A rectangular patio has a length of 12 1\2 feet and an area of 103 1\8 square feet. What is the width of the patio?

a. (2 - 2i√3)⁴ in polar form is 256(cos(-4π/3) + isin(-4π/3)) = 256cis(-4π/3)

b. (2 - 2i√3)⁴ in rectangular form is -128 + 128√3

To answer the question, we need to know what complex numbers are

Complex numbers are numbers of the form z = x + iy

Complex numbers in polar form z = r(cosθ + isinθ) where

Given that z = (2 - 2i√3)⁴ =

So,

So, converting to polar form

r = √(x² + y²)

= √[2² + (-2√3)²]

= √[4 + 4(3)]

= √[4 + 12]

= √16

= 4

θ = tan⁻¹(y/x)

θ = tan⁻¹(-2√3/2)

θ = tan⁻¹(-√3)

θ = -π/3

So, z = r(cosθ + isinθ)

= 4(cos(-π/3) + isin(-π/3))

A complex number z raised to power n is zⁿ = rⁿ(cosnθ + isin(nθ)]

z⁴ = (2 - 2i√3)⁴

= r⁴(cos4θ + isin4θ)

= 4⁴(cos(4 × -π/3) + isin(4 × -π/3))

= 256(cos(-4π/3) + isin(-4π/3))

= 256cis(-4π/3)

(2 - 2i√3)⁴ in polar form is 256(cos(-4π/3) + isin(-4π/3)) = 256cis(-4π/3)

The complex number z =  r(cosθ + isinθ) in rectangular form is z = x + iy where

Given that z⁴ = 256(cos(-4π/3) + isin(-4π/3)) in rectangular form,

x = rcosθ

= 256(cos(-4π/3)

= 256cos(-4 × 60°)

= 256cos(-240)

= 256cos(240)

= 256 × -1/2

= -128

y =  rsinθ

= 256sin(-4π/3)

= 256sin(-4 × 60°)

= 256sin(-240)

= -256sin240

= -256 × -√3/2

= 128√3

So, z⁴ = x + iy

= -128 + 128√3

So, (2 - 2i√3)⁴ in rectangular form is -128 + 128√3

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Answer:

Step-by-step explanation:

Answer: its c

Step-by-step explanation: im a smarty boy i hope u its right or not

The graph represents a function because (a) Yes, because it passes the vertical line test.

The information that completes the question is added as an attachment

For a graph to represent a function, the graph must pass a vertical line test.

The vertical line test is such that a line drawn from the x-axis must intersect with the graph at only one point.

Based on the criteria above, the given graph would pass the vertical line test.

Hence, the graph represents a function because (a) Yes, because it passes the vertical line test.

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Answer:it's 24

Step-by-step explanation:

its multiplying the 5, 6 times

Answer:

50%

the mean (46) marks the halfway point, so over the mean is 50% and under the mean is 50%

The experimental probability of rolling a 6 will be 13.3%

The probability will be calculated thus:

= Number of times that 6 occured / Total number if outcomes

= 4/(7 + 4 + 4 - 5 + 6 + 4)

= 4/30

= 0.133

= 13.3%

Therefore, the probability is 0.133 or 13.3%.

Table shows the results of rolling a die several times.

outcome: 1, 2, 3, 4, 5, 6

number of times outcome occurred: 7, 4, 4, 5, 6, 4

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Answer:

f(x) = 3x + 9:  y - intercept is option  c. (0,-9)

f(x) = 3x - 9:  y - intercept is option   b. (0, 9)

Step-by-step explanation:

option a and d cant be correct since y = 0 in those answer when the y - intercept is when x = 0

If the function f(x) = 3x + 9

than x = 0

f(x) = 3(0) + 9

f(x) = 0 + 9

f(x) = 9

x = 0 and y = 9 (0, 9)

If the function f(x) = 3x - 9

than x = 0

f(x) = 3(0) - 9

f(x) = 0 - 9

f(x) = -9

x = 0 and y = -9 (0, -9)

Answer:

[tex]x = 2, y = -3[/tex]

Step-by-step explanation:

Add the 2 equations together, then solve for x.

[tex](2x + 2y) + (3x - 2y) = (-2) + (12)\\ 2x + 3x + 2y - 2y = -2 + 12\\5x = 10\\x = 2[/tex]

Now that we know the value of x, we can easily find y by substitution.

[tex]3x - 2y = 12\\3(2) - 2y = 12\\6 - 2y = 12\\-2y = 6\\y = -3[/tex]

These are the answers

- Kan Academy Advance

Answer:

[tex] - 3x( - 4x + x) - x( - x - 2x) - 4x(4x + 3x) \\ \\ = 12 {x}^{2} - 3 {x}^{2} + {x}^{2} + 2 {x}^{2} - 16 {x}^{2} - 12 {x}^{2} \\ \\ = - 16{x}^{2} [/tex]

Answer:

Points on the inverse are [tex](1,-1), (4,2), \text{and } (0,0)[/tex]

Step-by-step explanation:

When writing the inverse function of a set of points, you simply switch the coordinates:

[tex]\text{Function}: (x,y)\\\text{Inverse}: (y,x)[/tex]

We are given the points

[tex](-3,9), (-1,1), (0,0), \text{and } (2,4)[/tex]

Using our rule for function, our new points will be

[tex](9,-3), (1,-1), (0,0), \text{and } (4,2)[/tex]

From the list, the points we have for the graph of the inverse are

[tex](1,-1), (4,2), \text{and } (0,0).[/tex]

Answer:

0.705

Step-by-step explanation:

| -1/2 - 1/8| + ( -3/4 + 5/6)

| -1/2 - 1/8| + ( -0.75 + 0.83)

| -1/2 - 1/8| + 0.08

| -0.5 - 0.125| + 0.08

|-0.625| +0.08

0.625+0.08

0.705

hope it helps

Answer: 18

Step-by-step explanation:

By the angle bisector theorem, [tex]\frac{x}{48} =\frac{12}{32} \longrightarrow x=\boxed{18}[/tex]

Answer:

18 1/8

Step-by-step explanation:

4 7/8 x 4 = 23 1/2

23 1/2 - 5 3/8 = 18 1/8

Answer:

  410 g

Step-by-step explanation:

Radioactive decay can be modeled by an exponential equation. The amount remaining (y) after a time period (t) can be expressed in terms of the initial amount (a) and the half-life (h).

  y = a(1/2)^(t/h)

__

We can use this equation with the given values to find the amount remaining.

  y = (680 g)(1/2)^((19 yrs)/(26 yrs)) ≈ (680 g)(0.602583)

  y ≈ 410 g

About 410 grams of element X will remain after 19 years.

Answer:

The first one with the number 38

Step-by-step explanation:

Answer:

4.22675 cups are equal to 1000 milliliters

Step-by-step explanation:

1000 milliliters is equivalent to __4.22675__ cups

Hope This Helped

Answer:

4.22675

Step-by-step explanation:

Order matters is permutation

Order doesn't matters is combination

So

The correct combinations are

Answer:

A. 3/10

B.1/7

Step-by-step explanation:

Answer:

12971

Step-by-step explanation:

13000-20-18 = 12971

Answer:

8060$

Step-by-step explanation:

20%+18%=38%

13000*38%=4940

13000-4940=8060 $

Answer:

648 in^2

Step-by-step explanation:

your must find the surface area of the rectangular prism

this can be modelled by

2(9 * 9) + 2(13.5 * 9) + 2(13.5 * 9)

or

2(9 * 9) + 4(13.5 * 9)

then you do whats inside the parenthesis

2(81) + 4(121.5)

and lastly you multiply and add

162 + 486 = 648

the answer is 648 in^2

Answer:

Solve v + 6 = 5v − 2 to find the value of v.

Step-by-step explanation:

Answer:

Option 3

Step-by-step explanation:

The correct method to find Meg's and Victor's ages is to equate the equations for their ages.

Hence. the answer is :

Solve v + 6 = 5v − 2 to find the value of v.

Answer:

341 cm²

Step-by-step explanation:

Formula :

Surface area = Area of 4 triangle faces + Area of square base

===============================================================

Solving :

⇒ Surface area = 4 × 1/2 × 11 × 10 + 11²

⇒ Surface area = 2 × 110 + 121

⇒ Surface area = 220 + 121

⇒ Surface area = 341 cm²

The surface area of the square pyramid is 341 square centimeter.

a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.

The surface area of a square pyramid is calculated by the equation S = B + 1/2 × P × S

where B is the area of the base,

P is the perimeter of the base, and

S is the slant height of the pyramid.

the area of the base =11×11

B=121 square centimeter

The perimeter of the base = 2(11+11)

P= 44 cm

Slant height (S) is 10 cm.

Surface Area = 121 + 1/2 (44×10)

=121+220

=341 square centimeter

Hence,  the surface area of the square pyramid is 341 square centimeter.

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Using the Empirical Rule, it is found that the interval that would represent a similar percentage of Great Danes would fall between 130 and 170 pounds.

It states that, for a normally distributed random variable:

68% fall within 1 standard deviation of the mean, hence for the Great Danes, the values are given as follows:

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Answer:

I can find at least 10 4-letter words out of hexagon.

Step-by-step explanation:

1.) Hexa (means 6)

2.) gone

3.) nage (a type of bullion)

4.) gane (to yawn)

5.) hage (a frightening old woman; a witch)

6.) hane (ghostly)

7.) axon (a part of a nerve cell)

8.) hang

9.) oxen

10.) hoax

Answer:

Step-by-step explanation:

The triangles are congruent when corresponding sides are congruent.

__

ΔFGH ≅ ΔABC means corresponding sides are ...

  (GH, BC) = (V, 16)

  (HF, CA) = (48, W)

Corresponding sides being congruent means ...

  V = 16

  W = 48

A phrase that 18c can represent is the product of 18 and a number c

The expression is given as:

18c

Rewrite as:

18c = 18 * c

The above represents the product of two factors; 18 and c

Hence, a phrase that 18c can represent is the product of 18 and a number c

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Answer:

B

Step-by-step explanation:

just find the equal difference of y values.

Step-by-step explanation:

to add to the explanation :

an arithmetic sequence is defined as

an = an-1 + d

so, every term of the sequence is created by adding the same constant d (the common difference) to the previous term.

therefore, you find the common difference by finding the difference of 2 sequential terms.

like here e.g.

a3 = 38

a4 = 53

53 - 38 = 15

bingo !

and to verify that it truly is an arithmetic sequence, we can quickly also check the differences between the other pairs. yes, they are all 15.

be prepared for a trap like

1 8

2 23

3 38

5 68

notice the sudden jump in x ? suddenly x is increased by 2.

that just means we compare

an and an-2 instead of an-1.

so, how is related to an-2 ?

an = an-1 + d = (an-2 + d) + d = an-2 + 2d

and so we would get

a3 = 38

a5 = 68

a5 - a3 = 2d = 30

d = 15

so, don't get confused by such jumps or gaps.