In circle B below, diameter RT, radius BE, and chord RE are drawn.
If m2TRE = 15° and BE = 9, then the area of sector EBR is

The correct value of (3cis(pi/6))³ is 27i.

Complex numbers are numbers that consist of two parts — a real number and an imaginary number. Complex numbers are the building blocks of more intricate math, such as algebra.

Given the complex number in polar coordinate expressed as

z = r(cos∅+isin∅)

zⁿ =  {r(cos∅+isin∅)}ⁿ

According to DeMoivre’s Theorem;

zⁿ =  rⁿ(cosn∅+isinn∅)

Given the complex number;

(3cis(pi/6))³

= {3(cosπ/6 + isinπ/6)}³

Using  DeMoivre’s Theorem;

= 3³(cos3π/6 + isin3π/6)

=  3³(cosπ/2 + isinπ/2)

= 3³(0 + i(1))

= 27i

Thus, the correct value of (3cis(pi/6))³ is 27i.

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Answer:

the second option is correct.

Step-by-step explanation:

that is the solution above.

The value of b that causes the system of equations to have infinite solutions is -6.

For that, we will try solving it first using the method of substitution in which we express one variable in another variable's form and then you can substitute this value in another equation to get a linear equation in one variable.

If there comes a = a situation for any a, then there are infinite solutions.

If there comes wrong equality, say for example, 3=2, then there are no solutions, else there is one unique solution to the given system of equations.

In the given problem, our equations are:

y = 6x + b

-3x + (1/2)^y = -3

So the value of b needs to be such that these two equations must be equal.

In the second equation:

[tex](1/2)^y = -3 + 3x\\y = -3^2 + 3x^2 \\y = -6 + 6x[/tex]

Then we must have:

6x - 6 = 6x + b

-6 = b

Thus, the value of b that causes the system to have infinite solutions is -6.

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Answer:

-6

Step-by-step explanation:

trust

Answer:

358in²

Step-by-step explanation:

9 × 11 = Area of Face One = 99in²

99 × 2 = Face One + Face One on the opposite side = 198in²

4 × 11 = Area of Face Two = 44in²

44 × 2 = Face Two + Face Two on the opposite side = 88in²

9 × 4 = Area of Face Three = 36in²

36 × 2 = Area of Face Three + Face Three on the opposite side = 72in²

Total Surface Area = 198 + 88 + 72 = 358in²

The attached image represents the triangle after it has been enlarged

The given parameters are:

From the graph, the coordinates of the triangle are:

A = (-4,2)

B = (-4,-4)

C = (-1,-4)

The rule of dilation is calculated using:

[tex](x,y) \to (k(x - a) + a, k(y - b) + b)[/tex]

So, we have:

[tex]A' = (-\frac 13(-4 +1) - 1, -\frac 13(2 - 2) + 2)[/tex]

A' = (0, 2)

[tex]B' = (-\frac 13(-4 +1) - 1, -\frac 13(-4 - 2) + 2)[/tex]

B' = (0, 4)

[tex]C' = (-\frac 13(-1 +1) - 1, -\frac 13(-4 - 2) + 2)[/tex]

C' = (-1, 4)

See attachment for the image of the triangle, after it has been enlarged

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Answer:

x = - 1

Step by step explanation:

The rational expression will be undefined if  the denominator is zero.

x+1 = 0

x =  -1

Hence, for x = -1, the given expression will be undefined.

Answer:

8 cups = 2 quarts

Step-by-step explanation:

Answer:

Eight cups will give you 2 quarts of water

Answer:

See the attached graph.

Step-by-step explanation:

Answer:

  B.  The function is nonlinear.

Step-by-step explanation:

A linear function graphs as a straight line. It is a polynomial function of degree 1. Any function that is not a linear function is a nonlinear function.

__

The function given is a polynomial function of degree 2. (Its highest-degree term is x^2, which has an exponent of 2.)

Since the degree is not 1, the function is nonlinear.

_____

Additional comment

A polynomial function will never be "linear at some points and nonlinear at other points." Such a description might apply to a piecewise-defined function.

The number of hours it will take to burn 4 1/4 inches of candle is 8.5 hours in decimal.

