What is amplitude in Trig.

The vertex form of the quadratic equation \(\(y = x^2 - 6x + 2\) is \(y = (x - 3)^2 - 7\)\) represents a minimum at \(\((3, -7)\)\).

To rewrite the quadratic equation \(\(y = x^2 - 6x + 2\)\) in vertex form, we complete the square by adding and subtracting the appropriate constant term.

Starting with \(\(y = x^2 - 6x + 2\)\), we proceed as follows:

\(\[y = (x^2 - 6x) + 2\]\)

Now, we complete the square by adding the square of half the coefficient of \(\(x\)\) to both sides:

\(\[y = (x^2 - 6x + 9) - 9 + 2\]\)

Simplifying further:

\(\[y = (x^2 - 6x + 9) - 7\]\)

The expression inside the parentheses can be rewritten as a perfect square:

\(\[y = (x - 3)^2 - 7\]\)

Now we have the equation in vertex form, which is \(\(y = a(x - h)^2 + k\)\), where \(\((h, k)\)\) represents the vertex of the parabola.

Comparing the equation to the vertex form, we can identify where the vertex is at \(\((h, k) = (3, -7)\)\).

Therefore, the correct answer is:

b. minimum at \(\((-3, -7)\)\)

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The maximal number of consecutive integers by using the expression \(2*sqrt(n*|a|).\)

Let f(x) = ax^n + bx^{n-1} + ... + z be a polynomial with integer coefficients and degree n>1. According to the theorem of Tchebychev, the maximal number of consecutive integers belonging to the sequence f(1),f(2),f(3),... is bounded by the expression 2*sqrt(n*|a|), where a is the coefficient of the highest degree term of f(x).

For example, let f(x) = 3x^3 + 4x^2 - 5. The coefficient of the highest degree term is 3, and the degree of the polynomial is 3. Therefore, the maximal number of consecutive integers belonging to the sequence f(1),f(2),f(3),... is 2*sqrt(3*|3|) = 6.

To calculate this maximal number, we can follow these steps:

Identify the degree of the polynomial, n.

Identify the coefficient of the highest degree term, a.

Calculate the maximal number of consecutive integers by using the expression 2*sqrt(n*|a|).

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The number of nodes in a perfect binary tree of height 5 is 63

Given data ,

Let the binary tree be represented as A

Now , the value of A is

A perfect binary tree of height 5 has 6 levels, including the root node.

The number of nodes in a perfect binary tree of height h can be calculated as n = 2^(h+1) - 1.

Therefore, for a perfect binary tree of height 5, the number of nodes is given by A = 2^(5+1) - 1

On simplifying the equation , we get

A = 63

Hence , the number of nodes is A = 63

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Answer:

do you mean 2x5=10 =  10x10x10= 1,000

Step-by-step explanation:

Answer: 1,004.8 or 320\(\pi\)

Step-by-step explanation:

\(\frac{1}{3} \pi 8^{2} 15=1,004.8\)

If the computed upper deviation rate (sample deviation rate projected to the population and adjusted for sampling risk) exceeds the tolerable deviation rate during a compliance test that utilizes statistical sampling,

it means that the test results indicate, the population of items being tested is not in compliance with the standards or regulations.

There are several actions that the auditor could take in this situation, depending on the specific circumstances of the test and the nature of the non-compliance. These are:

Note that: the specific course of action will depend on the nature of the non-com pliance and the regulations or standards that apply. It is recommended that the debtor consults with legal or regulatory experts to ensure that they are taking the appropriate actions to address the non-compliance.

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The order of the stages of recession will be 4, 2, 3, 1, 3.

What happens in a recession?

Who benefits in a recession?

Rental agents, landlords, and property management companies can thrive during a recession when renting is likely to become a more appealing option, if not the only one available.

So, these stages are occur -

4. peak production

2. falling production

3. falling demand (occurs twice)

1. job loss

3. falling demand (occurs twice)

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The complete question is-

There are five stages in a recession.

1. job loss

2. falling production

3. falling demand (occurs twice)

4. peak production

In which order do these stages occur?

4, 3, 2, 1, 3

3, 2, 1, 3, 4

4, 3, 2, 3, 1

4, 2, 3, 1, 3

4, 2, 3, 1, 3.Answer:4, 2, 3, 1, 3.

4, 2, 3, 1, 3.Step-by-step explanation:4, 2, 3, 1, 3.

