which equation has the solutions x equals 1 plus or minus the square root of 5​

The simplified form of the complex number in polar form is: 2 < (-7π/6)

To simplify the given complex number in polar form, we can apply the rules of exponentiation and division for complex numbers:

First, let's simplify the numerator:

(2 < 2π/3)^3 = (2^3) < (2π/3 * 3) = 8 < (2π)

(3 < 3π/2) remains the same.

Now, let's simplify the denominator:

4 < (7π/3) remains the same.

Next, let's divide the numerator by the denominator:

[(8 < (2π)) * (3 < (3π/2))] / (4 < (7π/3))

Using the rules of division for complex numbers, we can divide the magnitudes and subtract the angles:

(8/4) < (2π - 7π/3 - (3π/2)) = 2 < (2π/3 - 3π/2 - π/6) = 2 < (-7π/6)

Therefore, the simplified form of the complex number in polar form is:

2 < (-7π/6)

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9514 1404 393

Answer:

  (x -4)² +(y +3)³ = 4

Step-by-step explanation:

Each circle is centered on (h, k) = (4, -3). Each circle has a radius 1 unit smaller than the circle just outside of it. The innermost circle shown has a radius of 3, so the next in the pattern of smaller circles will have a radius of 2. The equation for a circle centered at (h, k) with radius r is ...

  (x -h)² +(y -k)² = r²

The next circle in the pattern is centered at (4, -3) and has radius 2, so its equation is ...

  (x -4)² +(y +3)² = 4

Answer:

20 ipads

Step-by-step explanation:

The ratio is 4 : 5

      4:5

*4             *4

   16c :20i

16 Computers and 20 Ipads.

Answer:

5 mugs

Step-by-step explanation:

1/2 converted into 10ths would be 5/10 ... meaning 5 mugs

Answer:

235.71cm^2

Step-by-step explanation:

Volume of cone = 1/3 pie r^2 h

1/3*22/7*5*5*9

= 235.71cm^2

Volume of a cone is 235.6 cm³.

The volume of a cone is calculated the using the formula:

[tex]V = \frac{1}{3} \pi r^{3} h[/tex]

Given,

         height of the cylinder is, h=9cm.

         The diameter of the base is 10cm. r = 5 cm

    put the values into the formula to get -

          V = [tex]\frac{1}{3} * \pi * 5^{2} * 9[/tex]

         [tex]V = 75 \pi[/tex]

Put value of π = 3. 14 ,

          V = 75 * 3.14

           V =  235.6 cm³

Therefore, Volume of a cone is 235.6 cm³.

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Answer:

Easy it's 40

Step-by-step explanation:

I think it's 40 because the other numbers are all with in the range of 10-20 except 40.

Answer:

Answer is 40! :)

Answer:

The value of “Y” is (6)

Step-by-step explanation:

the x value unit of “5” has the y value of “6.”

Answer:  6

EXPLANATION:

The x axis is the one on the bottom that goes like this : ---

The y axis is the one that is like a vertical line up like this: |

If you look at the x axis you can see that one the 5 and you go up you can see there is a dot that is on the 6.

Answer:

91

Step-by-step explanation:

Answer:

91

Step-by-step explanation:

(11 + 15) × 7 ÷ 2 = 26 × 7 ÷ 2 = 91

The 3 deals are worth the same price per unit of $0.1 a pencil.

Based on the given prices, we can calculate the price per pencil for each pack:

       Price per pencil = $1.29 / 12 = $0.1075 (approximately $0.11)

       Price per pencil = $2.35 / 24 = $0.0979 (approximately $0.10)

       Price per pencil = $5.45 / 50 = $0.109 (approximately $0.11)

In other words, the 3 deals are worth the same price per unit of the pencil.

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Answer:

12 8/11

Step-by-step explanation:

hope it helps you

Answer: look at the picture

Step-by-step explanation:

Removing the denominator by dividing both the numerator's terms by 2 is the needed next step for simplification. The result is: x=−2±2√6

Suppose the given quadratic equation is

[tex]ax^2 + bx + c = 0[/tex]

Then its solutions are given as

[tex]x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}[/tex]

Here, we're given the expression:

[tex]x = \dfrac{-4 \pm 4\sqrt{6}}{2}[/tex]

The next step to simplify is to make it look more simple.

[tex]x = \dfrac{-4}{2} \pm \dfrac{4\sqrt{6}}{2}\\\\x = -2 \pm 2\sqrt{6}[/tex]

Thus, removing the denominator by dividing both the numerator's terms by 2 is the needed next step for simplification. The result is: x=−2±2√6

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The correct statements from the line are given as follows:

When two parallel lines are cut by a transversal, corresponding angles are pairs of angles that are in the same position relative to the two parallel lines and also to the transversal.

Corresponding angles are congruent, which means that they have the same angle measure.

Two corresponding angles for this problem are given as follows:

<2 and <1.

Hence:

m < 2 = m < 1.

Angles 1 and 105º form a linear pair, meaning that they are supplementary, hence the measure of angle 1 is given as follows:

m < 1 + 105º = 180º.

m < 1 = 75º.

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Answer: one

Step-by-step explanation:

Answer:

A, 10 of the new puppies are male and 10 are female

Step-by-step explanation:

Really this is the one that makes the most since because if 10 of the puppies are male, then 10 must be female.

Answer: A

Step-by-step explanation:

Answer:

116+34+x=180

150+x=180

x=180-150

x=30

Answer:

the answer

= 17.5

Step-by-step explanation:

https://www.percentagecal.com/answer/.7-is-what-percent-of-4#:~:text=Percentage%20Calculator%3A%20.,%3D%2017.5

Answer:

C. 4i

Step-by-step explanation:

Answer:

C. 4i

Step-by-step explanation:

[tex]\sqrt{-16} = \sqrt{16} \sqrt{-1}[/tex] (because [tex]\sqrt{ab} =\sqrt{a} \sqrt{b}[/tex])

Since [tex]\sqrt{16}[/tex]=4, and [tex]\sqrt{-1}[/tex]=i, [tex]\sqrt{-16}[/tex]=4i

The graph which shows the function is exponential decay is on a coordinate plane, a curve approaches y = 0 in quadrant 1 and curves up in quadrant 2 thus, option (D) is correct.

In mathematics, an exponential function is a relationship of the type y = ax, where x is an independent variable that spans the entire real number line and is expressed as the exponent of a positive number.

As per the given,

The exponential function is a function that changes rapidly, for example, y = 6^x here as x approaches higher the y approaches rapidly higher.

Exponential decay is the exponential function that rapidly decreases as x increases for example y = 6^(-x).

The graph of the exponential decay has been graphed below.

Hence "The graph which shows the function is exponential decay is on a coordinate plane, a curve approaches y = 0 in quadrant 1 and curves up in quadrant 2".

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Answer:

D

Step-by-step explanation:

edge

hope this helps :)

Answer:

The total weight of the file was 64 mb.

Step-by-step explanation:

Given that Rachel downloaded a movie at a constant speed, and after she downloaded 40% of the movie, the remaining download time was 40 seconds, while after she downloaded 40 mb, the remaining download time was 16 seconds, to determine the total size of the movie rounded to the nearest mb, the following calculation must be performed:

100 - 40 = 60

60% = 40 seconds

40 mb = 16 seconds left

16/40 = 4/10

60/40 = 1.5

1.5% for every 1 second of download.

16 x 1.5 = 24

40 + 24 = 64

Thus, the total weight of the file was 64 mb.

Answer:

It would be 20

Answer:

6.4 in is the answer.

Step-by-step explanation:

a = 5 in

b = 4 in

c = ?

According to the Pythagorean theorem,

a² + b² = c²

5² + 4² = c²

25 + 16 = c²

c² = 41

c = 6.403

Round to the nearest tenth,

c = 6.4 in

∴ the length of the pencil is 6.4 in

Answer:

I think that actually all of them represent a function , except D .

hope it was helpful .

Answer:

yes. It's a right triangle.

Step-by-step explanation:

According to the Pythagoras theorem,

a² + b² = c²

20² + 21² = 29²

400 + 441 = 841

841 = 841

LHS = RHS

Answer: 33.3%

s Step-by-step explanation: The combined arc length of the red area is 120, which is 1/3 of 360, the full arc. So the probability is 1/3, or 33.3%. Hope this helps!

The probability that a randomly selected point within the circle falls

in the red shaded area will be 33.33%.

Probability is defined as the ratio of the number of favorable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.

Probability = Number of favorable outcomes / Number of sample

Given that the shaded red sector has an angle of 60 degrees and the radius of the circle is 4 cm. The probability will be calculated as:-

The formula for a circle's sector's area is (Ф/360°) x π(r²), where r is the circle's radius and is the sector's angle.

Area of shaded region =  (Ф/360°) x π(r²),

Area of shaded region = ( 60 / 360 ) x π (4²)

Area of shaded region = 8.377 square cm

Total shaded area = 2 x 8. 377 = 16.75 square cm

Total area of circle = π (4²) = 50.265 square cm

The probability is calculated by the formula below:-

Probability = Number of favorable outcomes / Number of sample

Number of favorable outcomes = 8.377

Number of sample = 50.265 square cm

Probability = 8.377 / 50.265 = 0.3333 = 33.33%

Therefore, the probability that a randomly selected point within the circle falls in the red-shaded area will be 33.33%.

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Answer:

1/2 or 0.5

Step-by-step explanation:

Answer:

1/18

Step-by-step explanation:

1/6÷1/3

1/3×1/6

1/3×6

1/18

Answer:

100 in is the answer.

Step-by-step explanation:

a = 60 in

b = 80 in

c = ?

According to the Pythagorean theorem,

a² + b² = c²

60² + 80² = c²

3600 + 6400 = c²

c² = 10000

c = 100 in

∴ the distance between the opposite corners of the bed is 100 in

Answer:X=10

Step-by-step explanation: 3x-2=2x+8 If that's what you're looking for

Answer:

7, 8, 9

-7, -8, -9

Step-by-step explanation:

2(x) + 12 ≤ 30

2x + 12 ≤ 30

2x ≤ 30 - 12

2x ≤ 18

x ≤ 9

x has to be less than OR equal to 9

Answer:

A: Find the area of the outer trapezoid and then subtract the area of the inner trapezoid

B: 15 square units

Step-by-step explanation:

A:

Find the area of the outer trapezoid and then subtract the area of the inner trapezoid

(because if the inner trapezoid wasn't there and you were looking for the shaded region, you'd find the area of the outer trapezoid. since you have to take away the area the inner trapezoid takes up, the shaded region = area of outer trapezoid - area of inner trapezoid)

B

The area of a trapezoid is ((a+b)/2)h, where a is the top or the trapezoid, b is the bottom and h is the height.

The top of the outer trapezoid ranges from 4 to 6, so a=6-4=2. The bottom of the outer trapezoid ranges from 2 to 8, so b=8-2=6. The height of the outer trapezoid ranges from 2 to 8, so h=8-2=6.

The area of the outer trapezoid = ((a+b)/2)h = ((2+6)/2)(6) = 4(6) = 24

The top of the inner trapezoid ranges from 4 to 6, so a=6-4=2. The bottom of the inner trapezoid ranges from 3 to 7, so b=7-3=4. The height of the inner trapezoid ranges from 3 to 6, so h=6-3=3.

The area of the inner trapezoid = ((a+b)/2)h = ((2+4)/2)(3) = 3(3) = 9

The are of the shaded region = the area of the outer trapezoid - the area of the inner trapezoid = 24 - 9 = 15 square units

Answer:

33

Step-by-step explanation:

The sum of the three interior angles in a triangle is ALWAYS equivalent to 180 degrees.

69 + 78 = 147

180 - 147 = 33

Hope this is helpful & accurate! Best wishes.