How do I find the area of the kite ?

The complex number can be written in polar form as 2 + ((2+m) + 3i) = √(m² + 6m + 25)∠tan⁻¹(3/(2+m)).

What is complex number?

A complex number is obtained by adding real and imaginary numbers. Complex numbers have the formula a + ib and are usually symbolized by the symbol z. Here the numbers a and real are both. The value "a" is known as the real component and is denoted Re(z), while "b" is known as the imaginary part and is denoted Im(z). Also known as imaginary number, ib. Hero of Alexandria, a Greek mathematician, first used the idea of complex numbers in the first century when he tried to calculate the square root of a negative integer.

a. A complex number is a number that consists of a real part and an imaginary part, where the imaginary part is the real number multiplied by the imaginary unit "i", defined as the square root of -1. The modulus of a complex number is the distance between the starting point and the point representing the complex number on the complex plane. This can be calculated using the Pythagorean theorem. For example, the real part of the complex number z = 3 + 4i is 3 and the imaginary part is 4, and its modulus is √(3²+4²)=5.

b. Let z = a + bi be a complex number, where a and b are real numbers. The modulus of z is defined as |z| = √(a² + b²). Therefore, for the complex number z = 1 + 2i, the modulus is |z| = √(1² + 2²) = √5.

c. To write the complex number 2 = ((2+ m) + 3i) in polar form, we need to find the modulus and argument of the complex number. The modulus is |2 + ((2+m) + 3i)| = |4 + mi + 3i| = √(4² + (m+3)²) = √(m² + 6m + 25). The argument is given by tan⁻¹(Im/Re) = tan⁻¹(3/(2+m)), which gives us the angle that the complex number makes with the positive real axis. Therefore, the complex number can be written in polar form as 2 + ((2+m) + 3i) = √(m² + 6m + 25)∠tan⁻¹(3/(2+m)).

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The first positive root of the function f(x) = x² - 3 is located between x = 1 and x = 2.

The Intermediate Value Theorem states that if a function is continuous on a closed interval [a, b] and takes on values f(a) and f(b) with opposite signs, then there exists at least one root (zero) of the function between a and b.

In this case, we have f(x) = x² - 3. To find the first positive root of the function, we need to look for a positive value of x where f(x) = 0.

We can start by evaluating f(0) and f(2), which are the values of the function at the endpoints of the interval [0, 2]:

f(0) = 0² - 3 = -3

f(2) = 2² - 3 = 1

Since f(0) is negative and f(2) is positive, by the Intermediate Value Theorem, there must be at least one root of the function between x = 0 and x = 2.

To further narrow down the location of the root, we can evaluate f(1), which is the midpoint of the interval [0, 2]:

f(1) = 1² - 3 = -2

Since f(1) is negative, we know that the root is between x = 1 and x = 2.

To summarize, the first positive root of the function f(x) = x² - 3 is located between x = 1 and x = 2.

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Answer:

Let x be the length of Danika's old running route in miles.

Then, her new running route can be represented by x + 4, since it is 4 miles longer than her old route.

Step-by-step explanation:

The probability of drawing three sevens in a row from a standard deck of cards when the drawn card is not returned to the deck each time is approximately 0.00012, or 0.012%.

To determine the probability of drawing three sevens in a row from a standard deck of cards without replacement, we can use the following method:

Step 1: Identify the total number of cards in a standard deck. A standard deck has 52 cards (13 ranks and 4 suits).

Step 2: Determine the number of sevens in the deck. There are 4 sevens (one from each suit).

The probability of drawing a seven from a standard deck of 52 cards is 4/52 or 1/13, since there are four sevens in the deck. After the first seven is drawn, there are 51 cards left in the deck, of which three are sevens. So the probability of drawing a second seven is 3/51. Similarly, after the second seven is drawn, there are 50 cards left in the deck, of which two are sevens. So the probability of drawing a third seven is 2/50.