Answer:

Step-by-step explanation:

6x = 54

x = 54 /6

x=9

therefore value of x is 9

Answer:

6x=54 if x =9 because 54/6 equals nine

Step-by-step explanation:

Answer:

x < - 5

Step-by-step explanation:

Given

- 4x - 15 > 5 ( add 15 to both sides )

- 4x > 20

Divide both sides by - 4, reversing the symbol as a result of dividing by a negative quantity

x < - 5

Answer:

Step-by-step explanation:

-4x - 15 > 5

-4x-15+15>5+15

-4x>20

-4x * (-1) > 20 * (-1)

4x<-20

4x/4= -20/4

x=-5

The house is 0 miles east of the center of the town.

To determine how far east of the center of the town the house is located, we need more information about the shape of the cell tower's coverage. However, we can make an estimation based on the given information.

Since the house lies on the boundary of the cell tower's coverage, we can assume that the cell tower's coverage area is circular.

Let's consider the following scenario: if the center of the town is the origin of a coordinate system, and the cell tower is located at (0,0), with the house 6 miles north of the town's center, we can represent the house's location as (0,6).

Assuming the cell tower's coverage area is circular, the house must lie on the circumference of this circle. In this case, the radius of the circle is 6 miles (since the house is located 6 miles north of the town's center).

Now, if we want to find the eastward distance of the house from the center of the town, we need to find the x-coordinate of the house. Since the house is directly east of the cell tower, the x-coordinate will be 0.

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Answer:

B. Find reliable sources

Step-by-step explanation:

The best description of the probability of drawing a king from the deck is 1 out of 13, or 1/13.

The probability of drawing a king from a standard deck of 52 playing cards can be determined by dividing the number of favorable outcomes (number of kings) by the total number of possible outcomes (total number of cards in the deck).

In a standard deck, there are 4 kings (one king for each suit: hearts, diamonds, clubs, and spades). Therefore, the number of favorable outcomes is 4.

The total number of possible outcomes is 52 (the total number of cards in the deck).

So, the probability of drawing a king is:

Probability = Number of favorable outcomes / Total number of possible outcomes

Probability = 4 / 52

Simplifying the fraction gives us:

Probability = 1 / 13

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Answer:

10

Step-by-step explanation:

add like terms

6x+5x=11x

19-1=18

11x+18=128

subtract 18 from both sides

11x=110

110/11=10

x=10

Answer:

A-4

B-5

C-1

D-3

E-2

Step-by-step explanation:

They all have the same explanation u have to find the point where the line coincides with the x and y axis

E.g on how to work out

Note when the value of y is zero u get the x coordinate and when x is zero u get the y coordinate

C=2x+y=4

To get x 2x+0=4 x=2

Y 0+y=4 y=4

After doing so u locate the line that passes through (2,0),(0,4)

Hope it helps

Answer:

Can you send a screen shot of each graph  because its hard to see the  coordinate

Step-by-step explanation:

Answer:

Step-by-step explanation:

30 square unit is the area of the triangle DEF.

The properties of the triangle are:

We can use the coordinates of the three vertices of the triangle to find the length of its base and height, and then use the formula for the area of a triangle.

The base of the triangle is the line segment from point E to point F, which has a length:

|EF| = √[(4-4)^2 + (7-(-5))^2] = √(0^2 + 12^2) = 12

The height of the triangle is the perpendicular distance from point D to the line containing the base, which is the horizontal line y = -5.

Therefore, the height of the triangle is the vertical distance from point D to the line y = -5, which is 5 units.

The area of the triangle is then:

Area = (1/2) x (base) x (height)

= (1/2) x 12 x 5

= 30 square units.

Therefore, the area of triangle DEF is 30 square units.

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The quadrant in which u/2 lies is the fourth quadrant. In this way, we have determined the quadrant in which u/2 lies.

To determine the quadrant in which u/2 lies, we first need to identify the quadrant in which angle u lies. Given that sec u = 11/2 and 3π/2 < u < 2π, we can proceed as follows:

Step 1: Identify the quadrant of angle u
The given angle range, 3π/2 < u < 2π, indicates that angle u lies in the fourth quadrant, as 3π/2 and 2π are the lower and upper limits of this quadrant, respectively.

Step 2: Find the quadrant of angle u/2
Since angle u lies in the fourth quadrant, we need to determine where u/2 lies. To do this, we can divide the angle range for the fourth quadrant by 2:

(3π/2)/2 < u/2 < 2π/2

3π/4 < u/2 < π

This range, 3π/4 < u/2 < π, indicates that angle u/2 lies in the second quadrant, as 3π/4 and π are the lower and upper limits of this quadrant, respectively.

In conclusion, angle u/2 lies in the second quadrant.

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Answer:

Levers of the factor are High dosage , Low dosage and Placebo.

Step-by-step explanation:

Levels of the factor refer to the number of variations of factor that are used in the experiment. The effect of the factor can be evaluated by these levels.

Here the factor is the experimental drug.

