \cdot (1-p)^{n-k}\)

where \(n\) is the number of trials, \(k\) is the number of desired successes, and \(p\) is the probability of a single success.

Substituting the values:

\(P(X=3) = \binom{5}{3} \cdot \left(\frac{1}{6}\right)^3 \cdot \left(\frac{5}{6}\right)^{5-3}\)

\(P(X=3) = 10 \cdot \left(\frac{1}{6}\right)^3 \cdot \left(\frac{5}{6}\right)^2\)

\(P(X=3) = 10 \cdot \frac{1}{216} \cdot \frac{25}{36}\)

\(P(X=3) = \frac{250}{7776}\)

\(P(X=3) \approx 0.03215 \text{ or } 3.215\%\)

So the correct answer from the provided options is C) 32.15%.

The chances of rolling exactly three successes when rolling a 6-sided die 5 times, where rolling a 2 is considered a success, is approximately 2.143%.

To find the chances of rolling exactly three successes, we need to use the concept of binomial probability. In this case, the probability of rolling a 2 (success) is 1/6, and the probability of not rolling a 2 (failure) is 5/6. We can use the formula for binomial probability: P(X=k) = (n choose k) * p^k * (1-p)^(n-k), where n is the number of trials, k is the number of successes, and p is the probability of success in one trial.

For this problem, n=5 (since the die is rolled 5 times), k=3 (we want exactly three successes), and p=1/6 (probability of rolling a 2). Plugging these values into the formula:

P(X=3) = (5 choose 3) * (1/6)^3 * (5/6)^(5-3)

Simplifying, we get:

P(X=3) = 10 * (1/6)^3 * (5/6)^2 = 10 * (1/216) * (25/36) = 250/11664 ≈ 0.02143 ≈ 2.143%

Given that csc θ = 14 and cot θ < 0, we find that sin θ = 1/14 and cos θ must be negative. We use the identity sin² θ + cos² θ = 1 to solve for the exact value of cos θ, selecting the negative solution. The remaining trigonometric functions are then found using these values.

Given that the cosecant of theta (csc θ) is 14 and cotangent of theta (cot θ) is less than zero, we can find the other trigonometric values. We begin by recalling that cosecant is the reciprocal of the sine function, so sin θ = 1/14. Subsequently, we are told cot θ < 0, which means either the cosine or the sine (or both) must be negative.

Since cot θ is negative and we know sin θ is positive (since csc θ is positive), then we can conclude that cos θ must be negative. However, the exact value of cos θ is not readily identifiable from these properties alone.

To find the trigonometric value of cos θ, we can utilize the identity sin² θ + cos² θ = 1. Substituting our known sin θ value, we solve for cos θ. This gives us two possible solutions for cos θ, either positive or negative. As previously deduced, we select the negative solution for cos θ. The remaining trigonometric functions can then be found given these values:

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