[tex]\dfrac{6\sqrt 3~ \text{cis} \left( \dfrac{7 \pi} 6 \right)}{3 \sqrt 5 ~\text{cis} \left( \dfrac{\pi}{3}\right)}\\\\\\=\dfrac{2\sqrt 3 \cdot e^{i\tfrac{7\pi}{6}}}{\sqrt 5\cdot e^{i \tfrac{\pi}{3}}}\\\\\\=\dfrac{2 \sqrt 3}{\sqrt 5} \cdot \left(e^i \right)^{\tfrac{7\pi}{6} - \tfrac{\pi }{3}}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~;\left[\text{cis}~ \theta = e^{i \theta}\right]\\\\\\=\dfrac{2 \sqrt{3}}{\sqrt 5} \cdot \left(e^i\right)^{\tfrac{5\pi}6}\\\\\\=\dfrac{2\sqrt{3}}{\sqrt 5}\cdot e^{i\tfrac{5 \pi}6}\\\\\\[/tex]
[tex]=\dfrac{2\sqrt{3}}{\sqrt 5} \left[ \cos \left(\dfrac{5\pi}{6}\right) + i \sin \left(\dfrac{5\pi}{6}\right) \right]~~~~~~~~~~~~~~~~~~;\left[e^{i\theta} = \cos \theta + i \sin \theta} \right]\\\\\\=\dfrac{2\sqrt{3}}{\sqrt 5}\left[ \cos \left(2 \times \dfrac{\pi}2 -\dfrac{\pi}{6} \right) + i\sin \left(2 \times \dfrac{\pi}2 -\dfrac{\pi}{6} \right) \right]\\\\\\=\dfrac{2\sqrt{3}}{\sqrt 5} \left[ -\cos \left(\dfrac{\pi}{6}\right) + i \sin \left(\dfrac{\pi}{6}\right) \right]\\\\\\[/tex]
[tex]=\dfrac{2\sqrt{3}}{\sqrt 5}\left( -\dfrac {\sqrt{3}}{2} + i \cdot \dfrac 12 \right)\\\\\\=-\dfrac{3}{\sqrt 5} + i \dfrac{\sqrt 3}{\sqrt 5}[/tex]
Answer:
Step-by-step explanation:
Just took the test:
6sqrt3 cis (7pie/6)/ 3sqrt5 cis (pie/3)=
2sqrt15/5 cis (5pie/6)
What is the value of x?
A. 6
B. 6√2
C. 12
D. 12√2
Answer:
the answer is c
Step-by-step explanation:
i got it right on my test. Hope This helps!
please help me with this. put the shapes in their correct place on the Venn diagram. Screen shot and edit if you have to.
View the answer in the Venn Diagram below.
A quadrilateral is a flat shape with four edges and four corners, also known as vertices. The quadrilateral has angles at each of its four vertices, or corners. The angles at the vertices of a quadrilateral ABCD are A, B, C, and D. A quadrilateral has the following sides: AB, BC, CD, and DA.
A simple (non-self-intersecting) quadrilateral with two sets of parallel sides is known as a parallelogram in Euclidean geometry.
A quadrilateral with equal angles and parallel opposing sides is referred to as a rectangle. Around us, there are a lot of rectangle items. The length and breadth of any rectangle form serve as its two distinguishing attributes. The width and length of a rectangle, respectively, are its longer and shorter sides.
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When a number is divided into by 8,9,and 6 the remainders are 7, 8 and 5 respectively. Find the number
Answer:71
Step-by-step explanation:
71 is the number when it is divided into by 8,9,and 6 the remainders are 7, 8 and 5
What is Number system?A number system is defined as a system of writing to express numbers.
Given that a number is divided into by 8,9,and 6 the remainders are 7, 8 and 5 respectively.
We need to find the number.
In division there are three parts the divider, dividend, quotient, and remainder.
