find y' if x^y = y^x​

hi,

the function is given with it's canonic form.  

canonic form is  :  f(x) = a ( x-α)² + β

α  and β are the value of the coordonnates of the vertex.

so here we  have : ƒ(x) = 2(x−1)² +3

with α = 1  and β = 3

so vertex is  V (1;3)

So yes, answer is   A.

The change in altitude between the maximum height and the height at which the balloon was recovered is 1300 meters

It is important to note that the maximum height is the peak altitude the balloon reached

To find the difference, we use the formula

Change = Maximum height - recovery height

Maximum height = 5000 meters

Recovery height = 3700 meters

Substitute the values

Change = 5000 - 3700

Change = 1300 meters

Thus, the change in altitude between the maximum height and the height at which the balloon was recovered is 1300 meters

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The common difference based on the sequence given is 15.

It should be noted that the sequence given Isa arithmetic sequence.

The common difference will be the second term minus the first term. This will be:

= 101 - 86

= 15

In conclusion, the difference is 15.

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The negative solution is -2.21 and positive solution is 12.21

Given the quadratic equation expressed as:

x^2-10x-27 = 0

Find the solution using the general formula

x^2-10x-27 = 0

x = 10±√(10)²-4(1)(-27)/2

x =  10±√100+108/2

x =  10±√208/2

x = 10±14.422/2

Simplify

x = 10+14.422/2 and x = 10-14.422/2

x = 24.422/2 and -4.422/2

x = 12.21 and -2.21

Hence the negative solution is -2.21 and positive solution is 12.21

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Answer:

[tex]-\frac{4}{3}[/tex](Your answer choices were really confusing, so I just put the plain answer)

Step-by-step explanation:

To find the slope of a line with just two points, we can use the formula [tex]\frac{y2-y1}{x2-x1}[/tex]. In this case, [tex]\frac{5-(-3)}{2-8}[/tex]. This is [tex]\frac{8}{-6}[/tex]. This reduces to [tex]-\frac{4}{3}[/tex]

The maximum amount of water that can be used by each house on a daily basis is 100 liters.

4,500 = 500 + 40x

4,500 - 500 = 40x

4,000 = 40x

x = 4,000 / 40

x = 100 liters

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Answer:

  A, D

Step-by-step explanation:

Lines are parallel if consecutive interior angles at a transversal are supplementary.

In the given figure, angles EAH and AED are consecutive interior angles associated with transversal AE. If they total 180°, then AC║EF.

Similarly, angles FCI and CFG are consecutive interior angles associated with transversal CF. If they total 180°, then AC║EF.

Either of these will prove AC║EF:

Levada borrows $30,900 from her bank to open a florist shop at rate of 0.98% per month.

If the initial amount (also called as principal amount) is P, and the interest rate is R% annually, and it is left for T years for that simple interest, then the interest amount earned is given by:

[tex]I = \dfrac{P \times R \times T}{100}[/tex]

It is given that Levada borrows $30,900 from her bank to open a florist shop. She agrees to repay the money in 18 months with simple annual interest of 5.5%.

P = $30,900

T = 18 months

Interest  = 5.5%

Interest rate =  P×R×T

5.5 = 30,900 × R × 18

R = 0.000988

Or, R = 0.98% per month.

The complete question is

"a) How much must she pay the bank in 18 months?"

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The value of the limit of the function given when the value of x tends to zero is 0

The limit of a function is a fundamental concept in calculus and analysis concerning the behavior of that function near a particular inputs.

Given the function limit below;

lim x→0 [1 − cos(2x) /x]

Substitute the value of x into the expression to have;

f(0) = 1-cos2(0)/0
f(0) = 1-1/0

f(0) = 0/0 (ind)

Apply the L'hospital rule to have:

lim x→0 [ − (-2sin2x)) /1]

Substitute the value of x into the result

f(0) = 2sin2(0)/1

f(0) = 2(0)

f(0) = 0

Hence the value of the limit of the function given when the value of x tends to zero is 0

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Mrs Kingsley cut the ribbon into a length of 12.75 inches each.

Division is the process of grouping a number into equal parts using another number. The sign used to denote division is ÷.