Step 3: Calculate the probability of drawing the first seven. This would be the number of sevens divided by the total number of cards:
P(1st Seven) = 4/52

Step 4: After drawing the first seven, there are now 51 cards left in the deck and only 3 sevens remaining. Calculate the probability of drawing the second seven:
P(2nd Seven) = 3/51

Step 5: After drawing the second seven, there are now 50 cards left in the deck and only 2 sevens remaining. Calculate the probability of drawing the third seven:
P(3rd Seven) = 2/50

Step 6: To find the probability of all three events happening in a row, multiply the individual probabilities:
P(Three Sevens) = P(1st Seven) * P(2nd Seven) * P(3rd Seven) = (4/52) * (3/51) * (2/50)

Step 7: Calculate the result:
P(Three Sevens) = (4/52) * (3/51) * (2/50) = 0.0012 (approximately)

The probability of drawing three sevens in a row from a standard deck of cards without replacement is approximately 0.0012, or 0.12%.

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The differential   [tex]dy=2[/tex] when [tex]x = 4[/tex]  and [tex]dx = 0. 2.[/tex]

To find the change in [tex]y,Δy[/tex] , when x changes from, we can use the [tex]4 to 4 +Δx = 4 + 0.2 = 4.2[/tex] formula:

[tex]Δy = y(x + Δx) - y(x)[/tex]

where[tex]y(x) = 5x^2.[/tex]

So, plugging in[tex]x = 4[/tex] and[tex]x + Δx = 4.2[/tex] , we get:

[tex]Δy = y(4.2) - y(4)[/tex]

[tex]= 5(4.2)^2 - 5(4)^2[/tex]

[tex]= 44.2[/tex]

Therefore, the change in y is [tex]44.2[/tex] when x changes from [tex]4 to 4.2.[/tex]

To find the differential dy when [tex]x = 4[/tex] and [tex]dx = 0.2,[/tex]  we can use the formula:

[tex]dy = f'(x) × dx[/tex]

where the derivative of y with respect to x, which is:

[tex]f'(x) = 10x[/tex]

Plugging in [tex]x = 4[/tex]   we get:

[tex]= 2[/tex]

Therefore, the differential [tex]dy = 2[/tex] when [tex]x = 4[/tex] and [tex]dx = 0.2.[/tex]

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There is 75% of getting at least two tiles of vowels

Fits, less than two of the tiles are vowels

= 11 + 39

= 50

Now, at least two of tiles are vowels

= 200 - 50/ 200

= 150/200

= 0.75 x 100

= 75%

There is 75% of getting at least two tiles of vowels

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Answer: 11.76

Step-by-step explanation:  you have to divide by 12 everything and multiply by 6 and you can get the answer

(a) First step of implicit differentiation:
-0.82dP/dt = dq/dt
The equation that results from differentiating each side of the equation with respect to P is:
-0.82 - 0.82P(d^2q/dP^2) = (dQ/dP)(dP/dt)/(dq/dt)
To find the elasticity of demand, we need to use the formula:
E = (dQ/Q)/(dP/P)
We can rewrite this as:
E = (dQ/dP) * (P/Q)
We know that dQ/dP = -0.82P(d^2q/dP^2), so we substitute that into the formula:
E = (-0.82P(d^2q/dP^2)) * (P/q)
Simplifying this expression, we get:
E = -0.82P^2(d^2q/dP^2)/q

(b)  We can solve the original equation for q by dividing both sides by -0.82:
q = (-1/0.82)P + D
Taking the derivative of q with respect to P, we get:
dq/dP = -1/0.82
We can use this result to calculate the elasticity of demand using the formula:
E = (dQ/dP) * (P/Q)
Substituting the values we found, we get:
E = (-1/0.82) * (P/((-1/0.82)P + D))
Simplifying this expression, we get:
E = -1/(P/((-1/0.82)P + D))
E = -1/((D/P) - 1.22)

(a) Interpretation: The elasticity of demand is a measure of how much the quantity demanded changes in response to a change in price. If E > 1, demand is considered elastic, meaning that a small change in price will result in a large change in quantity demanded. If E < 1, demand is considered inelastic, meaning that a change in price will result in a small change in quantity demanded. If E = 1, demand is unit elastic, meaning that a change in price will result in an equal proportional change in quantity demanded.
(b) Interpretation: The elasticity of demand in this case depends on the values of D and P. If D is relatively small compared to P, then the elasticity of demand will be close to -1.22, which is the upper limit of the elasticity. If D is relatively large compared to P, then the elasticity of demand will be close to zero, which means that demand is very inelastic.