Let us find the LCM of 8,9 and 6
LCM of 8, 9,6 is 72
72-1=71
Hence, 71 is the number when it is divided into by 8,9,and 6 the remainders are 7, 8 and 5
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if the first term is -2 and the rule is multiply by 6 and then subtract 13 whats the 3rd term
Answer:
-163
Step-by-step explanation:
-2,-25,-163
-2×6=-12 -12-13=-25
-25×6=-150 -150-13=-163
Answer:
The third term is = -163
Step-by-step explanation:
The first term is = -2
The second term = -2 ×6 = -12 Then - 13 = - 25
The second term = - 25
The third term = -25 × 6 = - 150 Then -13 = -163
The third term is -163
Mark brainliest
Jose paid $1.12 for a dozen eggs at his local grocery store. Determine the cost of 18 eggs.
Answer:
$1.68
Step-by-step explanation:
1 dozen is 12.
18 is the same as 12 + 6
6 eggs is half of 12 eggs.
Since 12 eggs cost $1.12, then 6 eggs cost half of $1.12, or $1.12/2 = $0.56.
18 = 12 + 6, so
the price of 18 eggs = the price of 12 eggs + the price of 6 eggs.
price of 18 eggs = $1.12 + $0.56 = $1.68
How do you write a proof for this
Answer: They're equal to each other yes corresponding parts of congruent triangles are equal
Step-by-step explanation:
The number of DVDs in a random person's home collection is counted for a sample population of 80 people. The mean of the sample is 52 movies, the entire population is known to have a standard deviation of 12 movies. Assuming a 99% confidence level, find the margin of error.
A) 59.4671
B) 2.6296
C) 38.6536
D) 3.4547
In a case whereby the number of DVDs in a random person's home collection is counted for a sample population of 80 people the mean of the sample is 52 movies, the entire population is known to have a standard deviation of 12 movies then the margin of error is 3.46 moves.
How can the the margin of error be calculated?The concept that will be used here is the formular to find the error
E=z∝/2 σ/√ n
n= number of the samples= 80
σ = standard deviation = 12 moves
confidence level = (1-∝) = (1- 0.99) = 0.001
σ/2 = 0.005
Then the looking up for Z value of Z(0.005) = 2.58
E= 2.58 *12/√80
= 3.46 moves.
Therefore, option D is correct.
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Choose all of the following angles that cannot
be an interior angle in a regular polygon.
40° 45° 108° 132° 179°
Answer:
40 45 because the minimum internal angle is 60
If a point is reflected over the y-axis, then the coordinates of (x, y) are changed to ______________.
Answer:
its opposite
Step-by-step explanation:
What are the domain and range of an exponential parent function?
Help please
The domain and the range of an exponential parent function, that is, y = eˣ are equal to all real numbers and non-negative numbers, respectively. (Correct choice: C)
How to determine the domain and range of an exponential function
In this problem we should determine what an exponential parent function is. The most common exponential functions have the following form:
[tex]y = A\cdot e^{B\cdot x} + C[/tex] (1)
(1) is an exponential parent function for A = 1, B = 1 and C = 0.
All functions are relations with a domain and range, the domain is an input set related to the range, that is, an output set. In the case of an exponential parent function, the domain and the range of the expression are [tex]\mathbb{R}[/tex] and y ≥ 0, respectively. (Correct choice: C)
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The volume of a cylinder is 8177 cm³. If the radius is 3 cm, what is the height
of the cylinder?
OA. 9 cm
OB. 18 cm
O C. 12 cm
O D .6cm
Answer:
None of the options are correct
О E. 289.2 cm
Step-by-step explanation:
Volume of a cylinder = v = л r² h
л = 3.1416 (aprox)
r = radius
h = height
8177 = 3.1416 * 3² * h
8177 = 3.1416 * 9 * h
8177 = 28.2744 * h
8177/282744 = h
h = 289.2 cm
a jacket is on sale for 30% of and its £42 after discount whats the original price
Answer:
£60
Step-by-step explanation:
70% of original price = £42
100% of original price = £42 * 10/7 = £6 * 10 = £60
100 points, PLEASE HELP MEEE
Answer:
b = 3a
Step-by-step explanation:
a = < - 1, 3 >
b = < - 3, 9 >
Thus
b = 3a
Answer:
b = 3a
Step-by-step explanation:
Alec paid the bill for dinner with his clients which totaled $140 before tax and tip. If an 8 percent sales tax was added to the cost of the meal, and an automatic tip was added in the amount of $25.00, what was the total cost of the dinner?
The total cost of the dinner is $176.20.
What is the total cost of the dinner?The total cost of the dinner is the sum of the bill for the dinner, the tax and the tip.
Total cost = tip + bill of the dinner + tip
Tax = 0.08 x 140 = $11.20
Total cost = $140 + $25 + $11.20 = $176.20
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Find p and q if, √3 −1 /√3 +1 = p + q√3
Answer: p=2, q=-1
Step-by-step explanation:
[tex]\frac{\sqrt{3}-1}{\sqrt{3}+1} \left(\frac{\sqrt{3}-1}{\sqrt{3}-1} \right)=\frac{3+1-2\sqrt{3}}{2}=\frac{4-2\sqrt{3}}{2}=2-\sqrt{3}\\\\\therefore p=2, q=-1[/tex]
Which angles are vertical angles select two options
The pair of the vertically opposite angles are ∠ABC = ∠DBE and ∠CBD = ∠ABE Then the correct options are B and E.
The complete question is attached below.
What is Vertically opposite angle?When two lines intersect, then their opposite angles are equal.
The diagram is given below.
∠ABC = ∠DBE
∠CBD = ∠ABE
Then the correct options are B and E.
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Rearrange the equation 4-4x-2y=0 into the form of y=mx+c
Answer:
y = -2x+2
Step-by-step explanation:
4-4x-2y=0
4-4x = 2y
2y = 4-4x
y = (4-4x)/2
y = 4/2-4x/2
y = 2 -2x
y = -2x+2
Which inequalities are true? Select the four correct answers.
O√5<23<√6
O√5<24<√6
O√4<√5<√√55
O√√8 <3<√9
O√8<2.9<√√9
O√4 <45<√√5
The correct anwer is option C and option E which are √4<√5<√√55 and √8<2.9<√√9.
What is inequality?
Inequality is the relationship between two expressions that are not equal, employing a sign such as ≠ “not equal to,” > “greater than,” or < “less than.”.
The two inequalities √4<√5<√√55 and √8<2.9<√√9. are true.
√4<√5<√√55 → 2 < 2.23 < 7.41
√8<2.9<√√9 → 2.82 < 2.9 < 3
Therefore correct answers is option C and option E which are √4<√5<√√55 and √8<2.9<√√9.
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step by step please, thank you so much
The equation of the parabola will be y = x² – 6x + 9. Then the correct option is C.
The complete question is attached below.
What is the parabola?It's the locus of a moving point that keeps the same distance between a stationary point and a specified line. The focus is a non-movable point, while the directrix is a non-movable line.
The equation of a quadratic function, of vertex (h, k), is given by:
y = a(x – h)² + k
where a is the leading coefficient.
The vertex of the parabola is at (3, 0). Then the equation of the parabola will be
y = (x – 3)² + 0
Then open the bracket, we have
y = x² – 6x + 9
Then the correct option is C.
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Construct a circle through points X, Y, and Z.
The image of the Constructed circle that passes through points X, Y, and Z is given in the image attached.
How is the circle constructed?The steps to construct the circle are:
Step one- Draw 3 circles and the center of each of then is one where one acts as one of the points, and the other side of the compass is said to be at another point.
Step two: Then the draw the circle and follow the way for each point and the three point do cross some where of each other in the middle.
Step three: Place your compass on that point and then begin to drawing side to link the points and so all 3 point will be on the circle.
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Graph the line that represents the equation
can someone please help meee
Answer:
-3/5
Step-by-step explanation:
put down the 5,0 and 0,3 then simply start at the 5,0 and count up how many boxes it takes to get to the three then count left how many boxes it takes to get to 0 so...3/5. then look at the line. its going down which means it is negative. so the slope is -3/5
Answer:
y is 3 and x is
Step-by-step explanation:
Let a and b be real numbers where a b 0. Which of the following functions could represent the graph below?
1f(x) = x(x-a)²(x - b)4
2f(x) = x(x - a)³(x- b)²
3f(x) = x²(x-a)(x- b)²
4f(x) = x²(x-a)5(x- b)
The polynomial function that could represent the graph is f(x) = x²(x - a)(x - b)² with four turning points
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
The maximum number of turning points of a polynomial function is always one less than the degree of the function.
Hence the polynomial represented by the graph is of degree 5 since it has 4 turning points. The polynomial function that could represent the graph is f(x) = x²(x - a)(x - b)²
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PLS HELP QUICKLY
f(x)= 3x² + 4x - 6
g(x) = 6x³5x² - 2
Find (f+g)(x).
A. (f+g)(x) = -6x³ +8x² + 4x - 4
B. (f+g)(x) = 6x³ - 2x² + 4x-8
c. (f+g)(x) = 6x³ + 3x²-x-8
D. (f+g)(x) = 9x³-x-8
Answer:
(A) 6x³+8x² + 4x - 4, but only if my change is correct to 6x³5x² - 2 is correct.
Step-by-step explanation:
Is "g(x) = 6x³5x² - 2" meant to be g(x) = 6x³-5x² - 2?
If so, (f+g)(x) = 3x² + 4x - 6 - (6x³-5x² - 2)
(f+g)(x) = 3x² + 4x - 6 - 6x³+5x² + 2
(f+g)(x) = 6x³+8x² + 4x - 4
(A)
Please help answer this question asap 4/11
find the total surface area of this triangular prism 21cm 29cm 20cm 22cm
Answer:
[tex]\huge\boxed{SA=1960cm^2}[/tex]
Step-by-step explanation:
We have:
2 rectangular triangles with legs 20cm and 21cm3 different rectangles 20cm × 22cm, 21cm × 22cm and 29cm × 22cmThe formula of an area of
a rectangular triangle:[tex]A_\triangle=\dfrac{a\cdot b}{2}[/tex]
a, b - legs
a rectangle a × b:[tex]A_{\square}=a\cdot b[/tex]
Calculate:
Rectangular triangle
[tex]A_\triangle=\dfrac{20\cdot21}{2}=210(cm^2)[/tex]
Rectangles:
[tex]A_{\square1}=20\cdot22=440(cm^2)\\\\A_{\square2}=21\cdot22=462(cm^2)\\\\A_{\square3}=29\cdot22=638(cm^2)[/tex]
Total surface:
[tex]SA=2A_\triangle+A_{\square1}+A_{\square2}+A_{\square3}\\\\SA=2\cdot210+440+462+638=1960(cm^2)[/tex]
−−→AB=(xy)
What values should x an y take?
The values x and y take are 5 and 0 respectively.
We know that in mathematics, a graph is a visual representation or diagram that shows data or values in an ordered way.
The relationships between two or more things are frequently represented by the points on a graph.
In this case, we have to determine the values of x and y.
Notice that in this graph, point A is located at A = 5 and point B is located at B = 0.
So, we can write (A, B) = (x, y) = (5, 0)
Therefore, the values x and y take are 5 and 0 respectively.
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How do I prove this so that angle 3 and angle 4 are complimentary?
Answer:
please see analysis
Step-by-step explanation:
Reason
1.) given
2.) definition of amptimentaly angle LS
3.) substitution property
4.)definition of amptimentaly angle
hope it helps thank me laterA television has increased in price by 5%
the new price is £194.25. what was the original price?
Answer:
let the original price be X
now new price = original price + increment
increment = 5 % of X = X/20
new price = 194.25
now, 194.25 = X + X / 20 = 21X / 20
X = 194.25 * 20 / 21
X = 185
original price = 185
Find the indicated side of the
right triangle.
30°
X
X
60
= [?]√]
7
Enter
Answer:
[tex]7\sqrt{3}[/tex]
Step-by-step explanation:
This is a special triangle with the angles being 30-60-90. The adjacent side to the angle of 30 degrees has a length of x * sqrt(3). The opposite side has a length of x. Since the opposite side has a length of 7 here you simply plug that into x * sqrt(3) to find the length of the adjacent side of the angle 30 degrees which gives you 7 * sqrt(3)