Using ratio to solve, find the ratio of candle length to the time taken to burn down

let

4 1/2 : 9 = 4 1/4 : x

9/2 ÷ 9 = 17/4 ÷ x

9/2 × 1/9 = 17/4 × 1/x

1/2 = 17/4x

1 × 4x = 2 × 17

4x = 34

x = 34/4

x = 8.5 hours

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Answer: B

Explanation: Key word: Atleast. This shows that you can still get 16 but it's the lowest you can get. Meaning, if you were to say, atleast get a 16% done. It'll mean that getting 16% is good but also, you'll want to get a higher number of course.

The probability that a student scored less than 55% on the exam is 0.134%.

It's the probability curve of a continuous distribution that's most likely symmetric around the mean. On the Z curve, at Z=0, the chance is 50-50. A bell-shaped curve is another name for it.

We have:

Mean of the sample = 70

Standard deviation = 5

= P(X<55%)

Z = (55-70)/5

Z = -3

P(X < -3)

From the Z table:

P(x<-3) = 0.0013499

or

P(x<-3) = 0.134%  

Thus, the probability that a student scored less than 55% on the exam is 0.134%.

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Answer:

x=60

Step-by-step explanation:

First get x all alone on 1 side of the equation. Add 14.5 to both sides of the equation to cancel out the negative. You will then be left with

x/5= 12

Multiply both sides of the equation by 5 to cancel out the division and you'll get x=60

Answer:

i can't see the question i would love to help though

Step-by-step explanation:

Answer:

17.5%

Step-by-step explanation:

1879/10730=17.5%

Answer:

18%

Step-by-step explanation:

Locate the "receives aid" column and "graduate" row. The value 1879 is in this row and column combo.

There are 10730 students total as shown in the bottom right hand corner.

Roughly 1879/10730 = 0.1751 = 17.51% of the students are graduates who receive aid. This rounds to 18%

Answer:

Pentagon

Step-by-step explanation:

Because as you can see, a regular pentagon is bigger than then the hexagon. If it's both in the circle below, the pentagon will most likely have an big advantage in this.

The half life of the radioactive isotope to the nearest tenth is  0.83 days.

The rate of radioactive decay is the rate at which a radioactive isotope is disintegrated. The half life is the time taken for half of the original amount of radioactive isotope to remain.

Given that;

t/12 = 0.693/k

Where;

t1/2 - half life

k =decay constant

t/12 = 0.693/0.84

t/12 = 0.83 days

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Answer:

- 8

Step-by-step explanation:

substitute q = - 14 and r = - 6 into the expression

q - r

= - 14 - (- 6)

= - 14 + 6

= - 8

Answer:

0, 3 , 8

Step-by-step explanation:

substitute n = 1, 2, 3 into the pattern rule

T₁ = 1² - 1 = 1 - 1 = 0

T₂ = 2² - 1 = 4 - 1 = 3

T₃ = 3² - 1 = 9 - 1 = 8

The value of x in the triangle is 20

From the triangle, we have the following equivalent ratios:

5x+ 10 : 121 = 10 : 11

Express as fraction

5x  + 10/121 = 10/11

Multiply both sides by 121

5x + 10 = 110

Subtract 10 from both sides

5x  = 100

Divide both sides by 5

x = 20

Hence, the value of x in the triangle is 20

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Outlet A sold the greatest number of copies of album x in July and August

The tables of values are given as:

July

Album X Album Y Album Z

Outlet A 14 8 6

Outlet B 7 13 4

Outlet C 2 11 1

August

Album X Album Y Album Z

Outlet A 12 14 10

Outlet B 5 12 8

Outlet C 16 12 7

In July, the total sales of album x are:

Outlet A  = 14

Outlet B = 7

Outlet C = 2

In August, the total sales of album x are:

Outlet A  = 12

Outlet B = 5

Outlet C = 16

Add both sales

A = 14 + 12 = 26

B = 7 + 5 = 12

C = 2 + 16 = 18

26 (in outlet A) is greater than 12 and 18

Hence, outlet A sold the greatest number of copies of album x in July and August

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Answer:

Outlet D

Step-by-step explanation:

they sold 28 of album x

outlet a only sold 26

Answer:

7ft; 8 minutes

Step-by-step explanation:

a. to find the height the person boarded at, plug in t=0 since this is right when the person got on the Ferris wheel. we then get:

h(0) = -45 * cos ((pi/4)*0) + 52 = 7 ft

b. to find the period, we have pi/4 * t = 2*pi, solve for t to get t=8

For proof of 3 divisibility, abc is a divisible by 3 if the sum of abc (a + b + c) is a multiple of 3.

The proof for divisibility of 3 implies that an integer is divisible by 3 if the sum of the digits is a multiple of 3.

111 = 1 + 1 + 1 = 3  (the sum is multiple of 3 = 3 x 1)  (111/3 = 37)

222 = 2 + 2 + 2 = 6 (the sum is multiple of 3 = 3 x 2)  (222/3 = 74)

213 = 2 + 1 + 3 = 6 ( (the sum is multiple of 3 = 3 x 2)  (213/3 = 71)

27 = 2 + 7 = 9  (the sum is multiple of 3 = 3 x 3)  (27/3 = 9)

Thus, abc is a divisible by 3 if the sum of abc (a + b + c) is a multiple of 3.

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Answer:

  rule: f(n) = n³

  missing numbers: 125, 216, 343, 512, 729

Step-by-step explanation:

Your familiarity with the cubes of small integers helps you recognize each of these numbers is a cube. Their sequence is the sequence of cubes of increasing natural numbers.

  1 = 1·1·1 = 1³

  8 = 2·2·2 = 2³

  27 = 3·3·3 = 3³

  64 = 4·4·4 = 4³

__

The rule is ...

  f(n) = n³

The cubes of 5 through 9 will complete the set of numbers ...

  1, 8, 27, 64, 125, 216, 343, 512, 729

The length of the diagonal shown in the rectangular prism is; 9.5 ft

First of all, we have to find the length of the diagonal base to get;

x = √(4² + 7²)

x = √65

Thus;

Length of the diagonal shown = √(5² + (√65)²)

Length of the diagonal shown = √90

Length of diagonal shown = 9.4868

Length of diagonal shown ≈ 9.5 ft

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Answer:

got 100% on Plato

Step-by-step explanation:

The equivalent expression of [tex]18x^2\sqrt{14x^8} \div 6\sqrt{7x^4}[/tex] is [tex]3x^4\sqrt{2}[/tex]

The expression is given as:

[tex]18x^2\sqrt{14x^8} \div 6\sqrt{7x^4}[/tex]

Start by dividing 18 by 6

[tex]3x^2\sqrt{14x^8} \div \sqrt{7x^4}[/tex]

Next, divide 14 by 7

[tex]3x^2\sqrt{2x^8} \div \sqrt{x^4}[/tex]

Take the square root of x^8 and x^4

[tex]3x^2 * x^4\sqrt{2} \div x^2[/tex]

Divide x^2 by x^2

[tex]3* x^4\sqrt{2}[/tex]

Evaluate

[tex]3x^4\sqrt{2}[/tex]

Hence, the equivalent expression of [tex]18x^2\sqrt{14x^8} \div 6\sqrt{7x^4}[/tex] is [tex]3x^4\sqrt{2}[/tex]

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Answer: B or 3x^4 sqrt 2

explanation: only simplified answer above

The equation c = 64 - d is a linear equation, and the value of c in the equation is 64 1/6

The equation is given as:

c = 64 - d

The value of d is given as:

d = -1/6

Substitute -1/6 for d in c = 64 - d

c = 64 - -1/6

Evaluate the difference

c = 64 1/6

Hence, the value of c in the equation is 64 1/6

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Answer:

25

Step-by-step explanation:

First we add 1 to both sides :

√x = 5

Now we square both sides :

x = 5²

x = 25

To check this answer we substitute our answer back into the original equation:

√25 - 1 = 4

5 - 1 = 4

4 = 4

✅

Hope this helped and brainliest please

Answer:

15

Step-by-step explanation:

To find the answer, plug the values of each variable into the equation and simplify. It may be easiest to plug one variable in at a time, simplify, then plug the next variable in. Remember, if the equation is asking you to subtract a negative number, the negatives cancel and you want to add the numbers.

b = 2          c = -4

3b - c + 5                                      <----- Original expression

3(2) - c + 5                                    <----- Plug 2 in for "b"

6 - c + 5                                        <----- Multiply 3 and 2

11 - c                                              <----- Add 6 and 5

11 - (-4)                                           <----- Plug -4 in for "c"

15                                                  <----- Add 11 and 4