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Answer:

A. 4^2 - 4(2)(26) = 16 - 208 = -192

B. This equation has no real roots.

C. (-4 + √-192)/(2×2) = (-4 + 8i√3)/4

= -1 + (2√3)i

The required manager should charge $1600 for one-bedroom units and $2250 for two-bedroom units to maximize revenue.

Let x be the number of $20 increases in the price of a one-bedroom unit, and y be the number of $60 increases in the price of a two-bedroom unit. Then the rental prices for one-bedroom and two-bedroom units can be expressed as:

One-bedroom price = $1200 + $20x

Two-bedroom price = $1800 + $60y

The total number of customers for one-bedroom units is 90 minus the number of customers lost due to the price increase, which is x. Similarly, the total number of customers for two-bedroom units is 100 minus the number of customers lost due to the price increase, which is 2y. Therefore, the total revenue can be expressed as:

Revenue = (90 - x) * ($1200 + $20x) + (100 - 2y) * ($1800 + $60y)

Expanding and simplifying this expression, we get:

Revenue = 216000 + 9600x - 240x² + 180000 + 108000y - 7200y²

Collecting like terms, we get:

Revenue = -240x² - 7200y² + 9600x + 108000y + 396000

To find the rental price that maximizes revenue, we need to find the values of x and y that maximize the revenue. We can do this by taking partial derivatives of the revenue function with respect to x and y and setting them equal to zero:

dRevenue/dx = -480x + 9600 = 0

dRevenue/dy = -14400y + 108000 = 0

Solving for x and y, we get:

x = 20

y = 7.5

Therefore, the rental prices that maximize revenue are:

One-bedroom price = $1200 + $20x = $1600

Two-bedroom price = $1800 + $60y = $2250

So the manager should charge $1600 for one-bedroom units and $2250 for two-bedroom units to maximize revenue.

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The dimensions of section B are 36 inches by 48 inches, and the area of the piece of sheet metal after both sections are cut and removed is 6336 square inches.

Given the width and length of a rectangular piece of sheet metal as 60 inches and 44 inches, we need to find the dimensions of section B and the area of the piece of sheet metal after both sections are cut and removed.

The length of rectangle B can be found as TR = SR - ST = PQ - ST, where SR and PQ are opposite sides of the rectangle. Here, PQ is the length of the rectangular sheet metal, which is 60 inches, and ST is the width of the rectangle WVTX, which is 24 inches. Therefore, the length of rectangle B is:

TR = PQ - ST = 60 - 24 = 36 inches

The breadth of rectangle B can be found as UR = QR - QV - VT - TU. Here, QR and PS are opposite sides of the rectangle PQRS, so QR = PS = 144 inches. Also, QV is the width of rectangle WVTX, which is 36 inches, and VT and TU are the lengths of rectangle WVTX, which are both 24 inches. Therefore, the breadth of rectangle B is:

UR = QR - QV - VT - TU = 144 - 36 - 24 - 36 = 48 inches

So, the dimensions of section B are 36 inches by 48 inches.

Next, we need to find the area of the piece of sheet metal after both sections are cut and removed.

