Answer:
d. x2 – 2x – 4 = 0
Step-by-step explanation:
simplify the following complex number, without changing the polar form and leave your answer in polar form:
[tex]\frac{(2\ \textless \ \frac{2\pi }{3})^{3} (3\ \textless \ \frac{3\pi }{2}) }{4\ \textless \ \frac{7\pi }{3} }[/tex]
The simplified form of the complex number in polar form is: 2 < (-7π/6)
How to simplify the complex numberTo 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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A classroom had 16 computers. If the ratio of computers to ipads was 4 : 5, how many ipads does the classroom have?
Answer:
20 ipads
Step-by-step explanation:
The ratio is 4 : 5
4:5
*4 *4
16c :20i
16 Computers and 20 Ipads.
aced or higher please hellp i beg :C
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
What is 1/6 divided by 1/3 in simplest form
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
someone please help me answer this!!
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
Find the value of x.
help please !
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.
Solve the Following inequality by choosing all of Possible range of Values that make the Statement True.
2 (x) + 12 ≤ 30
Group of answer choices
9, 10, 11
7, 8, 9
-7, -8, -9
9.001, 9.002, 9.003
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
Will give Brainly
Find the probability that a
randomly
selected point within the circle falls
in the red shaded area.
60°
60°
r= 4 cm
[? ]%
Round to the nearest tenth of a percent.
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%.
What is probability?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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The owner of a pet shop predicts that 10 out of 20 new puppies are male. He randomly selects 10 of the puppies, and notes that all 10 are male. Which of the following conclusions best supports his findings?
Select one:
10 of the puppies are male and 10 are female.
More than 10 of the puppies are male.
All 20 puppies are male.
Less than 10 of the puppies are male.
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:
Rachel downloaded a movie at a constant speed.
After she downloaded 40% of the movie, the remaining download time was 40 seconds.
After she downloaded 40 mb, the remaining download time was 16 seconds.
Compute the total size of the movie (in mb) rounded to the nearest mb.
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.
what % of 4 is 7
i need this to be answered as quickly as possible please
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
Denise made 1/2 of a liter of hot chocolate. Each mug holds 1/10 of a liter. How many mugs will Denise be able to fill?
Answer:
5 mugs
Step-by-step explanation:
1/2 converted into 10ths would be 5/10 ... meaning 5 mugs
Pictures in order !
Answer:X=10
Step-by-step explanation: 3x-2=2x+8 If that's what you're looking for
someone please help me answer this
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
find the value of x
HELP please !
Answer:
116+34+x=180
150+x=180
x=180-150
x=30
HELP! How many triangles can be made from the following three lengths: 1.6 centimeters, 7.4 centimeters, and 5.9 centimeters?
none
one
more than one
Answer: one
Step-by-step explanation:
pls help
#1
isjsbijsj
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.
Find the volume of a cone with a base diameter of 10 cm and a height of 9 cm
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.
Why is the volume of a cone?The volume of a cone with height h and radius r is 1/3πr2h, which is exactly one third the volume of the smallest cylinder that it fits inside. This can be proved easily by considering a cone as a solid of revolution, but I would like to know if it can be proved or at least visual demonstrated without using calculus.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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Which graph represents exponential decay?
On a coordinate plane, a straight line has a negative slope.
On a coordinate plane, a curve approaches y = 0 in quadrant 2 and curves up in quadrant 1.
On a coordinate plane, a straight line has a positive slope.
On a coordinate plane, a curve approaches y = 0 in quadrant 1 and curves up in quadrant 2.
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.
What is an exponential function?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 :)
In the figure, lines a and b are parallel. Which statements are true? Select each correct answer. Responses m∠2=m∠1 measure of angle 2 equals measure of angle 1 m∠3=m∠1 measure of angle 3 equals measure of angle 1 m∠1=75° measure of angle 1 equals 75 degrees m∠2=105° measure of angle 2 equals 105 degrees
The correct statements from the line are given as follows:
m∠2=m∠1m∠1=75°What are corresponding angles?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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What is the square root of –16?
A. –8i
B. –4i
C. 4i
D. 8i
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
Theo is using the Quadratic Formula to solve a quadratic equation. Which of the following is the next step for simplifying
x=−4±4√6/2
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
How to find the solution to a standard quadratic equation?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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Please Help Me Fast.
FAST FAST FAST
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 this please!!!
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
Find the equation of the line specified.
The slope is -7, and it passes through ( 5, -3).
a.
y = -7x - 3
c.
y = -14x + 32
b.
y = -7x + 32
d.
y = -7x - 38
Write an equation for a circle that follows the same pattern as the other circles. Explain how your equation follows the same pattern you identified.
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
Which following relations represent a function
Answer:
I think that actually all of them represent a function , except D .
hope it was helpful .
Answer to this problem
The 3 deals are worth the same price per unit of $0.1 a pencil.
Price per unit of itemsBased on the given prices, we can calculate the price per pencil for each pack:
Pack of 12 pencils: $1.29Price per pencil = $1.29 / 12 = $0.1075 (approximately $0.11)
Pack of 24 pencils: $2.35Price per pencil = $2.35 / 24 = $0.0979 (approximately $0.10)
Pack of 50 pencils: $5.45Price 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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QUICK HELP with the Image below
Answer:
12 8/11
Step-by-step explanation:
hope it helps you
Find the area of the figure.
Answer:
91
Step-by-step explanation:
Answer:
91
Step-by-step explanation:
(11 + 15) × 7 ÷ 2 = 26 × 7 ÷ 2 = 91