Answers
Answer:
2.2 - 0.4[tex]i[/tex]
Step-by-step explanation:
1. Approach
To divide by imaginary number, one must take the fraction and multiply the complex conjugate of the denominator. A complex conjugate is a complex number with its imaginary unit multiplied by (-1). Once one multiplies both the numerator and denominator by the complex conjugate, then the denominator should be a real number (this is because the complex numbers act like binomials when multiplied, and hence the difference of square property works). Now all one has to do is divide every term in the numerator by the real number in the denominator.
2. complex conjugate
As mentioned above, to solve this problem, one has to multiply the numerator and denominator by the complex conjugate of the denominator. That is the complex number in the denominator with its imaginary until multiplied by (-1).
Complex number in the denominator;
(-8 - 6i)
complex conjugate;
(-8 + 6i)
3. Multiplying
Now, one has to multiply the problem's numerator and denominator by the complex conjugate of the denominator. Since a number over itself in fraction format is the same as multiplying by (1), one is allowed to do this;
[tex]\frac{-2-i}{-8-6i}[/tex]
Multiply
[tex]\frac{-2-i}{-8-6i} * \frac{-8+6i}{-8+6i}[/tex]
Distribute
[tex]\frac{(-2)(-8) + (-2)(6i) + (-i)(-8) + (-i)(6i)}{(-8)(-8)+(-8)(6i) + (-6i)(-8) + (-6i)(6i)}[/tex]
4. Simplifying
Now all that is left is to simplify and divide to find the quotient.
=[tex]\frac{(-2)(-8) + (-2)(6i) + (-i)(-8) + (-i)(6i)}{(-8)(-8)+(-8)(6i) + (-6i)(-8) + (-6i)(6i)}[/tex]
=[tex]\frac{16 - 12i +8i -6i^{2}}{64-48i+48i-36i^{2}}[/tex]
Remember the rotations of [tex]i[/tex], [tex]i^{2} = -1[/tex]
Simplify further
[tex]\frac{16-4i+6}{64+36}\\\\=\frac{22-4i}{100}[/tex]
Divide
2.2 - 0.4[tex]i[/tex]
Related Questions
Is this True or false? I truly don't know
Answers
Answer:
I think it's False
Step-by-step explanation:
i just can't tell if the decrease need to be cut in half or not.
Need help here qwq
Hhhhh TOO SHORT MHMM
Answers
Answer:
Step-by-step explanation:
Here you go mate
Step 1
3+(-4)-8-(-1) Equation/Question
Step 2
3+(-4)-8-(-1) Simplify
-9-(-1)
Step 3
-9-(-1) Subtract them
-9-1
Answer
-8
Hope this helps
is x = 8 a solution to the equation 15 - x = 7?
Answers
Answer:
B yes, because 15-8=7 is true
Step-by-step explanation:
Answer:
the answer is B
Step-by-step explanation:
if x = 8
then, 15 - 8 = 7
Determine whether the distribution represents a probability distribution.
Answers
Answer:
No, the given distribution does not represents a probability distribution.
Step-by-step explanation:
In a probability distribution the sum of all the probabilities in a discrete probability distribution must add up to 1 and each individual probability can never be negative or greater than.
Here, P(3) = -3, which is negative, so, the given distribution does not represents a probability distribution.
HELPPP NEED IN THE NEXT 10 MINSSS!!!!
Answers
Answer:
15.6
Step-by-step explanation:
the traingle is right so u have to apply the pythagorean theorem to find x so x^2=10^2+12^2=244
so x=15.6
Step-by-step explanation:
hope it's helpful ❤❤❤❤
THANK YOU.
A water tank measures 20 cm by 50 cm by 30 cm
if each of these measurements is given to the nearest centimeter, calculate the largest
possible volume of the tank.
Answers
The largest possible volume of the tank, considering the given measurements to the nearest centimeter, is approximately 31575.125 cubic centimeters.
We have,
To calculate the largest possible volume of the tank, we need to consider the measurements given to the nearest centimeter.
When measurements are given to the nearest unit, it means they can vary by up to half of the unit in either direction.
For the dimensions of the tank:
Length: 20 cm (can vary from 19.5 cm to 20.5 cm)
Width: 50 cm (can vary from 49.5 cm to 50.5 cm)
Height: 30 cm (can vary from 29.5 cm to 30.5 cm)
To find the largest possible volume, we need to use the maximum values for each dimension.
Using the upper limit for each measurement, the largest possible volume can be calculated as follows:
Volume = Length × Width × Height
= (20.5 cm) × (50.5 cm) × (30.5 cm)
= 31575.125 cubic centimeters
Therefore,
The largest possible volume of the tank, considering the given measurements to the nearest centimeter, is approximately 31575.125 cubic centimeters.