Length of each ribbon = 102 / 8 = 12.75 inches

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See below for the examples of sectors and arcs of a circle

The area of a sector is calculated as:

[tex]A = \frac{\theta}{360} * \pi r^2[/tex] ---- when the angle is in degrees

[tex]A = \frac{\theta}{2} *r^2[/tex] ---- when the angle is in radians

Take for instance, we have the following problems involving sector areas

Calculate the area of a sector where the radius of the circle is 7, and

Using the above formulas, the sector areas are:

1. [tex]A = \frac{30}{360}* \frac{22}{7} * 7^2 = 12.83[/tex]

2.  [tex]A = \frac{\pi}{12} * 7^2 = 12.83[/tex]

3. [tex]A = \frac{90}{360}* \frac{22}{7} * 7^2 = 38.5[/tex]

4. [tex]A = \frac{\pi}{2} * 7^2 = 38.5[/tex]

5. [tex]A = \frac{180}{360}* \frac{22}{7} * 7^2 = 77[/tex]

The length of an arc is calculated as:

[tex]L= \frac{\theta}{360} * 2\pi r[/tex] ---- when the angle is in degrees

[tex]L = r\theta[/tex] ---- when the angle is in radians

Take for instance, we have the following problems involving arc lengths

Calculate the length of an arc where the radius of the circle is 7, and

Using the above formulas, the arc lengths are:

1. [tex]L = \frac{30}{360}* 2 * \frac{22}{7} * 7 = 3.7[/tex]

2.  [tex]L = \frac{\pi}{12} * 7 = 3.7[/tex]

3. [tex]L = \frac{90}{360}*2 * \frac{22}{7} * 7 = 11.0[/tex]

4. [tex]L = \frac{\pi}{4} * 7 = 11[/tex]

5. [tex]L = \frac{180}{360}*2 * \frac{22}{7} * 7 = 22[/tex]

The examples include:

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Hence, the missing internal angle is [tex]15[/tex].

What is the angle?

An angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle. Angles formed by two rays lie in the plane that contains the rays.

Angles are also formed by the intersection of two planes. These are called dihedral angles.

Here given that,

[tex]Q = 87 + 40Q = 127X + 127 + 38 = 180X = 180 - 127 - 38X = 15[/tex]

Hence, the missing internal angle is [tex]15[/tex].

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The blank space in the task content should be filled with; Wages.

A wage by it's primitive definition is a fixed regular payment usually paid on a daily or weekly basis by the employer to an employee which could be skilled or unskilled.

Commission, and salary which is a monthly analogue of wages is another form of employee compensation.

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Answer:

325 adult tickets

Step-by-step explanation:

Let adult tickets be x, student tickets are 75 less than adult tickets, so let student tickets be x-75

The total is 575

x+x-75 = 575

2x = 650

x = 325 adult tickets

Answer:

19.50

Step-by-step explanation:

32m = 624

m = 19.50

need more words

The size of the corner you need to cut in order for your box to have this area is 0.5 inches

The base length is given as:

Length = 7

When the edges are removed, the new length becomes

New length = 7 - x - x

Evaluate

New length = 7 - 2x

The base width is given as:

Width = 4

When the edges are removed, the new length becomes

New width = 4 - x - x

Evaluate

New width = 4 - 2x

The area of the bottom of the box is calculated as:

Area = New length * New width

This gives

Area = (7 - 2x) * (4 - 2x)

Rewrite as:

A(x) = (7 - 2x) * (4 - 2x)

The area is given as:

Area = 16

So, we have:

(7 - 2x) * (4 - 2x) = 16

Expand

28 - 14x - 8x + 4x^2 = 16

Rewrite as

4x^2 - 14x - 8x + 28 - 16 = 0

Evaluate the like terms

4x^2 - 22x + 12= 0

We have:

4x^2 - 22x + 12= 0

Expand the equation

4x^2 - 24x - 2x + 12 = 0

Factorize the equation

4x(x - 6) - 2(x - 6) = 0

Factor out x - 6

(4x - 2)(x - 6) = 0

Solve for x

x = 0.5 or x = 6

The value of x = 6 is too big for the dimensions of the box.

So, x = 6 is an extraneous solution for the equation

Hence, the size of the corner you need to cut in order for your box to have this area is 0.5 inches

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Answer:

11.863 g

Step-by-step explanation:

5.623 g + 6.24 g = 11.863 g

Answer:

361

Step-by-step explanation:

discriminant = b² - 4ac

= (21)² - 4(1)(20)

= 441 - 80

= 361

The missing angle is B = 65° and the missing sides are a ≈ 7.461 and c ≈ 6.762.

In this case, we know two angles (A = 25°, C = 90°) and a side of a triangle (b = 16) and Euclidean properties and the law of the sines must be used to find the rest of variables:

B = 180° - A - C

B = 180° - 25° - 90°

B = 65°

a = 16 × (sin 25°/sin 65°)

a ≈ 7.461

c = 16 × (sin 25°/sin 90°)

c ≈ 6.762

The missing angle is B = 65° and the missing sides are a ≈ 7.461 and c ≈ 6.762.

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Answer:

y = 3x + 1

Step-by-step explanation:

The formula for equation of a line in slope intercept form is;

y = mx + c

Where;

m is slope

c is y-intercept

Now, since we have coordinates, we will get the equation as;

(y - y1)/(x - x1) = m

(y - 1)/(x - 0) = 3

y - 1 = 3x

y = 3x + 1

The two bottom graphs demonstrate translations.

We will have a translation only if:

The images where the figures are only moved a little bit are the ones that demonstrate just a translation, and these are the two lower ones.

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Answer:

D. 4

Step-by-step explanation:

[tex]\sqrt{2-\left( 4\right)^{2} } =\sqrt{2-16} =\sqrt{-12}[/tex]

since ,√(-12) is not a real number

Then

The function f is not defined for x = 4

Answer:

D. 4

Step-by-step explanation:

thank you for your help 4 was the correct answer took the test and got it right

Hope that helps...........................

None of the three points (A, B, C) lies on the circumference of the unit circle.

Unit circles are circles centered at the origin and with a radius of 1. A point is on the circumference if and only if the distance of the point respect to the origin is equal to 1. The distance of each point is determine by Pythagorean theorem:

Point A

[tex]d = \sqrt{4^{2}+3^{2}}[/tex]

d = 5

Point B

[tex]d = \sqrt{\left(\frac{1}{2} \right)^{2}+\left(\frac{1}{5}\right)^{2} }[/tex]

d = √29 /10

d ≈ 0.539

Point C

[tex]d = \sqrt{\left(\frac{3}{4} \right)^{2}+\left(\frac{7}{4} \right)^{2}}[/tex]

d = √58 /4

d ≈ 1.904

None of the three points (A, B, C) lies on the circumference of the unit circle.

The statement presents a typing mistake, correct form is shown below:

A(x, y) = (4, 3), B(x, y) = (1/2, 1/5), C(x, y) = (3/4, 7/4). Which point lies on the circumference of the unit circle?

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[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textbf{Equation:}[/tex]

[tex]\mathsf{-\dfrac{3}{12}}[/tex]

[tex]\huge\textbf{Simplify:}[/tex]

[tex]\mathsf{-\dfrac{3}{12}}[/tex]

[tex]\mathsf{= \dfrac{-3\div 3}{-12\div3}}[/tex]

[tex]\mathsf{= -\dfrac{1}{4}}[/tex]

[tex]\huge\textbf{Therefore, your answer should be:}[/tex]

[tex]\huge\boxed{\frak{- \dfrac{1}{4}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

The equation of a line parallel to the given line and passing through the point (0, 8) is 5y - 3x = 40

The equation of a line in point-slope form is expressed as;

y - y0 = m(x -x0)

where

m is the slope

(x0, y0) is the point on the line

Given the following parameters

Point (0,8)

Slope from the equation = 3/5

Substitute

y - 8 = 3/5(x - 0)
5(y -8) =3x

5y - 40 = 3x

5y - 3x = 40

Hence the equation of a line parallel to the given line and passing through the point (0, 8) is 5y - 3x = 40

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The perimeter of the decking area is 800cm.

It is important to note that the decking area takes the shape of a rectangle

The formula for determining the perimeter of the decking area is given as;

Perimeter = 2 multiplied by the sum of the length and width of the rectangle

It is mathematically written as;

Perimeter = 2 ( length + width)

Where;

Now, let's substitute the values into the formula

Perimeter = 2 ( 150 + 250)

Sum the bracket

Perimeter = 2 ( 400 )

Perimeter = 2 × 400

Perimeter = 800 cm

Thus, the perimeter of the decking area is 800cm

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