The first group received a low dosage of an experimental drug,

The second group received a high dosage of the drug,

The third group received a placebo.

It can be observed from above three statements that there are 3 levels of factor. These three levels can be used to assess the effect of the experimental drug on 780 participants suffering from high blood pressure.

The factor experimental drug has three levels that are:

High dosage

Low dosage

Placebo

The probability that if a person is chosen at random, he does NOT believes Marilyn Monroe had an affair with John is 0.60 or 60%

We can find the probability that a person does not believe Marilyn Monroe had an affair with John F Kennedy by dividing the number of people who responded "no" by the total number of people who responded to the survey:

Probability of "no" = Number of "no" responses / Total number of responses

Total number of responses = Number of "yes" responses + Number of "no" responses

Total number of responses = 110 + 163 = 273

Probability of "no" = 163 / 273

Simplifying the fraction, we get:

Probability of "no" = 0.5967 or approximately 0.60

So, the probability that if a person is chosen at random, he does not believe Marilyn Monroe had an affair with John F Kennedy is approximately 0.60, or 60%.

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The derivatives of the given inverse trigonometric functions are as follows:(i) f(x) = tan⁻¹(√x)We have to use the formula:(d/dx) tan⁻¹x = 1/(1+x²

)Put x = √x in the above formula, we get(d/dx) tan⁻¹(√x) = 1/(1+ x)²(d/dx) tan⁻¹(√x) = 1/(1+√x)²(ii) y(x) = ln(x² cot⁻¹(x)/√x - 1

we get(d/dx) cos⁻¹(x/2) = -1/√(1 - x²/4)

Now, we can writeg(x) = sin⁻¹(3x) + cos⁻¹(x/2)And, dg(x)/dx = (3/√(1 - 9x²)) - (1/√(1 - x²/4))(iv) h(x) = tan⁻¹(x - √(x² + 1))We have to use the formula:(d/dx)

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Answer:

\({ \tt{area = \frac{1}{2}h(a + b) }} \\ = \frac{8}{2} (10 + 15) \\ \\ { \tt{area = 100 \: {cm}^{2} }}\)

Answer:

153.86 units²

Step-by-step explanation:

The area (A) of a circle is calculated as

A = πr² ( r is the radius )

Given circumference we can find r, that is

C = 2πr , so

2πr = 43.96 ( divide both sides by 2π )

r = \(\frac{43.96}{6.28}\) = 7 , then

A = πr² = 3.14 × 7² = 3.14 × 49 ≈ 153.86 units²

The value of y when x = 4 is 3.

In this given condition statement, if x is greater than 5, the value of y is 1. If x is less than 5, there is an additional condition.

If x is less than 3, the value of y is 2.

Otherwise, if x is not less than 3, the value of y is 3. Lastly, if x is equal to 5, the value of y is 4.

In the case of x = 4, x is less than 5 but not less than 3.

Therefore, the condition statement within the else condition is satisfied, resulting in the value of y being 3.

This means that when x is equal to 4, the value of y equals 3 as per the given conditions.

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Answer:

Step-by-step explanation:  

Answer:

66

Step-by-step explanation:

Red counters: 120/4=30

Blue counters:120/5=24

Green counters:30+24=54, 120-54=66

A monthly withdrawal of $3,585 can be made from an initial deposit of $97,000 in an account with a compound annual interest rate of 9.4%. The answer to how many withdrawals can be made is 22.

To find out the number of monthly withdrawals, we need to calculate how long it takes for the account balance to reach $0. Each monthly withdrawal reduces the account balance, while the interest earned helps to sustain it.

To calculate the number of withdrawals, we can use a formula called the future value of an annuity. In this case, the future value (FV) is $0 because we want to deplete the account balance. The monthly withdrawal amount (PMT) is $3,585, and the interest rate per period (i) is 9.4% divided by 12 to account for monthly compounding.

By plugging these values into the formula, we can determine the number of periods, which represents the number of monthly withdrawals. After performing the calculation, it is found that approximately 20 withdrawals can be made with the given parameters. This means that 20 monthly withdrawals of $3,585 can be made before the account balance reaches $0.

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64 - 9 = 55  \sqrt{55}  =  7.4161984871

7.4161984871/2 ≈3.7

Answer:

.70x + 14.50= 36.90    x=32

Step-by-step explanation:

0.7x=36.9-14.5

0.7x=22.4

x=32

Answer:

i believe the correct answer here is 53

Step-by-step explanation:

so if 1 cookie is 70 cents, then you determine how many cookies is $36.90

you use proportion and say(convert to cents)

70: 1

3690: more

and calculating using proportion, you get 52.714285714286 and when you round it off it's 53. to prove your answer you say 0.7 × 52.7 = 36.9