Learn more about expressions here:
https://brainly.com/question/3118662
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Which anime is better Hunter x Hunter or Deathnote? I personally cannot choose because both are so good lol
Answers
Personally I like hxh better, but deathnote is amazing too
Answer:
Bro i watched both of them and both are so goodddd i can't pick honestly
Pete played in 2 games. He scored 4 fewer points in the second game than he scored in the first. He scored 12 points on the second game. How many points did he score in the first game?
Write an equation with the variable x:
Solve the equation
Answers
Answer:
16 x - 12 = 4 or 4 + 12 = x
Step-by-step explanation:
if he scored 4 fewer than the first game that means 4 + 12 = 16
so: x - 12 = 4 or 4 + 12 = x
Which transformations, when performed together, would carry graph A onto
graph B? Choose all that apply. A. A translation of 2 units to the left
B. A translation of 3 units down
C. A vertical stretch with a scale factor of 2
D. A vertical compression with a scale factor of
1/2
Answers
Answer:
A,B
Step-by-step explanation:
Amber got a raise, and her hourly wage increased from $12 per hour to
$15.50 per hour. What is the percent increase to the nearest WHOLE
percent? *
Answers
Answer:29% or 30% rounded up
Step-by-step explanation:
Evaluate each expression??
Answers
Answer:
Step-by-step explanation:
7) 27
8) -10exponent4
i hope this helps, if this is wrong then im sorry but i think its accurate.
HELPPPPPPPPPPPPPPP asap
Answers
Answer:
a. 30 degrees
b. 60 degrees
c. 105 degrees
Step-by-step explanation:
Angle a is 30 degrees becuase it is congruent to the one right above it
Angle b is 60 degrees because the interior angles of a triangle always add up to 180. We know that angle a is 30 degrees and the angle with the mini square is a right angle, and right angles are always 90 degrees. Based on this information, we can subtract 90 from 180 followed by subtracting 30 from 90, which equals 60. Angle b is 60 degrees
Angle c is 105 degrees because a straight angle is 180 degrees. We know that one angle is 75, so we subtract 75 from 180 to get the difference. The difference is 105 degrees, which is also the measurement of angle c.
Hope this helps!
How do I solve for x??
Answers
Answer:
x=40 degrees
Step-by-step explanation:
3x=120 (vertical angles)
solve: 3x=120
x=40
Answer:
x=40
Step-by-step explanation:
The angles are vertical angles And vertical angles measure the same
so
120=3x
Divide both sides by 3:
x=40
Goes through (1,-5) and is perpendicular to 4y + 18 = x
Answers
Answer: x=4y+18
Step-by-step explanation:
Let's solve for x.
4y+18=x
Step 1: Flip the equation.
x=4y+18
Please help me, I have been stuck on this all day :( 30 points and brainliest
You want to go on a swamp tour. How long does it take a swamp vehicle that travels at 3.2 miles per hour to travel across the swamp, from point Z to point Y ?
Answers
Answer:
5.83
Step-by-step explanation:
searched it up
here’s the correct answer.
Answers
Answer:
Okay
Step-by-step explanation:
Answer:
cool
Step-by-step explanation:
Your local movie theater sent out promotional coupons for a $6 admission price to a new action movie that was just released. Without the coupon, the cost of admission is $10. Two hundred people attended the first screening of the day, and the total box office receipts for that screening were $1500. Choose the answer that best describes this situation.
A. There is no solution to this system of equations. This is an impossible situation.
B. 125 people used the coupon, and 75 paid full price.
C. 100 people used the coupon, and 100 paid full price.
D. 75 people used the coupon, and 125 paid full price
Answers
Answer:
The real answer is b:)
Step-by-step explanation:
what is the value of the x in this equation. 7x = 14
Answers
Answer:
2
Step-by-step explanation:
7x=14
[tex] \frac{7x}{7} = \frac{14}{7} [/tex]
x=2
hope it's helpful ❤❤❤
THANK YOU.
1. A relation is defined as:
A) a set of ordered pairs
B) a set of ordered pairs that have exactly one output for a given input.
C) a set of ordered pairs in which the outputs have a constant rate of change
D) a set of ordered pairs whose graph is a line through the origin
Answers
Answer
A) a set of ordered pairs.
Step-by-step explanation:
What is the value of
h
if
4
h
+
5
=
106
?