The area of rectangle B is the product of its length and breadth, which is:

Area of rectangle B = length × breadth = 36 × 48 = 1728 square inches

The area of rectangle WVTX is the product of its length and breadth, which is:

Area of rectangle WVTX = length × breadth = 24 × 24 = 576 square inches

The area of rectangle PQRS is the product of its length and breadth, which is:

Area of rectangle PQRS = PQ × PS = 60 × 144 = 8640 square inches

Therefore, the area of the piece of sheet metal after both sections are cut and removed is:

Area of the piece of sheet metal = Area of rectangle PQRS - Area of rectangle B - Area of rectangle WVTX

= 8640 - (1728 + 576)

= 8640 - 2304

= 6336 square inches

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A call that lasts for a length of 4 minutes would cost the same at either hotel.

For Hotel A: Cost = 2(4) + 5 = 13

For Hotel B: Cost = 4(4) - 3 = 13 minutes

We can determine the length of phone call that would cost the same at either hotel by the following equations.

Given:

Hotel A, cost of the call:

Cost for Hotel A = 2x + 5

For Hotel B, the cost of the call:

Cost for Hotel B = 4x - 3

For the length of the call that would cost the same at either hotel, we shall set these two equations equal to each other and solve for x:

2x + 5 = 4x - 3

Subtracting 2x from both sides, we get:

5 = 2x - 3

Adding 3 to both sides, we get:

8 = 2x

Dividing both sides by 2, we get:

x = 4

So, a call that lasts 4 minutes would cost the same at either hotel.

We can verify this, let's plug x = 4 into both equations:

For Hotel A: Cost = 2(4) + 5 = 13

For Hotel B: Cost = 4(4) - 3 = 13

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The only option that has a number that is divisible by both 5 and 6 is: D.193.560

We want to find a number that is divisible by both 5 and 6.

Now, looking at the options, since they are all decimals, the one that would be the most appropriate is the one that does not contain a recurring decimal.

Thus:

A) 132.359/5 =26.4718

132.359/6 = 22.0598333..

B) 142.645/5 = 28.529

142.645/6 = 23.77416666666..

C) 164.780/5 = 32.956

164.780/6 = 27.46333333

D) 193.560/5 = 38.712

193.560/6 = 32.26

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Broker U's package costs $156.02 less money than Broker V's package. The Option C is correct.

Broker U: 2.8% commission

2 par value bonds $1,000 x 96.674% = $1,933.48

3 par value bond $500 x 109.330% = $1,639.95

2 par value bonds $1,000 x 103.851% = $2,077.02

Silvia's total investment:

= ($1,933.48 + $1,639.95 + $2,077.02) x 1.028

= $5,808.66

Broker V: $65 per bond plus

4 par value bonds $500 x 105.142% = $2,102.84

1 par value bond $500 x 85.990% = $429.95

3 par value bonds $1,000 x 97.063% = $2,911.89

Silvia's total investment:

= $2,102.84 + $429.95 + $2,911.89 + (8 x $65)

= $5,964.68

By how much of less that these bond package cost is:

= Broker V's offer - Broker U's offer

= $5,964.68 - $5,808.66

= $156.02

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Answer:166.2 feet^2

Step-by-step explanation:

By assuming that Pete's yard is a rectangle, we can get the perimeter by using an equation that looks like this:

perimeter = l+l+w+w

Where l = length, and w = width.

This is because you are adding the measures of every side together, which is the definition of the value of a perimeter.

Furthermore, to get the area of the figure, you would need to multiply 52.7 by 30.4, which would be 1602.08 feet^2

Answer:

THESE NUTS

Step-by-step explanation:

Answer:

The sum of the interior angles of any quadrilateral is 360 degrees.

So, let x be the measure of the fourth angle. Then we can write the equation:

98 + 139 + 80 + x = 360

Simplifying this equation gives:

317 + x = 360

Subtracting 317 from both sides gives:

x = 43

Therefore, the measure of the fourth interior angle of this convex quadrilateral is 43 degrees.

Step-by-step explanation:

The measure of the fourth interior angle of the convex quadrilateral is 43 degrees. To find the measure of the fourth interior angle of a convex quadrilateral, we'll use the following terms: interior, angles, quadrilateral, and measure.

Step 1: Remember that the sum of interior angles of a quadrilateral is always 360 degrees.

