Answers
Any complex number [tex]z[/tex] can be written in polar/exponential form as
[tex]z = |z| e^{i\arg(z)} = |z| (\cos(\arg(z)) + i \sin(\arg(z)))[/tex]
In the complex plane, the given complex number belongs to the third quadrant since both its real and imaginary parts are negative. This means the argument must be between π and 3π/2, so the first two options are eliminated.
The difference between the remaining two options is the coefficient [tex]|z|[/tex]. We have
[tex]z = -2\sqrt3 - 6i \implies |z| = \sqrt{(-2\sqrt3)^2 + (-6)^2} = 4\sqrt3[/tex]
so (D) (the last option) is the correct choice.
Related Questions
what is 4x-5/3+2x=7+2/9x+2
Answers
Simplifying the expression gives 36x^2 - 82x - 10 = 0
How to simplify the expressionGiven the expression;
4x-5/3+2x=7+2/9x+2
[tex]\frac{4x - 5}{3 + 2x} = \frac{9}{9x + 2}[/tex]
Cross multiply
[tex]4x - 5( 9x + 2) = 9 (3 + 2x)[/tex]
Expand the bracket
[tex]36x^2 + 8x - 45x - 10 = 27x + 18x[/tex]
Collect like terms
36x^2 + 8x - 45x - 27x - 18x = 0
Add the like terms
36x^2- 82x - 10 = 0
Thus, simplifying the expression gives 36x^2- 82x - 10 = 0
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Please help me with this
Answers
Answer:
altitude: 16 cmbase: 12 cmStep-by-step explanation:
The given relation can be used with the formula for the area of a triangle to give an equation for the altitude or base.
SetupLet b represent the length of the base. Then the altitude (height) is (b+4). The area formula tells us the area is ...
A = 1/2bh
Using given values, the equation becomes ...
96 = 1/2b(b +4)
SolutionSimplifying the equation and multiplying by 2, we have ...
192 = b² +4b
Adding (4/2)² = 4 will complete the square.
196 = b² +4b +4 = (b +2)²
Taking the square root gives ...
14 = b +2 . . . . . . we are not interested in the negative root
12 = b . . . . . . . . subtract 2
16 = b+4 . . . . . find the altitude
The base is 12 cm; the altitude is 16 cm.
David has kept track of his family’s grocery bills for the past 10 weeks, as shown in the table.
Week 1 2 3 4 5 6 7 8 9 10
Bill ($) 92 106 129 115 100 84 110 156 98 87
Would you choose to use a histogram, a circle graph, or a line graph to display the data? Explain your choice. Then make a display.
Answers
The best option that would be used to show the data would be the line graph.
Why the line graph is the bestThe reason I chose the line graph is that it would show us the trend in the data. This is in a way that we would see the periods there was a high bills.
Also the line graph is very simple to understand. The relationship and the changes in the data is easily seen.
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Which systems of equations have no real number solutions? Check all that apply.
Oy=x² + 4x + 7 and y = 2
□ y=x²-2 and y=x+5
-Oy=-x²-3 and y = 9 + 2x
y=-3x-6 and y = 2x² - 7x
y=x² and y = 10 - 8x
Answers
Answer + Step-by-step explanation:
Recall That the number of solution
of a quadratic equation ax² + bx + c = 0
depends on the discriminant b² - 4ac :
if b² - 4ac > 0 , the equation has two distinct solutions.
if b² - 4ac = 0 , the equation has only one solution.
if b² - 4ac < 0 , the equation has no solutions.
=======================================
System 1 :
y = x² + 4x + 7 and y = 2
⇔ x² + 4x + 7 = 2
⇔ x² + 4x + 5 = 0
→ b² - 4ac = 4² - 4×1×5 = 16 - 20 = -4 < 0
Then the quadratic equation has no solutions
Therefore the system has no solutions.
System 2 :
y = x² - 2 and y = x + 5
⇔ x² - 2 = x + 5
⇔ x² - x - 7 = 0
→ b² - 4ac = (-1)² + 4×7 = 29 > 0
Then the quadratic equation has two solutions
Therefore the system has two solutions.
System 3 :
y = -x² - 3 and y = 9 + 2x
⇔ -x² - 3 = 9 + 2x
⇔ -x² - 2x - 12 = 0
→ b² - 4ac = (-2)² - 4×(-1)×(-12) = 4 - 48 = -44 < 0
Then the quadratic equation has no solutions
Therefore the system has two solutions.
System 4 :
y = -3x - 6 and y = 2x² - 7x
⇔ -3x - 6 = 2x² - 7x
⇔ 2x² - 4x + 6 = 0
→ b² - 4ac = (-4)² - 4×(2)×(6) = 16 - 48 = -32 < 0
Then the quadratic equation has no solutions
Therefore the system has two solutions.
System 5 :
y = x² and y = 10 - 8x
⇔ x² = 10 - 8x
⇔ x² + 8x - 10 = 0
→ b² - 4ac = 8² - 4×1×(-10) = 64 + 40 = 104 > 0
Then the quadratic equation has two solutions
Therefore the system has two solutions.
Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.
Match each expression to make pairs of equivalent expressions.
Answers
The equivalent expressions indicated are;
1) 1/a^6b^4
2) a^6/b^6
3) a^6/b^5
4) b^6/a^6
5) a^5b^3
What is the result of the equivalent expressions?
We have to note that when we talk about the equivalent expressions, we mean the expressions that we have to get from each other when we carry out a little computational work on the original expression.
Thus, the equivalent expression has shown that the expression that is in the bracket is the same as the original expression by the use of the laws of exponents.
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Which of the following is equal to the expression below?
(4^-5)^3
A. -4^2
B. 1/4^15
C. -4^15
D. 1/4^2
Answers
Answer: B
Step-by-step explanation:
[tex](4^{-5})^3=4^{-15}=\frac{1}{4^{15}}[/tex]
A square has a perimeter of 12x 52 units. which expression represents the side length of the square in units?
Answers
Answer:
X
Step-by-step explanation:
KHAN ACADEMY
5th grade algebra. Pls help with these am offering brainliest + bonus points! :D
Answers
Answer:
3. 6 5. 3
Step-by-step explanation:
PEMDAS
3. 0.5 x (24) / 3 + 2
12/3 +2
4 + 2
6
5. (4 + 6/3) x 0.5
(4 + 2) x 0.5
6 x 0.5
3
Answer: number 3. is 6 and number 5. is 3
hope it helped
Here is a list of numbers: 2 , 8 , 1 , 7 , 4 , 10 , 1 , 15 , 20 State the median.
Answers
Answer:
7
Step-by-step explanation:
1, 1, 2, 4, 7, 8, 10, 15, 20
median = 7
What is the scale factor of this dilation? Triangle A B C. Side A C is 8, C B is 10, A B is 6. Triangle A prime B prime C prime. Side A prime C prime is 4, C prime B prime is 5, B prime A prime is 3. One-fifth One-half 1 2
Answers
Answer:
The scale factor from the original triangle to the image is 1/2. The scale factor from the image to the original is 2.
Step-by-step explanation:
I make a sketch of the information. Look at the corresponding sides. Side AC on the big triangle is 8 and A'C' is 4. It is half of the size of the large triangle. That is true for each pair of sides.
If I went the other way, the original sides are twice as big as the images sides.
the market price of article is rs 3000. a discount of 30% was agreed. find the sale price of the article and the amount of discount.
Answers
Answer: 2400
Step-by-step explanation:
3000 x 20/100 = 600
Discount = 600
Sale price of the article: 3000-600 = 2400
How many terms are in the sequence shown?
38, 36, 34, ..., -20
Answers
Answer:
30 terms
Step-by-step explanation:
In the sequence, the value of each term decreases by 2.
38, 36, 34, 32, 30, 28, 26, 24, 22, 20, 18, 16, 14, 12, 10, 8, 6, 4, 2, 0, -2, -4, -6, -8, -10, -12, -14, -16, -18, -20.
1+ (38 - (-20))/2 = 1+ 29 = 30
Drag the tiles to the correct boxes to complete the pairs. Suppose you roll a fair six-sided die. Then you roll a fair eight-sided die. Match each probability to its correct value. the probability that both numbers are odd numbers and their product is greater than 10 the probability that the second number is twice the first number the probability of getting numbers whose sum is a multiple of 4 the probability that the sum of the two numbers is greater than 11 the probability that the second number rolled is less than the first number arrowRight arrowRight arrowRight arrowRight arrowRight
Answers
The probability will be:
Case 1 matches with 5/48.
Case 2 matches with 1/12.
Case 3 matches with 1/4.
Case 4 matches with 1/8.
Case 5 matches with 5/16.
How to illustrate the probability?We have a total sample space of six-sided die and an eight sided die.
(1,1),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(1,8)
(2,1),(2,2),(2,3),(2,4),(2,5),(2,6),(2,7),(2,8)
(3,1),(3,2),(3,3),(3,4),(3,5),(3,6),(3,7),(3,8)
(4,1),(4,2),(4,3),(4,4),(4,5),(4,6),(4,7),(4,8)
(5,1),(5,2),(5,3),(5,4),(5,5),(5,6),(5,7),(5,8)
(6,1),(6,2),(6,3),(6,4),(6,5),(6,6),(6,7),(6,8)
Case 1: The Probability that both numbers are odd numbers and their product is greater than 10. are: (3,5),(3,7),(5,3),(5,5),(5,7)
And the total number of outcomes are: 48.
The required probability is 5/48.
Case 2: The probability that the second number is twice the first number are:
(1,2),(2,4),(3,6),(4,8)
And the total number of outcomes are 48.
So, the required probability is 1/12.
Case 3: The probability of a number whose sum is a multiple of 4 are:
(1,3),(1,7),(2,2),(2,6),(3,1),(3,5),(4,4),(4,8),(5,3),(5,7),(6,2),(6,6).
And the total number of outcomes are: 48.
The required probability is 12/48 = 1/4
Case 4: The probability that the sum of two numbers is greater than 11.
(4,8),(5,8),(6,7),(6,8),(5,7),(6,6)
And a total number of outcomes are 48.
So, the required probability is 6/48 = 1/8.
Case 5: The probability that the second number rolled is less than the first number are:
(2,1),(3,1),(3,2),(4,1),(4,2),(4,3),(5,1),(5,2),(5,3),(5,4),(6,1),(6,2),(6,3),(6,4),(6,5)
And the total number of outcomes are: 48.
The required probability is 15/48 = 5/16.
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Solve each of the following equations show the solution on a number line check your answers 5-|n-1|=-2
Answers
n=8
n=-6
What is a number line?A number line is a horizontal line with evenly spaced number increments. The numbers on the line will determine how the number on the line can be answered.
The numbers on the number line increase as one moves from left to right and decrease as one moves from right to left.
Solution for the above equation 5-|n-1|=-2What is the modulus?A modulus function is a function that returns the absolute value of a number or variable. It yields the magnitude of the number of variables. It is also known as an absolute value function. This function's output is always positive, regardless of the input.
Open modulus with a positive sign.
5-|n-1|=-2
-|n-1|=-2-5
n+1= 7
n= 8
Open modulus with a negative sign.
5-|n-1|=-2
-|n-1|=-2-5
n-1= -7
n= -6
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Help, please. I just need an answer, so if anyone is bored, for the love of god please...
Answers
Answer:B & E
Step-by-step explanation:
We can first rearrange the function to isolate y. Then, we can find the slope as the function is in the form y=mx+b.
[tex]3x-4y=7\\-4y=-3x+7\\y=\frac{3}{4}x-\frac{7}{4}[/tex]
Since parallel lines have the same slope, we can put the slope of 3/4 into the point slope form to get the answer.
For reference, the point-slope form is [tex]y-y_1=m(x-x_1)[/tex]
[tex]y+2=\frac{3}{4}(x+4)\\y+2=\frac{3}{4}x+3\\y=\frac{3}{4}x+1[/tex]
The first line is found in option E, so option E is one of the correct options.
We can also move the x to the other side, as two of the 5 options have both variables on the left (B and C).
[tex]-\frac{3}{4}x+y=1[/tex]
If we multiply the whole equation by -4, we can get rid of the fraction.
[tex]-4(-\frac{3}{4}x+y)=-4(1)\\3x-4y=-4[/tex]
Hence, option B is also correct.
On a coordinate plane, a curved line with minimum values of (negative 2, 0) and (1.05, negative 41), and a maximum value of (negative 0.5, 5), crosses the x-axis at (negative 2, 0), (0, 0), and (1.5, 0), and crosses the y-axis at (0, 0).
Which statement is true about the end behavior of the graphed function?
As the x-values go to positive infinity, the function’s values go to positive infinity.
As the x-values go to zero, the function’s values go to positive infinity.
As the x-values go to negative infinity, the function’s values are equal to zero.
As the x-values go to negative infinity, the function’s values go to negative infinity.
Answers
The statement which is true about the end behaviour of the graphed function is; As the x-values go to positive infinity, the function’s values go to positive infinity.
Which statement is true about the end behaviour of the graphed function?The graph given according to the task content is described to have its first minimum at (-2,0), and then a maximum at; (-0.5, 5) and finally a minimum at; (1.05, -41).
Additionally, since the graph has 3 zeroes as given, it follows that the graph is that of a cubic function which takes the w-form.
Consequently, it can be inferred from the statements above that; As the x-values go to positive infinity, the function’s values go to positive infinity.
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Answer:
A
Step-by-step explanation:
edge 23
See photo to answer!
Answers
The length of AB of the triangle is 13 units.
How to find the side of a triangle?The side AB of the triangle can be found using cosine law,
Therefore,
c² = a² + b² - 2ab cos C
c² = 7² + 8² - 2 × 7 × 8 cos 120
c² = 49 + 64 - 112 cos 120
c²= 113 - (-56)
c² = 113 + 56
c² = 169
c = √169
c = 13 units
Therefore, the value of AB is 13 units
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PLEASE HELP!!! I'LL MARK AS BRAINLIEST TO THE FIRST PERSON THAT CAN ANSWER!!!
When two exponents with the same base are multiplied together, this reflects the _______ of powers property.
Answers
Can anyone please help me with this i am stuck and i really need help.Explain how u got the answer
Answers
The measure of m<1, m<2 and m<3 are 90, 63 and 63 degrees respectively
What is a kite?A kite is a quadrilateral whose four sides can be grouped into two pairs of equal-length sides that are adjacent to each other.
The given figure is a kite with two intersecting lines that are perpendicular to each other.
Since the lines are perpendicular to each other, hence;
m<1 = 90 degrees
For the measure of m<2
m<2 + 90 + 27 =180
m<2 + 117 = 180
m<2 = 180 - 117
m<2 = 63degrees
Since the opposite sides are congruent, hence the measure of m<2 is congruent to m<3. Hence m<3 = 63 degrees
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Which is the completely factored form of 12x4 + 39x3 + 9x2?
3x2(x – 3)(4x – 1)
3x2(x + 3)(4x + 1)
3x(x + 3)(4x + 1)
3x(x – 3)(4x + 1)
Answers
Answer:
The second option, 3x^2(x+3)(4x+1)
Step-by-step explanation:
Factor out the common term, which is 3x^2
This then becomes 3x^2(4x^2+13x+3)
Factor the inside term and it becomes
(3x^2)(x+3)(4x+1)
Lesson 13:Find a Sequence
Describe a sequence of reflections, rotations, and translations that takes ABCD onto
A'B'C'D'.
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The sequence of transformation will be;
Rotate 120 degrees Counterclockwise around B, then Translate B to B' and reflect over segment BA.
How to Identify the Transformation?
We want to find the transformation that maps Quadrilateral ABCD onto Quadrilateral A'B'C'D'.
Looking at the given image, the sequence of transformation will be;
Rotate 120 degrees Counterclockwise around B, then Translate B to B' and reflect over segment BA.
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help me please im in a rush
Answers
Answer:
a.1
b. 17
Step-by-step explanation:
So the | | around an equation makes it an absolute value which can be defined as the "distance from zero" or in other words, if a value is positive, it stays positive, and if a value is negative, it becomes positive.
|-8 + 9| = |1| = 1
|-8| + 9 = 8 + 9 = 17
Select the correct answer.
If vector u = <-3.5, -1.5> and vector v = <-1.25, 2.25>, which graph shows the resulting vector for 2v - u?
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The graph that aligns with the information is graph D.
How to illustrate the graph?We know that vector addition is scalar addition.
Given vectors are u = <-3.5, -1.5> and v = <-1.25, 2.25>
2v = < -2.5, 4.5>
2v - u = < -2.5, 4.5> - <-3.5, -1.5> = < -2.5 - (-3.5) , 4.5 -(-1.5) >
2v-u = < 1 , 6 >
This vector is basically i + 6j which is drawn in option D
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A dog gave birth to 9 puppies, of which 2 are brindle. What is the ratio of brindle puppies to non-brindled puppies?
Answers
Answer:
2:7
Step-by-step explanation:
If 2 of the puppies are brindle that leaves 7 that are not out of the nine making the ratio 2:7.
The Smith family bought carpet for their basement. It originally cost $1,600. The company offered and installment plan for 12 monthly payments of $150. How much was the carpet?
Answers
Answer:
$1,800
Step-by-step explanation:
If the Smiths agree to the installment plan and pay $150 every month for 12 months, it will add up to $1,800 at the end of the year.
Pherris is graphing the function f(x) = 2(3)x. He begins with the point (1, 6). Which could be the next point on his graph?
(2, 12)
(2, 18)
(2, 7)
(3, 7)
Answers
Answer: (2, 18)
Step-by-step explanation:
When x=2, [tex]f(2)=2(3)^{2}=18[/tex].
So, it should pass through (2, 18).
An architect wants an artistic flair to the house he is building, so he designs windows that are three fourths of a circle in shape. The builder is making trim for the windows and needs to know the length of the arc of the outer rim of the window. If the central angle is 270 degrees, and the radius of the partial circle is 30 inches, how much trim is needed for each window? Round your answer to the nearest inch, and enter the number only.
Answers
The amount of rim needed for each window is 141.4 in
How to find the length of the outer rim?Since the outer rim is the length of an arc, we use the formula for length of an arc of a circle.
What is an arc?An arc is part of section of the circumference of a circle
What is the length of an arc?So, length of arc, L = Ф/360 × 2πR where
Ф = central angle of arc and R = radius of circle.Gven that for the window rim
Ф = angle of the rim = 270° and R = radius of the rim = 30 inSubstituting the values of the variables into the equation for L, we have
L = Ф/360 × 2πR
L = 270°/360° × 2π × 30 in
L = 3/4 × 2π × 30 in
L = 3/2 × π × 30 in
L = 3 × π × 15 in
L = 45π in
L = 141.37 in
L ≅ 141.4 in
So, the amount of rim needed for each window is 141.4 in
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6. a. Sixty students in a class took an examination in Physics and Mathematics. If 17 of them passed Physics only, 25 passed in both Physics and Mathematics and 9 of them failed in both subjects, find i. the number of students who passed in Physics ii. the probability of selecting a student who passed in Mathematics 17
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Let [tex]C[/tex] be the set of all students in the classroom.
Let [tex]P[/tex] and [tex]M[/tex] be the sets of students that pass physics and math, respectively.
We're given
[tex]n(C) = 60[/tex]
[tex]n(P \cap M') = 17[/tex]
[tex]n(P \cap M) = 25[/tex]
[tex]n((P \cup M)') = n(P' \cap M') = 9[/tex]
i. We can split up [tex]P[/tex] into subsets of students that pass both physics and math [tex](P\cap M)[/tex] and those that pass only physics [tex](P\cap M')[/tex]. These sets are disjoint, so
[tex]n(P) = n(P\cap M) + n(P\cap M') = 25 + 17 = \boxed{42}[/tex]
ii. 9 students fails both subjects, so we find
[tex]n(C) = n(P\cup M) + n(P\cup M)' \implies n(P\cup M) = 60 - 9 = 51[/tex]
By the inclusion/exclusion principle,
[tex]n(P\cup M) = n(P) + n(M) - n(P\cap M)[/tex]
Using the result from part (i), we have
[tex]n(M) = 51 - 42 + 25 = 34[/tex]
and so the probability of selecting a student from this set is
[tex]\mathrm{Pr}(M) = \dfrac{34}{60} = \boxed{\dfrac{17}{30}}[/tex]
In a bag are three red marbles and three white marbles. If
two marbles are taken from the bag at the same time,
what is the probability that both marbles will be red?
Answers
The probability is 1/5.
How to find the probability?
There are 3 red marbles and 3 white marbles, for a total of 6.
The probability that the first marble is red is:
P(red) = 3/6
The probability that the second marble is also red is:
P(red') = 2/5 (because now there are 2 red marbles and a total of 5).
The joint probability is:
P = (3/6)*(2/5) = 1/5
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What is the time 100 minutes after 13:15
Answers
Therefore the time is 14:55.
Hope it helps : )