Answer:
Step-by-step explanation:
Given the following complex numbers, we are to expressed them in the form of a+bi where a is the real part and b is the imaginary part of the complex number.
1) (2-6i)+(4+2i)
open the parenthesis
= 2-6i+4+2i
collect like terms
= 2+4-6i+2i
= 6-4i
2) (6+5i)(9-2i)
= 6(9)-6(2i)+9(5i)-5i(2i)
= 54-12i+45i-10i²
= 54+33i-10i²
In complex number i² = -1
= 54+33i-10(-1)
= 54+33i+10
= 54+10+33i
= 64+33i
3) For the complex number 2/(3-9i), we will rationalize by multiplying by the conjugate of the denominator i.e 3+9i
= 2/3-9i*3+9i/3+9i
=2(3+9i)/(3-9i)(3+9i)
= 6+18i/9-27i+27i-81i²
= 6+18i/9-81(-1)
= 6+18i/9+81
= 6+18i/90
= 6/90 + 18i/90
= 1/15+1/5 i
4) For (3 − 5i)(7 − 2i)
open the parenthesis
= 3(7)-3(2i)-7(5i)-5i(-2i)
= 21-6i-35i+10i²
= 21-6i-35i+10(-1)
= 21-41i-10
= 11-41i
Simplified form of the given expressions will be,
1). 6 - 4i
2). 64 + 33i
3). [tex]\frac{1}{15}+\frac{1}{5}i[/tex]
4). [tex]\frac{31}{53}-\frac{31}{53}i[/tex]
1). In a complex number (a + bi),
a = Real part of the complex number
bi = Imaginary part
Expression given in the question → (2 - 6i) + (4 + 2i)
Rule to solve the given expression,
"Add real part and imaginary part of two complex numbers separately"
(2 - 6i) + (4 + 2i) = (2 + 4) + (-6i + 2i)
= 6 + (-4i)
= 6 - 4i
Therefore, simplified form of the given expression will be (6 - 4i).
2). Given expression → (6 + 5i)(9 - 2i)
Rule to solve the expression → i² = -1
(6 + 5i)(9 - 2i) = 6(9 - 2i) + 5i(9 - 2i)
= 54 - 12i + 45i - 10i²
= 54 - 12i + 45i + 10 [Since, i² = -1]
= (54 + 10) + (45i - 12i)
= 64 + 33i
Therefore, simplified form of the given expression will be (64 + 33i).
3). Given expression → [tex]\frac{2}{3-9i}[/tex]
Multiply numerator and denominator with the conjugate of (3 - 9i) to convert the expression into (a + bi).
[tex]\frac{2}{3-9i}= \frac{2(3+9i)}{(3-9i)(3+9i)}[/tex]
[tex]=\frac{2(3+9i)}{3^2-(9i)^2}[/tex]
[tex]=\frac{6+18i}{9-81(-1)}[/tex]
[tex]=\frac{6+18i}{9+81}[/tex]
[tex]=\frac{6+18i}{90}[/tex]
[tex]=\frac{6(1+3i)}{90}[/tex]
[tex]=\frac{1}{15}+\frac{1}{5}i[/tex]
Therefore, simplified form of the given expression will be [tex]\frac{1}{15}+\frac{1}{5}i[/tex]
4). Given expression → [tex]\frac{(3-5i)}{(7-2i)}[/tex]
Multiply numerator and denominator with the conjugate of the denominator.
[tex]\frac{(3-5i)}{(7-2i)}=\frac{(3-5i)(7+2i)}{(7-2i)(7+2i)}[/tex]
[tex]=\frac{3(7+2i)-5i(7+2i)}{7^2-(2i)^2}[/tex]
[tex]=\frac{21+4i-35i-10i^2}{49-4(-1)}[/tex]
[tex]=\frac{21-31i+10}{53}[/tex]
[tex]=\frac{31-31i}{53}[/tex]
[tex]=\frac{31}{53}-\frac{31}{53}i[/tex]
Therefore, simplified form of the given expression will be [tex]\frac{31}{53}-\frac{31}{53}i[/tex].
Learn more,
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16x^2-1=0
help algebra 2
Answer:
16x²=1
x²=1/16
x=√(1/16)
x=+- (1/4)
A tortoise and a hare are competing in a 2000-meter race. The arrogant hare decides to let the tortoise have a 510-meter head start. When the start gun is fired the hare begins running at a constant speed of 8 meters per second and the tortoise begins crawling at a constant speed of 6 meters per second. -Let t represent the number of seconds that have elapsed since the start gun was fired. 1) Write an expression in terms of t that represents the hare's distance from the starting line (in meters) 2) Write an expression in terms of t that represents the tortoise's distance from the starting line (in meters) 3) Write an expression in terms of t that represents the number of meters the tortoise is ahead of the hare.
Answer:
1. 8t
2. 510 + 6t
3. 510 - 2t
Step-by-step explanation:
1. Since the hare moves at a speed of 8 metres per second, the distance it moves from the starting line is d = speed × time = 8t
2. Since the rabbit moves at a speed of 6 metres per second, and gets a head start of 510 metres, the distance it moves from the starting line is d = 510 m + speed × time = 510 + 6t
3. The distance the tortoise is ahead of the hare is thus, distance moved by rabbit - distance moved by hare in time, t.
d' = 510 + 6t - 8t
= 510 - 2t
If John has drank three drinks per day how many will he have drank in 3 day's?
Answer:
9 drinks
Step-by-step explanation:
3+3+3=9
Or 3*3=9
Answer:
9
Step-by-step explanation:
What is 8.038×108 in standard form?
Answer:
The answer is: 803,800,000
Step-by-step explanation:
None
It was guessed, and I got it right.
(4 - 7m) - (-n + 2m - 1) pls helppp
Step-by-step explanation:
4 - 7m + n - 2m + 1
5 + 5m + n
i think is complicated
Find the domain of the function.
f(x)=9x+7
Inferential statistics allow you to decide whether a difference between the experimental and the control group is due to:________
a. manipulation; chance
b. manipulation; experimental error
c. sampling error; independent variable
d. independent variable; experimental error
Answer:
Option (A)
Step-by-step explanation:
There are 2 main branches of statistics. They are:
1. Descriptive Statistics
2. Inferential Statistics
Descriptive statistics describes the characteristics of observed subjects or items while Inferential statistics makes inferences, based on given or derived data.
Inferential Statistics allow you to decide whether a difference between the experimental group and control group is due to manipulation or chance.
The Experimental group is the group that an effect is tested on while the Control group is the group that is left untested or uninfluenced. Inferential statistics allow you to decide whether a difference between these 2 groups is due to
- manipulation or interference by any force (which may be the experimenter/researcher)
or
- probability which is chance.
Option a. manipulation; chance
Inferential statistics is a statistical method for estimating the characteristics of a larger population from a small but representative sample. In other words, it enables the researcher to make generalizations about a larger group based on a smaller subset of that group.
Inferential statistics allow you to decide whether a difference between the experimental and the control group is due to a. manipulation; chance
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Find the 10th term of a geometric sequence if a1=5 and the common ratio r=2
Answer:
The 10th term of the GP is 2560.
Step-by-step explanation:
It is given that,
The first term of the GP, a = 5
Common ratio, r = 2
We need to find the 10th term of the GP. The nth term of a GP is given by :
[tex]T_n=ar^{n-1}[/tex]
Put n = 10
[tex]T_{10}=5\times 2^{10-1}\\\\T_{10}=2560[/tex]
So, the 10th term of the GP is 2560.
HURRRRYYYYYYY PLEASE Write the equation of the line that passes through the points (-8,-1) and (5,−7). Put your answer in fully reduced point-slope form, unless it is a vertical or horizontal line.
Answer:
y + 8 = 2x + 2
Step-by-step explanation:
Use the points given to find the slope. Divide the difference in y-values by the difference in x-values.
(-1) - (-7) = 6
5 - (-8) = 3
6/3 = 2
The slope is 2.
Now, pick one of the points to put in point-slope form. It doesn't matter which. You will get the right answer either way. I will use (-1, -8).
y - y₁ = m(x - x₁)
y - (-8) = 2(x - (-1))
y + 8 = 2(x + 1)
y + 8 = 2x + 2
What is the quotient of 8,595 ÷ 24?
a. 334 R 3
b. 334 R 7
c. 358 R 3
d. 358 R 7
help please! and fast.
Answer:
358.125
Step-by-step explanation:
Your welcome!
EVALUATE !!!! ILL GIVE YOU BRAINLIST HAVE TO GET IT RIGHT !!!!
N = 3/4 , x = 8 , y = 6 , m = 3
Answer:
12Step-by-step explanation:
[tex]nxy\div m\\\\n =3/4\\x =8\\y =6\\m=3\\\\\frac{3}{4} \times 8 \times 6 \div 3\\\\\mathrm{Divide\:the\:numbers:}\:6\div \:3=2\\=\frac{3}{4}\times \:8\times \:2\\\\\mathrm{Convert\:element\:to\:fraction}:\quad \:8=\frac{8}{1}\\=2\times \frac{3}{4}\times \frac{8}{1}\\\\\mathrm{Convert\:element\:to\:fraction}:\quad \:2=\frac{2}{1}\\=\frac{3}{4}\times \frac{8}{1}\times \frac{2}{1}\\\\Multiply\:fractions\\=\frac{3\times \:8\times \:2}{4\times \:1\times \:1}\\\\=\frac{48}{4}\\\\Simplify\\=12[/tex]
Answer:
it is 12
Step-by-step explanation:
3/4×8×6÷3=12
I HOPE this help plz mark me as brainliest
15 POINTS FOR CORRECT PERSON!! PLEASE HELP The product (5+ i ) (5-i) is a real number, 26. What are the factors (5+i) and (5-i) called? Imaginary units Complex conjugates Imaginary numbers Or complex numbers?
Answer:
Complex numbers
Step-by-step explanation:
Given
[tex](5 + i)[/tex] and [tex](5 - i)[/tex]
Required
Determine what both factors are called
From the list of given options. option "complex numbers" answer the question correctly
This is because when numbers are written in form [tex]a + bi[/tex] where [tex]b \neq 0[/tex] and [tex]i = \sqrt{-1}[/tex]; such a number are referred to as complex number
Some other examples are:
[tex]-7 + 3i[/tex]
[tex]2 - 7i[/tex]
[tex]4 + i[/tex]
And lots more
What the of x is in 3x+5=12
Answer: 2.333
Step-by-step explanation:
Subtract 5 from both sides of equation
Divide each side of equation by 3
Wayne flips a weighted magic trick coin 100 times. If the coin landed on heads just 19 times out of 100 , how many times is the coin expected to land on tails out of 800 flips? (Hint: the probability that the coin will land on heads is not equal to 0.5 .) A 152 B 648 C 800 D 912
Answer:
152 (Answer A)
Step-by-step explanation:
The experimental probability of obtaining a head is 19/100, or 0.19.
If the coin is flipped 800 times, the expected number of heads will thus be:
0.19(800 flips) = 152 (Answer A)
What is the difference between math content and math skills
Answer
B
Step-by-step explanation:
Took quiz
Write each improper fraction as a mixed number in simplest form -72/27=
drag each statement to show it true,based on the graph.
Answer:
1). Cinnamon costs $7 per one pound
2). Price per pound of the cinnamon equals $[tex]\frac{5.25}{0.75}[/tex].
Step-by-step explanation:
x-values on the graph define the weight of cinnamon and y-values define the price.
Slope of the line drawn from the origin (0, 0) and (0.75, 5.25) will determine the per lb price of the cinnamon.
Slope of a line passing through two points [tex](x_1, y_1)[/tex] and [tex](x_2,y_2)[/tex] will be,
Slope = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
If the points on the given line re (0,0) and (0.75, 5.25),
Slope = [tex]\frac{5.25-0}{0.75-0}[/tex]
= 7
Therefore, two options are the correct options.
1). Cinnamon costs $7 per one pound
2). Price per pound of the cinnamon equals $[tex]\frac{5.25}{0.75}[/tex].
mike, dave and john worked for a total of 56 hours. Dave worked 6 more than 4 times as many hours as mike. John worked 6 less than 3 times as many hours as Mike. How long did Dave work?
Answer:
1. Dave worked for 34 hours.
2. Perimeter of the rectangle is 172 cm.
Step-by-step explanation:
1. Determination of the hours Dave worked.
Let D represent Dave.
Let M represent Mike.
Let J represent John.
Tota time worked by Dave, Mike and John is 56 hours. This can be written as:
D + M + J = 56 ..... (1)
Dave worked 6 more than 4 times as many hours as Mike. This can written as:
D = 6 + 4M .....(2)
John worked 6 less than 3 times as many hours as Mike. This can be written as:
J = 3M – 6 ........ (3)
Substituting the value of F and J into equation 1, we have:
D + M + J = 56
D = 6 + 4M
J = 3M – 6
6 + 4M + M + 3M – 6 = 56
6 – 6 + 4M + M + 3M = 56
8M = 56
Divide both side by 8
M = 56/8
M = 7
Substitute the value of M into equation (2) to obtain the value of D.
D = 6 + 4M
M = 7
D = 6 + 4(7)
D = 6 + 28
D = 34
Therefore, Dave worked for 34 hours .
2. Determination of the perimeter.
Length (L) = 64 cm
Width (W) = 22 cm
Perimeter (P) =?
P = 2(L + W)
P = 2 (64 + 22)
P = 2 (86)
P = 172 cm
Therefore, the perimeter of the rectangle is 172 cm
Drag the fraction that is equivalent to each repeating decimal. Each fraction may be used only once.
Answer:
Step-by-step explanation:
The easiest way to do any of these is to put the fraction into your calculator and see what comes up.
So for 32/9 you get 3.5555555555 which is the same as 3.5 with a bar over it.
7/30 is the same as .23333333333 which is the same as 0.23 with a bar over the three.
5/3 = 1.6666666 which is 1.6 with a bar over the 6
4/9 is 0.4444444 which is the same as 0.4 with a bar over the 4.
What percent of 150 is 33.5?
Answer:
22.33
Step-by-step explanation:
x%(150)=33.5
x/100 x 150=33.5
x/2 x 3=33.5
x=2/3 x 33.5
x=67/3
x=22.33
Answer:
Click at the above pic and the ans will appear.
Hope it helps :)
Six classes of 31,28,27,32,24 and 26 students are to travel on buses that each hold 36 students. How many buses are needed?
Answer:
5 buses
Step-by-step explanation:
You add all the students up to get 168, because that's the total number of students, and divide it by 36. The buses can only carry 36 people, so you will need 4.666 buses, but you can't have 0.666 of a bus, so you will need 5 buses to fit everyone.
Multiply 60 x 0.75. Please help me.
The answer to 60 x 0.75 is 45
Answer:
45
Step-by-step explanation:
Multiply
0.75 x 60
A(-2, 1), B(-4,-1), and C(0, -1) and is
reflected in the line x = 2.
What is the coordinate of C'?
Veronica has been wanting to learn to ice skate for years!
When the Glacier Zone Ice Rink opened, Veronica bought 12
ice-skating lessons during their grand-opening sale. Veronica
paid $305.40 in all. How much did each lesson cost?
Answer:
25.45 per lesson
Step-by-step explanation:
divide $305.40 by 12
Write the equation 9y=12x+0.2 in standard form identify A B C
Answer:
60x-45y=-1
A = 60
B = -45
C =-1
Step-by-step explanation:
[tex]9y=12x+0.2\\Re-write\:0.2\:as\:1/5-12x =-9y+\frac{1}{5} \\\\Multiply\:all \:terms \:by\:-1\\-1(-12x=-9y+1/5)\\\\12x =9y-\frac{1}{5} \\\\Multiply\: through\: by \:5\\5(12x =9y - \frac{1}{5} )\\\\60x = 45y -1\\\\60x-45y =-1[/tex]
TUV = 9x + 1 TUW = 7x-9 WUV 5x-11
Answer:
7
Step-by-step explanation:
9x + 1 = 7x - 9 + 5x - 11
9x + 1 = 12x - 20
9x + 1 - 1 = 12x - 20 - 1
9x = 12x - 21
9x - 12x = 12x - 12x -21
-3x = -21
-3x/3 = -21/-3
x = 7
Hope that helps!
Find an equation of the plane.
The plane through the point (1, -1, - 1 ) and parallel to the plane 5x - y - z = 6
Answer: equation of the plane is 5x - y - z - 7 = 0
same as ( 5x - y - z = 7 )
Step-by-step explanation:
Given data;
5x - y - z = 6
therefore vector of plane is n° = ( 5, -1, -1)
so equation will be
n°(x-x₀, y-y₀, z-z₀) = 0
( 5, -1, -1) (x-x₀, y-y₀, z-z₀) = 0
5(x- (1)) -1(y - (-1)) -1(z - (-1)) = 0
5x - 5 - y - 1 - z - 1 = 0
5x - y - z - 7 = 0
Therefore equation of the plane is 5x - y - z - 7 = 0
same as ( 5x - y - z = 7 )
Alisa types 900 words in 20 minutes. What is her typing speed words per minute?
Answer:
45 words per minute!
Step-by-step explanation:
Divide 900 by 20!
Answer:
Her typing speed is 45 word per minute
Step-by-step explanation:
20x = 900
divided 20 on both sides
x = 45
what five parts make up a data table
Answer:
Step-by-step explanation:
Check boxes.
Sorting (on columns)
Icons that communicate alerts.
Pagination.
Headers Row.
4(z – 2) + 3z
Need help
Answer:
5z-8
Step-by-step explanation:
(8z-8)+3z=
5z-8
Answer:
z-8
Step-by-step explanation:
4(z -2)+3z
4z -8 +3z
-3 -3
z -8