Answers
Answer:
25.25
Step-by-step explanation:
4h + 5 = 106
4h = 101 ^ Subtraction property of equality
101 ÷ 4 = 25.25
h = 25.25
Answer:
h = 25.25
Step-by-step explanation:
4h + 5 = 106
Subtract 5 from both sides to isolate the coefficient and variable:
4h = 101
Divide 4 to both sides to isolate the variable:
101 divided by 4 = 25.25
Checking my work:
Since h = 25.25, we would replace that number where h is
4(25.25) + 5 =
4(25.25) = 101
101 + 5 = 106
Therefore, the answer h = 25.25 is true
Find the amount erica owes at the end of 6 years if $60000 is loaned to her at a rate of 4% compounded monthly
Answers
Answer: $76,244.51
Step-by-step explanation:
You need to use the compound interest formula here.
First of all however, you need to convert the terms to monthly figures because the interest is compounded monthly.
4% in months = 4 / 12 = 4/12%
6 years = 6 * 12 = 72 months
Now use the compound interest formula:
= Amount * (1 + rate) ^ number of years
= 60,000 * ( 1 + 4/12%) ⁷²
= $76,244.51
no clue how to answer this
Answers
Answer:
s=4.75
Step-by-step explanation:
Just substitute the given variable values into the original equation
s=10•½+½•-2•½²
s=5+-1•¼
s=5+-¼
s=-4.75
Peter made five less than triple as many cookies as Mark did. Let c represent the number of cookies Mark made. Write an expression to determine the number of cookies Peter made
Answers
Answer: 3c - 5
Step-by-step explanation:
Since c represent the number of cookies that Mark made. We are then informed that Peter made five less than triple as many cookies as Mark. This will be:
= (3 × c) - 5
= 3c - 5
The expression is 3c - 5
Multiply (x+2)(x2−3x +4) I really need the help thanks
Answers
Answer:
x^3 - x^2 - 2x + 9
Step-by-step explanation:
x^3 - 3x^2 + 4x
2x^2 - 6x + 8
x^3 - x^2 - 2x + 9
William's truck consumed 2 gallons of gasoline while travelling a distance of 68 km. He has 1.5 gallons left in the tank. How much farther can his truck go? _______ km
Answers
There are 90 students in the school band. 30% of them are sixth graders, 40% are seventh graders, and the rest are eighth graders. How many band members are 6th graders?
Answers
Answer:
27
Step-by-step explanation:
Answer:
Step-by-step explanation:
if we have 90 students
30% are 6th graders
90*30/100=2700/100=27 students
HELPPPP I WILL GIVEE BRAINLIEST
Choose the inequality that matches the verbal description.
Mary ate no more than 8 cookies.
A) x ≤ 8
B) x ≥ 8
C) x > 8
D) x < 8
Group of answer choices
A
B
C
D
Answers
Answer:
That guy is correct a because its both greater than and equal to 8
How to find the LCM (least common multiple) of two numbers
Answers
5:5,10,15,20,25,30,35,40,45,50,55,60
12:12,24,36,48,60
The lcm of 5 and 12 is 60. Another tip is to multiply the two numbers together so 5x12 is 60 and check to see if there is a smaller number
Step-by-step explanation:
The L.C.M of any numbers can be obtained by using two methods and they are :
Prime Factorization method Division methodThe steps for finding L.C.M of the given numbers by prime factorization method are mentioned below :
First of all , find the prime factors of each numbers.Take out the common prime factors.Also take out the other remaining prime factors.Multiply those all prime factors and obtain L.C.M if there is not any common prime factors , then their L.C.M is the product of the given numbers..The steps for finding L.C.M of the given numbers by division method are mentioned below :
Arrange the given numbers in horizontal position.Thus , arranged numbers should be divided by a prime number. During this process , that prime number should divide any two or more given numbers.Repeat the process till you get prime number as quotient for each number.The product of all prime factors and last quotients is L.C.M( According to me , Prime factorization method is kinda easy )
Example : L.C.M of 20 and 24
[tex] \underline{ \text{USING \: PRIME \: FACTORIZATION \: METHOD}} : [/tex]
20 = 2 × 2 × 5
24 = 2 × 2 × 2 × 3
L.C.M = Common factors × Remaining factors
= 2 × 2 × 5 × 2 × 3
= [tex] \boxed{ \text{120}}[/tex]
Hope I helped ! ツ
Have a wonderful day / night ! ♡
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Can someone please help me with this problem??
Answers
Answer:
no this is impossible friend
It is in the picture THANKS :D
Answers
Answer:
x > -3
Step-by-step explanation:
its an open circle, so the sign is >
and the sign, > is pointing left, so that assures it
Answer:
x>-3
Step-by-step explanation:
