What is the polar form of -9-91√3 ?
09 (cos()+ i sin())
O 9 (cos (4T) + i sin (4))
O 18 (cos ()+sin())
O 18 (cos (4) + i sin (4T))
3
Answers
The polar form of the rectangular form - 9 - i 9√3 is 18 · [cos (4π / 3) + i sin (4π / 3)]. (Correct choice: A)
What is the polar form of a complex number in rectangular number?
Herein we find a complex number in rectangular form, that is, a complex number of the form a + i b, whose polar form has to be found. Complex numbers in polar form are defined by the following expression:
z = r · (cos θ + i sin θ)
r = √(a² + b²)
θ = tan⁻¹ (b / a)
Where:
r - Norm of the complex number.θ - Direction of the complex number, in radians.a, b - Components of the complex number in rectangular form.If we know that a = - 9 and b = - 9√3, then the complex number in polar form is:
r = √[(- 9)² + (- 9√3)²]
r = 18
θ = tan⁻¹ √3
θ = 4π / 3
The polar form is 18 · [cos (4π / 3) + i sin (4π / 3)].
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Related Questions
what is the arithmetic mean of all of the positive two-digit integers with the property that the integer is equal to the sum of its first digit plus its second digit plus the product of its two digits?
Answers
The arithmetic mean is 59.
What is arithmetic mean?
It is the sum of collection of numbers divided by the count of the numbers.
Conider AB is the nuber satisfying the condition. Hence,
[tex]10A+B=A+B+A\times B\\9A=A\times B\\[/tex]
Since AB is a two digit number hence, [tex]A\neq 0\\[/tex]. Hence, divide both sides by [tex]A[/tex].
[tex]9=B[/tex]
Hence, B is 9 and A can take any value from 1 to 9.
Hence, numbers are 19, 29, 39, 49, 59, 69, 79, 89,99.
Now, calculate arithmetic mean as follows:
[tex]AM=\frac{Sum \ of \ numbes}{Count \ of \ numbers}\\=\frac{19+29+39+49+59+69+79+89+99}{9}\\=59[/tex]
Hence, arithmetic mean of numbers is 59.
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Question number three in the photo provided.
Answers
Using the Central Limit Theorem, the formulas are given as follows:
Standard deviation: [tex]\sigma_{\overline{p}} = \sqrt{\frac{p(1 - p)}{n}}[/tex].Mean: [tex]\overline{p} = p[/tex].What does the Central Limit Theorem state?The Central Limit Theorem states that a random variable X with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] can have the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
A distribution of proportions, with a proportion p in a sample of size n, also respects the Central Limit Theorem, as the the sampling distribution of the sample proportion will be approximately normal with mean and standard deviation given as follows:
Mean: [tex]\overline{p} = p[/tex].Standard deviation: [tex]\sigma_{\overline{p}} = \sqrt{\frac{p(1 - p)}{n}}[/tex].More can be learned about the Central Limit Theorem at https://brainly.com/question/25800303
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Find the requested angle supplement of 123^%A/246B/33C/57D/237
Answers
Given: The angle
[tex]123^0[/tex]To Determine: The supplement of the given angle
Solution
Please note that two angle are supplement if they are add up to 180⁰
So if the supplement is x. Therefore
[tex]\begin{gathered} x+123^0=180^0 \\ x=180^0-123^0 \\ x=57^0 \end{gathered}[/tex]Hence, the supplement of 123⁰ is 57⁰, OPTION C
Find the total surface area of this prism where the cross section is an isoceles triangle 5 14 24 10
Answers
Total surface area = 620
Moreover, The total area covered by an isosceles triangle is called its area. For an isosceles triangle, the area is easily calculated if the height and base are known. Multiplying the height by the base and dividing it by 2 gives us the area of an isosceles triangle.
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486,162,54 the next 3 terms of geometric sequence
Answers
This is a geometric sequence since there is a common ratio between each term. In this case, multiplying the previous term in the sequence by
1
3
gives the next term. In other words,
a
n
=
a
1
r
n
−
1
.
Geometric Sequence:
r
=
1
3
This is the form of a geometric sequence.
a
n
=
a
1
r
n
−
1
Substitute in the values of
a
1
=
486
and
r
=
1
3
.
a
n
=
486
(
1
3
)
n
−
1
Apply the product rule to
1
3
.
a
n
=
486
1
n
−
1
3
n
−
1
One to any power is one.
a
n
=
486
1
3
n
−
1
Combine
486
and
1
3
n
−
1
.
a
n
=
486
3
n
−
1
Substitute in the value of
n
to find the
n
th term.
a
5
=
486
3
(
5
)
−
1
Simplify the denominator.
Tap for more steps...
a
5
=
486
81
Divide
486
by
81
.
a
5
=
6
A triangle with sides 10, 24, and 25 is a right triangle True/ False
Answers
Answer:
False
Step-by-step explanation:
Check using Pythagorean theorem (proof for right triangles)
[tex]10^2+24^2=25^2[/tex]
[tex]100+576=625[/tex]
[tex]676\neq 625[/tex]
False
due in an hour pls help!!
Answers
Answer:
I think it's (4,5)
Step-by-step explanation:
X 79°
y
Z
m
n
Helpppppppppppppppp
Answers
Step-by-step explanation:
79 degrees plus X would make 180 degrees, because these two angles make up a straight angle.
So, 79 + X = 180
-79 -79
X=101 degrees.
Y is 79 degrees because it is an alternate interior angle to the other 79 degree angle.
Z is 101 degrees because X and Z are corresponding angles, which means they are equal.
If Z is 101 degrees, Y must be 79 degrees because Y and X make up a straight angle.
Answer:
X is 101 degrees. Y is 79 degrees. Z is 101 degrees.
Hope this helped! :)
Find an equation for the perpendicular bisector of the line segment whose
endpoints are (-3, 2) and (7, 6).
Answers
Answer:
The perpendicular bisector of the line segment whose endpoints are (-3, 2) and (7, 6) is y = - 2.5x + 9================
Given Points (-3, 2) and (7, 6)To findThe equation of the perpendicular bisector of the segment with given endpoints.SolutionFind the midpoint of the segment and its slope to determine the perpendicular line passing through the midpoint.
The midpoint has coordinates:
x = ( - 3 + 7)/2 = 4/2 = 2,y = (2 + 6)/2 = 8/2 = 4.The slope:
m = (6 - 2)/(7 - (-3)) = 4/10 = 2/5We know perpendicular lines have opposite/reciprocal slopes.
So the slope of the perpendicular bisector is:
m = - 1/ (2/5) = - 5/2 = - 2.5Use the coordinates of the midpoint and point-slope equation to determine the line:
y - 4 = -2.5(x - 2)y - 4 = - 2.5x + 5y = - 2.5x + 5 + 4y = - 2.5x + 9Answer:
[tex]y=-\dfrac{5}{2}x+9[/tex]
Step-by-step explanation:
A perpendicular bisector is a line that intersects another line segment perpendicularly and divides it into two equal parts.
Given endpoints of the line segment:
(x₁, y₁) = (-3, 2)(x₂, y₂) = (7, 6)Substitute the given endpoints into the slope formula to find the slope of the line segment:
[tex]\implies \textsf{Slope $m$}=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{6-2}{7-(-3)}=\dfrac{4}{10}=\dfrac{2}{5}[/tex]
If two lines are perpendicular to each other, their slopes are negative reciprocals.
Therefore, the slope of the perpendicular line is -⁵/₂.
Find the midpoint of the given line segment by substituting the given endpoints into the midpoint formula:
[tex]\implies \textsf{Midpoint}=\left(\dfrac{x_2+x_1}{2},\dfrac{y_2+y_1}{2}\right)[/tex]
[tex]\implies \textsf{Midpoint}=\left(\dfrac{7-3}{2},\dfrac{6+2}{2}\right)[/tex]
[tex]\implies \textsf{Midpoint}=\left(\dfrac{4}{2},\dfrac{8}{2}\right)[/tex]
[tex]\implies \textsf{Midpoint}=\left(2,4\right)[/tex]
To find the equation of the perpendicular bisector, substitute the found slope and midpoint into the point-slope form of a linear equation:
[tex]\implies y-y_1=m(x-x_1)[/tex]
[tex]\implies y-4=-\dfrac{5}{2}(x-2)[/tex]
[tex]\implies y-4=-\dfrac{5}{2}x+5[/tex]
[tex]\implies y=-\dfrac{5}{2}x+9[/tex]
Therefore, the equation for the perpendicular bisector of the line segment whose endpoints are (-3, 2) and (7, 6) is:
[tex]\boxed{y=-\dfrac{5}{2}x+9}[/tex]
x-intercepts of -14 and -2; passes through (-16, -8)
Answers
The equation of the parabola in intercept form exists
y = -2/7(x + 14)(x + 2).
What is meant by the equation of the parabola in intercept form?The intercept form exists y = a(x - r)(x - s), where r and s exists the x-intercepts on the graph. The intercept form will tell us if there exists two x-intercepts, one x-intercept, or no x-intercepts.
Let x-intercepts of -14 and -2; passes through (-16, -8)
The equation of the parabola in intercept form y = a(x - r)(x - s)
substitute the values in the above equation, and we get
-8 = a(-16 + 14)(-16 + 2)
simplifying the above equation, we get
-8 = a(-2)(-14)
-8 = 28a
a = -2/7
y =-2/7(x + 14)(x + 2)
Therefore, the equation of the parabola in intercept form exists
y = -2/7(x + 14)(x + 2).
The complete question is:
Write an equation of the parabola in intercept form X-intercepts of -14 and -2; passes through (-16, -8)
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3. x^3= 25
4.x² = 125
Answers
Step-by-step explanation:
Hope this helps..............
brainliest please
The janitor at a school discovered a leak in a pipe. The janitor found that it was leaking at a rate of 14 fl oz per hour. How fast was the pipe leaking in gallons per day? 2 SEE ANSWERS
Answers
Since there are 128 fluid ounces in one gallon, we need to divide 14 by 128 to change ounces into gallons.
Since there are 60 minutes per hour, we need to multiply 14 by 60 to change per minute into per hour.
Combining these: 14 fl oz / min x (1 gal / 128 fl oz) x (60 min / hr) = 6.5625 gal per hour.
Written as a mixed fraction: 6 9/16 gal per hour.
Help me pleaze its hard !!
Answers
It is to be noted that the Diagonals of a parallelogram bisect each other. Here in PQSR, it does bisect PT =ST and QT = TR). Hence, PQSR is a parallelogram.
IGHJ is a paralellogram. This is because the opposite sides of a parallelogram are congruent. Here, H = I and G = J. Hence, IGHJ is a parallelogram.
CABD is a parallelogram because of the alternative interior angles ACB = CBD and ABC = BCD.
VWYX is NOT a parallelogram. The rule states that if opposites sides are congruent then the quadrilateral is a parallelogram. In this case, clearly, line VW ≠ XY and VX ≠ WY.
What is a parallelogram?A parallelogram, rhombus, rectangle, or square is a quadrilateral with opposing sides that are congruent and parallel.
There are six crucial parallelogram qualities to understand:
Contrary sides are equivalent (AB = DC).Angles opposite each other are congruent (D = B).Consecutive angles are additive (A + D = 180°).If one angle is correct, all angles are correct.A parallelogram's diagonals cross one other.A parallelogram is divided into two congruent triangles by its diagonals.Learn more about parallelograms:
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what are the coordinates of a’?
Answers
Answer:
(1,3)
Step-by-step explanation:
You are at (-3,5). Ordered pairs are written (x,y) The x tells you how far right or left you are from the origin (0,0) and the y tells you how high above or below You are from the origin (0,0).
(-3+ 4,5 -2) We are 3 unit to the right of (0,0) to begin with and the directions tell us to go 4 more units right. We will now be 1 units to the right of zero. We started at 5 units above zero, the directions tells us to move two units down. That would be at 3.
So, our new order pair will be (1.3)
Rewrite the function f(x) = 7(1/2)^3x using the properties of exponents.
A) f(x) = 7(3/6)^x
B) f(x) = 7(1/8)^x
C) f(x) = 21(3/6)^x
D) f(x) = 343(1/8)^x
Answers
Answer:
B
Step-by-step explanation:
[tex]f(x) = 7( { \frac{1}{2} })^{3x} \\ f(x) = 7 ({ \frac{1 \times 1 \times 1}{2 \times 2 \times 2} })^{x} \\ f(x) = 7 ({ \frac{1}{8} })^{x} [/tex]
Rida writes a fitness blog. At a certain point, she has 6,218 followers. Then the following events happen, in order: 92 people stop following Rida's blog. 417 people start following Rida's blog. The number of followers doubles. Use the drop-down menus to answer the questions below.
Answers
The number of followers Rita has is 13086.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
The number of followers Rida has = 6,218
92 people stop following Rida's blog.
This means,
6218 - 92 = 6126
417 people start following Rida's blog.
This means,
6126 + 417 = 6543
The number of followers doubles.
This means,
6543 x 2 = 13086
Thus,
The number of followers Rita has is 13086.
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Write an equation of a line that is parallel to the
given line. Then, write one that is perpendicular.
x = -4
Answers
Answer:
X=ℝ, Y=ℝ
Step-by-step explanation:
Parallel means they have the same slope so it can be anything on the x-axis, perpendicular meaning opposite slope which is y=.
-1 (4/5) in the simplest form
Answers
What is the area of a triangle whose vertices are D(1, 1), E(3, −1), and F(4, 4)
Answers
6 square units is area of a triangle whose vertices are D(1, 1), E(3, −1), and F(4, 4)
What is triangle?A triangle is a three-sided polygon that consists of three edges and three vertices.
The given three vertices are D(1, 1), E(3, −1), and F(4, 4)
we need to find the area of triangle
Area of triangle=1/2|x₁(y₂-y₃)+x₂(y₃-y₁)+x₃(y₁-y₂)|
x₁=1, x₂=3, x₃=4, y₁=1, y₂=-1, y₃=4
put in the formula
Area of triangle=1/2|1(-1-4)+3(4-1)+4(1-(-1))|
=1/2|-5+9+8)|
=1/2 |12|
=6 square units.
Hence 6 square units is area of a triangle whose vertices are D(1, 1), E(3, −1), and F(4, 4)
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Please help me with this, i really need help
Answers
Answer:
See below, where we have used the definitions of vertical angles and complementary angles, and used the substitution property of equality.
Step-by-step explanation:
You want a proof that angles complementary to congruent angles are congruent. That is, ∠1 ≅ ∠4.
Statement . . . . Reason1. ∠1 and ∠3 are complementary . . . . given
2. ∠2 and ∠4 are complementary . . . . given
3. ∠2 ≅ ∠3 . . . . vertical angles are congruent
4. ∠1 +∠3 = 90° . . . . definition of complementary
5. ∠2 +∠4 = 90° . . . . definition of complementary
6. ∠1 +∠3 = ∠2 +∠4 . . . . substitution property of equality
7. ∠1 +∠2 = ∠2 +∠4 . . . . substitution property of equality
8. ∠1 = ∠4 . . . . subtraction property of equality
9. ∠1 ≅ ∠4 . . . . definition of angle congruence
__
Additional comment
The idea of congruence applies to the shape of the geometry. The idea of equality applies to the measures of the angles. Angles are congruent when they have the same measure.
need help on this, thanks
Answers
For the given parallel lines with transversal ,and the pair of interior angles 72° and (7x +24)°, the value of x = 12°.
As given in the question,
Two parallel lines with transversal are given.
72° and (7x +24)°are pair of interior angles
Simplify the given relation to get the value of x we have,
72° + (7x +24)° =180°
⇒ 7x + (72 +24)° =180°
⇒ 7x + 96° = 180°
⇒ 7x = 180° - 96°
⇒ 7x = 84°
⇒ x = 84° /7
⇒ x = 12°
Therefore, for the given parallel lines with transversal ,and the pair of interior angles 72° and (7x +24)°, the value of x = 12°.
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Given :R is the midpoint of QSQR = 6x - 9 RS = 2x - 1 We need to find QS
Answers
Given :
R is the midpoint of QS
QR = 6x - 9
RS = 2x - 1
We need to find QS
So, as R is the midpoint
[tex]\begin{gathered} QR=RS \\ 6x-9=2x-1 \end{gathered}[/tex]Solve the equation to find x :
[tex]\begin{gathered} 6x-9=2x-1 \\ 6x-2x=-1+9 \\ 4x=8 \\ \\ x=\frac{8}{4}=2 \end{gathered}[/tex]Substitute with x to find QR and QS
[tex]\begin{gathered} QR=6\cdot2-9=12-9=3 \\ RS=2\cdot2-1=4-1=3 \\ \\ QS=QR+RS=3+3=6 \end{gathered}[/tex]An altitude is drawn from the vertex of an isosceles triangle, forming a right angle and two congruent triangles. As a result, the altitude cuts the base into two equal segments. The length of the altitude is 21 inches, and the length of the base is 18 inches. Find the triangle’s perimeter. Round to the nearest tenth of an inch.
Answers
Answer:
63.7 inches to nearest tenth.
Step-by-step explanation:
The legs of the right triangles formed are 21 inches and 1/2*18 = 9 inches.
So, the hypotenuse (which is one of the congruent sides of the isosceles triangle)
= √(21^2 + 9^2
= √522 inches
Therefore, the triangles perimeter
= 2 * √522 + 18
= 63.695 inches.
the box contains 8 blue and 4 black pencils. 5 pencils are drawn at random from the box. find the probability that out of 5 pencils taken, 2 are blue and 3 are black.
Answers
The probability that out of 5 pencils taken, 2 are blue and 3 are black is 0.4381.
What is probability?Probability simply means the likelihood that something will occur or happen.
In this case, the the box contains 8 blue and 4 black pencils. The probability of drawing 2 blue balls will be:
= 8/12 × 7/11
= 0.4242
The probability of drawing 3 blacks will be:
= 4/12 × 3/12 × 2/12
= 1/3 × 1/4 × 1/6
= 0.0139
The probability will be the addition of the values. This will be:
= 0.4242 + 0.0139
= 0.4381
The probability is 0.4381.
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8
(b) Then determine whether the above relation is a function.
A) Function
B Not a function
Answers
The above relation is not a function
What is a function?
A function from either a set X to just a set Y allocates precisely one element of Y to each element of X. The set X is known as the function's domain, while the set Y is known as the function's codomain. The Persian mathematicians Al-Biruni and Sharaf al-Din al-Tusi are credited with the first known attempt to the concept of function. Originally, functions were the idealization of how a variable quantity depended on another quantity. A planet's location, for example, is a function of time. Historically, the notion was developed with the infinitesimal calculus at the end of the 17th century, and the functions investigated were differentiable until the 19th century.
The above relation is not a function
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I need help with this
Answers
y-intercept= 0
asymptote =[tex]lim_{n}[/tex]→-0 (8/x) = -∞
[tex]lim_{n}[/tex]→+0 (8/x) = +∞
range = R : { x ∈ R / {0} }
What is Range ?
When the sample maximum and minimum are subtracted, the range of a collection of data is the difference between the greatest and lowest values. It uses the same units as the data to express itself.
I think the formula is:
f(x) = 8/x
(You wrote 8x; since a linear function has no asymptotes and you wrote 8x, I'm assuming the true function was 8/x.)
The amount that makes f(x) equal to 0 is the y-intercept.
Keep in mind that there is no value of x such that 8/x = 0 (because the quotient cannot be zero if the numerator is never zero).
Therefore, there is no y-intercept.
The asymmetry:
These are the four:
If the negative side of x tends to zero, then 8/x tends to negative infinity.
If x from the positive side approaches to zero, then 8/x tends to positive infinity.
These two asymptotes are expressed as follows:
[tex]lim_{n}[/tex]→-0 (8/x) = -∞
[tex]lim_{n}[/tex]→+0 (8/x) = +∞
Additionally, there are two cases where x tends to plus infinity (and 8/x goes to zero) and when x tends to minus infinity, where the function tends to zero once more. These two cases are denoted by the formulas:
[tex]lim_{n}[/tex]→-∞ (8/x) = -∞
[tex]lim_{n}[/tex]→∞ (8/x) = +∞
Lastly, the scope:
Only on limitations, y never reaches the following value:
y = 0
If so, the set of all real numbers excluding zero is the range, or
R : { x ∈ R / {0} }
Hence, y-intercept= 0
asymptote =[tex]lim_{n}[/tex]→-0 (8/x) = -∞
[tex]lim_{n}[/tex]→+0 (8/x) = +∞
range = R : { x ∈ R / {0} }
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Solve −5d +2≥7 or 2d −2>8
Answers
Answer:
for the first one: d ≥ 1
for the second one: d > 5
What is the value of the digit 5 in the answer to 8500 divided by 10? D 5000 C 500 B 50 A 5.
thanks
Answers
Answer:
B) 50
Step-by-step explanation:
its in tens place
hope this helps you!!!
Answer:
8500/10=850
value of digit 5=50
raul and a friend bought two tickets to see a soccer game each ticket cost $6.75 the friends pain a total of $23.50 which included a fee parking near the stadium how much did each friend pay for the parking fee what is the parking fee as a percent increase in the cost of a ticket
Answers
Answer:
Each friend paid $5 for parking.
Step-by-step explanation:
[tex]23.5[/tex] - [tex](6.75[/tex][tex](2)[/tex][tex])[/tex] = [tex]10[/tex]
[tex]10[/tex] ÷ [tex]2 = 5[/tex]
I'm not sure about the rest of the question.
HElP ME Please!!!!!!!! I need help
Answers
Answer:
b x 8 = 40 and 40 / 8 =b
Step-by-step explanation:
well, 8 charms makes one bracelet, so add up 8 until you run out of charms:
8 8 + 8 = 16 16 + 8 = 24 24 + 8 = 32 32 + 8 = 40We only have 40 charms, so we can make 5 bracelets!
Now, plug this number (5) back into the equations:
b x 8 = 40
(5) x 8 = 40
40 = 40
this checks out!
40 - 8 = b
40 - 8 = (5)
32 = 5
32 does not equal 5, so this equation doesn't work.
40 / 8 = b
40 / 8 = (5)
5 = 5
This equation works :)
b + 8 = 40
(5) + 8 = 40
13 = 40
13 does not equal 40, so this is also a bad equation..
since b x 8 = 40 and 40 / 8 = b both produced the right results, we know those two are our answers!