Step 2: Add the three given interior angles: 98 + 139 + 80 = 317 degrees.

Step 3: Subtract the sum of the three angles from the total sum of quadrilateral angles (360 degrees) to find the measure of the fourth angle: 360 - 317 = 43 degrees.

The measure of the fourth interior angle of the convex quadrilateral is 43 degrees.

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Answer:

[tex]\frac{62}{9}[/tex] or  6.8888889

Step-by-step explanation:

The explanation is on the attachment below

Answer:

The answer is 10 and -10

You get this answer because in the middle in a number line is 0 and if it 10 units from 0 then the other side of 0 will be -10 (negative ten) units from 0

To find a polynomial function f(x) of least degree having only real coefficients and zeros of 5 and 2-i, we know that the complex conjugate of 2-i, which is 2+i, must also be a zero. This is because complex zeros of polynomials always come in conjugate pairs.

So, we can start by using the factored form of a polynomial:

f(x) = a(x - r1)(x - r2)(x - r3)...

where a is a constant and r1, r2, r3, etc. are the zeros of the polynomial. In this case, we have:

f(x) = a(x - 5)(x - (2-i))(x - (2+i))

Multiplying out the factors, we get:

f(x) = a(x - 5)((x - 2) - i)((x - 2) + i)
f(x) = a(x - 5)((x - 2)^2 - i^2)
f(x) = a(x - 5)((x - 2)^2 + 1)

To make sure that f(x) only has real coefficients, we need to get rid of the complex i term. We can do this by multiplying out the squared term and using the fact that i^2 = -1:

f(x) = a(x - 5)((x^2 - 4x + 4) + 1)
f(x) = a(x - 5)(x^2 - 4x + 5)

Now, we just need to find the value of a that makes the degree of f(x) as small as possible. We know that the degree of a polynomial is determined by the highest power of x that appears, so we need to expand the expression and simplify to find the degree:

f(x) = a(x^3 - 9x^2 + 24x - 25)
Degree of f(x) = 3

Since we want the least degree possible, we want the coefficient of the x^3 term to be 1. So, we can choose a = 1:

f(x) = (x - 5)(x^2 - 4x + 5)
Degree of f(x) = 3

Therefore, the polynomial function f(x) of least degree having only real coefficients and zeros of 5 and 2-i is:

f(x) = (x - 5)(x^2 - 4x + 5)
To find a polynomial function f(x) of least degree with real coefficients and zeros of 5 and 2-i, we need to remember that if a polynomial has real coefficients and has a complex zero (in this case, 2-i), its conjugate (2+i) is also a zero.

Step 1: Identify the zeros
Zeros are: 5, 2-i, and 2+i (including the conjugate)

Step 2: Create factors from zeros
Factors are: (x-5), (x-(2-i)), and (x-(2+i))

Step 3: Simplify the factors
Simplified factors are: (x-5), (x-2+i), and (x-2-i)

Step 4: Multiply the factors together
f(x) = (x-5) * (x-2+i) * (x-2-i)

Step 5: Expand the polynomial
f(x) = (x-5) * [(x-2)^2 - (i)^2] (by using (a+b)(a-b) = a^2 - b^2 formula)
f(x) = (x-5) * [(x-2)^2 - (-1)] (since i^2 = -1)
f(x) = (x-5) * [(x-2)^2 + 1]

Now we have a polynomial function f(x) of least degree with real coefficients and zeros of 5, 2-i, and 2+i:
f(x) = (x-5) * [(x-2)^2 + 1]

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There are 84 different ways to seat three adults and three children at a circular table such that each child must be next to two adults.

To seat three adults and three children at a circular table such that each child must be next to two adults, we can use the following steps:

There are 2! options for the other two adults and 3! options for children.

The number of ways for two adults and children:

= 2! × 3!

= 2 × 6

= 12 ways to seat them

There are 3 ways to pick the two children, two ways to seat them, and two ways for them to begin the circle, for a total of six options.

The third child has a pair of choices:

6 × 2 so far

Then, there are 3! =6  ways to seat the adults.

6 × 2 × 6 = 72 ways

Putting it all together, the total number of seating arrangements is:

12+72 = 84 ways  

Therefore, there are 84 different ways to seat three adults and three children at a circular table such that each child must be next to two adults.

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When reading a graph it’s the same as reading most books from left to right and since the line goes up from left to right it is a positive slope.

The choice that matches the graph of the function as is defined to us is:  Graph A.

We are given a function f(x) as:

    f(x)=   2x    if x < 3

 and        4     if  x ≥ 3

This means that in the region (-∞,3) the graph of a function is a straight line that passes through the origin and has a open circle at x=3.

Also, in the region [3,∞) the graph is a straight horizontal line i.e. y=4.

Hence, the graph of this function is Graph A.

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On a piece of paper, graph f(x)={2x if x <3

{4 if x >3. Then determine which answer choice matches the graph you drew

The coordinates of the point (-7,-3) after a 90 degree clockwise rotation about the origin are (-3,-7).

To rotate a point 90 degrees clockwise about the origin, we need to swap its x and y coordinates and negate the new x coordinate.

So, starting with point (-7,-3):

Swap the x and y coordinates to get (3,-7)

Negate the new x coordinate to get (-3,-7)

Therefore, the coordinates of the point (-7,-3) after a 90 degree clockwise rotation about the origin are (-3,-7).

In mathematics, coordinates are used to specify the position of a point or an object in a particular space. The number of coordinates needed depends on the dimension of the space in which the point or object exists.

In two-dimensional space (also called the Cartesian plane), a point is located by two coordinates, usually denoted as (x, y), where x represents the horizontal distance from a fixed reference point called the origin, and y represents the vertical distance from the origin.

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Answer: 120

Step-by-step explanation:V= 8x5x3 =120 ^3

a. The correlation matrix p =  [tex]\left[\begin{array}{ccc}1&1/3&2/5\\1/3&1&-3/5\\2/5&-3/5&1\end{array}\right][/tex]. b. The correlation between X1, and i/2X2 + 1/2X3 is 0.3.

a. The correlation matrix p can be calculated by dividing the covariance matrix by the product of the standard deviations of the variables:

p = [tex]\left[\begin{array}{ccc}1&1/3&2/5\\1/3&1&-3/5\\2/5&-3/5&1\end{array}\right][/tex]

b. To compute the correlation between X1 and i/2X2 + 1/2X3, we first need to calculate the standard deviations of the variables:

σ1 = sqrt(4) = 2

σ2 = sqrt(9) = 3

σ3 = sqrt(25) = 5

Then, we can calculate the covariance between X1 and i/2X2 + 1/2X3:

cov(X1, i/2X2 + 1/2X3) = cov(X1, i/2X2) + cov(X1, 1/2X3)

= i/2 * cov(X1, X2) + 1/2 * cov(X1, X3)

= i/2 * 1 + 1/2 * 2

= 1.5

Finally, we can compute the correlation using the formula:

corr(X1, i/2X2 + 1/2X3) = cov(X1, i/2X2 + 1/2X3) / (σ1 * σ2/2 + σ3/2)

= 1.5 / (2 * 3/2 + 5/2)

= 0.3

Therefore, the correlation between X1 and i/2X2 + 1/2X3 is 0.3.

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Answer:

I believe (3, 5) and (10, 1) is the answer

Step-by-step explanation:

The value of function f(- 3) for the piece-wise function is,

⇒ f (- 3) = - 1

We have to given that;

The piece-wise function is,

f (x) = (x + 2) ; if x < 2

      = (x + 1) ; if x ≥ 2

Hence, At x = - 3;

Function is,

⇒ f (x) = x + 2

Hence, Substitute x = - 3;

⇒ f (- 3) = - 3 + 2

⇒ f (-3) = - 1

Thus, The value of function f(- 3) for the piece-wise function is,

⇒ f (- 3) = - 1

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Answer:5

explanation:

you are doing great finding the slopes: