Answer:
If Z is a complex number:
Z = a + b*i
where a and b are real numbers, and i is an imaginary number.
Then "a" is the real part.
"b*i" is the imaginary part.
The conjugate of Z is:
Zc = a - b*i
So the sign of the imaginary part changes.
Then:
Sum:
Z + Zc = (a + bi) + (a - bi) = 2*a + 0 = 2*a
and remember that a is a real number, then 2*a is also a real numer.
The correct answer is "A real number".
Difference:
Z - Zc = (a + bi) - (a - bi) = 2b*i
and this is a pure imaginary number, so here the correct answer is: "a pure imaginary number"
Answer: a pure imaginary number
explanation:
The sum of a complex number and its conjugate will always be two times the real part of that complex number.
Z=a+b*i
where a and b are real numbers, and i is an nonexistent number.
Then a is the real part.
"b*i" is the imaginary part.
The connection of Z is:
Zc = a - b*i
So the sign of the imaginary part changes.
Sum:
Z + Zc = (a + bi) + (a - bi) = 2*a + 0 = 2*a
and remember that a is a real number, then 2*a is also a real number.
The correct answer is "A real number".
Difference:
Z - Zc = (a + bi) - (a - bi) = 2b*i
Calculate the median, the range and identify the Q1 and Q3 for the following set: 5, 1, 6, 8, 1, 7, 4, 5, 6, 11, 3, 4, 4, 2, 5, 5 (hint draw a box and whisker plot)
Answer:
Arrange the data in ascending order
1,1,2,3,4,4,4,5,5,5,5,6,6,7,8,11
n=16
position of median = (n+1)/2 = 17/2 = 8.5 th item
8.5 th item is the average of 8 and 9th item
median = (5+5)/2 = 5
Range = largest value - smallest value
= 11 -1 = 10
position of Q1= (n+1)/4 = 17/4 = 4.25 th item
Q1 = 4 + 0.25(5th item - 4th item )
4 + 0.25(4-3)
= 4.25
position of Q3= (n+1)/4 = 3*17/4 = 12.75 th item
Q1 = 12 + 0.75(13th item - 12th item )
12 + 0.75(6-6)
= 12
Step-by-step explanation:
When dividing two numbers with the same base
Answer:
you subtract the exponents
What is the absolute value of 3 2/3
Answer:
-3 2/3
Step-by-step explanation:
If the number is positive and they are asking for the absolute value it's always going to be negative of the number they are asking you for the absolute value of. Same thing if it was a negative 3 2/3 then the absolute value of -3 2/3 would be positive 3 2/3.
I hope this helped! <3
Answer: 3.66..
Step-by-step explanation: absolute value is the value of the number from the number 0 on the number line so, 3 ⅔ in decimals is 3.66... so the answer is 3.66... because that is how much the number is if you are counting from 0.
A freight company using a semi truck has been hired to transport a container with a mass of 64,0000 mg. The truck can carry a maximum load of 5920 kg. Can the truck safely carry the container?
Answer:
Yes, many times over.
Step-by-step explanation:
I'm sure there is a typo in the question.
640,000 mg = 0.64 kg
Find the coordinates of the midpoint of a segment with the endpoints (9.–3) and (5,1).
Answer:
(7,-1)
Step-by-step explanation:
Answer:
(7,-1)
Step-by-step explanation:
Midpoint = [(x1+x2)÷2] , [(y1+y2)÷2]
= [(9+5)÷2] , [(-3+1)÷2]
= (7 ,-1)
Solve for the length of BC
Answer:
BC= 9cm
Step-by-step explanation:
You'll need to use the Pythagorean theorem:a^2 + b^2 = c^2
12^2 + b^2 = 15^2The slanted side of the triangle is always going to be 'c' because it is the longest side of the triangle.
Now simplify: 144 + b^2 = 225I got these numbers because 12^2= 144 and 15^2= 225
Subtract. 225 - 144 = 81Now find the square root of 81. The answer is 9.round 6(2f-4)=31 i need help with this
Answer:
f ≈ 5
Step-by-step explanation:
Step 1: Write equation
6(2f - 4) = 31
Step 2: Solve for f
Distribute 6: 12f - 24 = 31
Add 24 on both sides: 12f = 55
Divide both sides by 12: f = 55/2
Simplify: f = 4.58333
Round: f ≈ 5
Dariaun uses his credit card to buy a $3,000 laptop for college. The credit card
company charges him a simple interest rate of 18%.
How much does he owe the credit card company after six months?
Answer:
$3,270
Step-by-step explanation:
A = P(1 + rt)
First, converting R percent to r a decimal
r = R/100 = 18%/100 = 0.18 per year.
Putting time into years for simplicity,
6 months / 12 months/year = 0.5 years.
Solving our equation:
A = 3000(1 + (0.18 × 0.5)) = 3270
A = $3,270.00
The total amount accrued, principal plus interest, from simple interest on a principal of $3,000.00 at a rate of 18% per year for 0.5 years (6 months) is $3,270.00.
If there are 2.2 pounds in 1 Kilogram, how many pounds are there in x kilograms?
A)2.2x
B)2.2/x
C)x/2.2
D)2.2+c
Answer:
The answer is A
Step-by-step explanation:
If there are 2.2 in 1 kilogram and you are trying to find out how many are in many kilograms then you multiply.
Hopefully this helps you :)
pls mark brainlest ;)
The expression that represents the pound of weight in x kilogram can be written as 2.2x, where x represents the weight in kilograms.
What is Units conversion?Unit conversion is a way of converting some common units into another without changing their real value. for, example, 1 centimetre is equal to 10 mm, though the real measurement is still the same the units and numerical values have been changed.
As it is given that there are 2.2 pounds in 1 Kilogram. Therefore, the expression that represents the pound of weight in x kilogram can be written as 2.2x, where x represents the weight in kilograms.
Learn more about Units conversion:
https://brainly.com/question/4736731
Find an equation of the line that passes through the points (3,-2) and (-7,6).
Answer:
y = -4/5x + 2/5
Step-by-step explanation:
Answer:
y = -0.8x + 0.4 or
y= -4/5x + 2/5
Step-by-step explanation:
what type of angle is <CEB?
Answer:
obtuse angle
Step-by-step explanation:
m(<CEA)=m(<BED)=88 (vertically opposite angles)
So m(<CEB)+m(<AED)=360-(88+88)=182
m(<CEB)=m(<AED)= 182÷2=92
Points F, G and H are collinear. If GH = 16, what is FH?
Answer:
FH = 36 units
Step-by-step explanation:
Points F, G and H are collinear.
Therefore, by joining segments FG and GH we get a segment FH.
FH = FG + GH
By substituting the values of the segments given in the question,
FH = (3x - 1) + (2x + 2)
= 5x + 1
Since, GH = 16
2x + 2 = 16
2x = 14
x = 7
Therefore, FH = (5x + 1)
= 35 + 1
= 36 units
Measure of segment FH = 36 units.
What is the area of this circle?
2cm
Area = [?] cm?
Round your answer to 2 decimal places
Answer:
12.57
Step-by-step explanation:
Not rounded it would be 12.56637
If you are just replacing pi with 3.14. than your answer would be exactly 12.56.
what is 6.257 x 10^-7
Answer:
-62570000
Step-by-step explanation:
6.257× -10000000
-62570000
i’m taking a test
hello
f r eee e e e
poI nT s
my last account got B A N N E D
Answer:
yayz fwee pwoints thwank ywuo
Step-by-step explanation:
A wheel whose radius is 50 centimeters completes 6 radians in 1 seconds. What is the linear speed of a point on the rim of the wheel? Convert your answer to meters per second (m/s).
Answer:
3m/seconds
Step-by-step explanation:
In this problem we are required to solve for linear speed of the rotating wheel
The linear speed =angular speed x raduis
Given data
Radius r= 50cm
Converting from cm to m
50/100= 0.5m
Angular velocity w= 6rad/s
V=wr
V= 6*0.5m
V=3m/s
The linear speed is 3m/seconds
Answer:
get from (4,1) to (2,9) go up 8 and over 2 left (-2) - (4 - 2, 1 + 8), do this again (2 - 2, 9+8) and end up at (0,17) which is the y how do you change 7x+3y=3 into slope intercept form.
jifejrknt ertjerjktner tjertkre terjtklremt rejtlermter terjtlermterl tretkeml
Which fraction is equal a whole number ?
A. 3/6 B.7/8 C.10/4 D.8/4
Answer:
D. 8/4
Step-by-step explanation:
Actually, 8/4 is basically 8 divided by 4, which is 2. And 2 is a whole number not decimal number, so that would be your answer.
The fraction number (8/4) that is equal to the whole number is 2. Then the correct option is D.
What is a fraction number?A fraction number is a number that represents the part of the whole, where the whole can be any number. It is in the form of numerator and denominator.
A. The fraction number is given as
[tex]\dfrac{3}{6}[/tex]
And it can be written as
[tex]\dfrac{1}{2}[/tex]
B. The fraction number is given as
[tex]\dfrac{7}{8}[/tex]
C. The fraction number is given as
[tex]\dfrac{10}{4}[/tex]
And it can be written as
[tex]\dfrac{5}{2}[/tex]
D. The fraction number is given as
[tex]\dfrac{8}{4}[/tex]
And it can be written as 2.
More about the fraction number link is given below.
https://brainly.com/question/78672
Estimate \sqrt(80) the nearest tenth. Then locate \sqrt(80)on a number line.Estimate \sqrt(80) the nearest tenth. Then locate \sqrt(80)on a number line.
Answer:
8.9
Step-by-step explanation:
We know that 81 = 9², so √80 will be slightly less than 9. We can get a pretty good estimate by averaging 9 with 80/9. That result is 8.94, so about 8.9.
The attached graph shows that point on a number line.
How do I solve this problem?
Ms.Samuel has taken a survey of college students and found that 1 out of 7 students are liberal arts majors. If a college has 12,000 students, what is the best estimate of the number of students who are liberal arts majors
Answer:
1714 studentsStep-by-step explanation:
If 1 out of 7 students are liberal arts majors based on Ms. samuel survey, the estimate of the number of students who are liberal arts majors if the total number of student in the college s 12,000 can be gotten using the equality expression.
7 students = 1 liberal art major student
12,000 = x liberal art major students
cross multiply
7*x = 12000*1
7x = 12000
divide both sides by 7
7x/7 = 12000/7
x = 1714.29
x≈ 1714
Hence the best estimate for the number of students who are liberal arts majors is 1714 students.
whats he approximete value of the square root of 8
Answer:
the approximate value of the square root of 8 is 2.828
2a + 6
what is the verbal expression for this is expression
Answer:
The sum of two times a number and six.
or
Two times a number plus six.
Step-by-step explanation:
Step 1: Convert 2a into words
2a = two times a number
Step 2: Convert + 6
+ 6 = the sum of 6 or plus 6
Step 3: Combine to make sentence
The sum of two times a number and six.
Two times a number plus six.
Nicole lives in a home worth $135000. She has a mortgage of $88000. She owes $42000 on her car that is worth $11000. She has a credit card balance of $28000. She also has a checking account with a balance of $900 and $300 in gift cards. What is Nicole's net worth?
Answer:
305,200
Step-by-step explanation:
is anyone elses brainly down
Answer:
may I have brainly??
Step-by-step explanation:
Petra is shopping with 2 of her friends. She buys a note book and six identical pencils. The note book costs the same as 2 of the pencils. Her bill is £16.80. How much does a note book cost?
Answer: £4.20
Each 2 of pencils is £4.20 multiply that by 3 your get 12.60, the notebook is the same price of 2 pencils so that must mean it is £4.20
4.20 x 4 = 16.80
3 £4.2 from the 6 pencils
and 1 £4.2 from the notebook
Hope this helps!
The required cost of a notebook would be an amount of £4.20.
What is the equation?The equation is defined as mathematical assertions that have a minimum of two terms containing variables or numbers that are equal.
Let's assume that n is the cost of a notebook, p is the cost of a pencil, and b is the total bill.
We know that the notebook costs the same as two pencils, so we can write this as an equation:
n = 2 × p
We also know that Petra's bill is £16.80, so we can write this as an equation:
b = n + 6 × p
Substituting the first equation into the second equation, we get:
b = n + 6 × p
b = (2 × p) + 6 × p
b = 8 × p
We can now solve for p by dividing both sides of the equation by 8:
p = b / 8
p = £16.80 / 8
p = £2.10
Since the notebook costs the same as two pencils, we can now solve for n by substituting the value of p into the first equation:
n = 2 × p
n = 2 × £2.10
n = £4.20
Therefore, the cost of a notebook is £4.20.
To learn more about the equations click here:
brainly.com/question/10413253
#SPJ3
What is 3.18 written as a rational?
Answer:
[tex]\frac{318}{100}[/tex]
Step-by-step explanation:
A rational number can be expressed as
[tex]\frac{a}{b}[/tex] ← where a and b are integers
The 8 in 3.18 is in the hundredths position, thus
3.18 = [tex]\frac{318}{100}[/tex] ← as a rational number
The line through (4,-1) and (k,5) is parallel to the line y=-3x+5. FInd the value of k.
Answer:
k = 2
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = - 3x + 5 ← is in slope- intercept form
with slope m = - 3
Parallel lines have equal slopes, thus the 2 points have a slope of - 3
calculate the slope using the slope formula and equate to - 3
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (4, - 1) and (x₂, y₂ ) = (k, 5)
m = [tex]\frac{5+1}{k-4}[/tex] = [tex]\frac{6}{k-4}[/tex] = - 3 ( multiply both sides by (k - 4) )
- 3(k - 4) = 6 ( divide both sides by - 3 )
k - 4 = - 2 ( add 4 to both sides )
k = 2
Enter the equation of the line in slope-intercept form. Slope is -6,and (4,3) is on the line. The equation of the line is
Answer:
Step-by-step explanation:
y - 3 = -6(x - 4)
y - 3 = -6x + 24
y = -6x + 27
100 pts f f(x) = 8.3x + 8.1, solve f(x) = 65.37. Type your answer as a decimal rounded to the nearest tenth.
Answer: x=6.9
Step-by-step explanation:
In the problem, it is stated that y=65.37. All we have to do is plug that into y and solve for x.
65.37= 8.3x + 8.1 [subtract both sides by 8.1]
57.27=8.3x [divide both sides by 8.3]
x=6.9
Now, we know x=6.9.
Answer:
6.9
Step-by-step explanation:
whats the answer for -2x^2-28x-102=0
Answer:
NO REAL SOLUTIONScomplex solutions: x = -7 ± i√2
Step-by-step explanation:
[tex]-2x^2-28x-102=0\\{}\qquad\qquad^{\div(-2)}\qquad\ \ ^{\div(-2)}\\x^2+14+51=0\quad\implies\quad a=1\,,\ b=14\,,\ c=51\\\\\\x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}=\dfrac{-14\pm\sqrt{14^2-4\cdot1\cdot51}}{2\cdot1}=\dfrac{-14\pm\sqrt{196-204}}{2}[/tex]
[tex]x=\dfrac{-14\pm\sqrt{-8}}{2}[/tex] means NO REAL SOLUTIONS (as there is no real √[-8])
However in complex numbers we have:[tex]x=\dfrac{-14\pm\sqrt{-8}}{2}=\dfrac{-14\pm2\sqrt{-2}}{2}=\dfrac{2(-7\pm\sqrt{-2})}{2}=-7\pm\sqrt{-2}\\\\\\x_1=-7+i\sqrt2\ ,\qquad x_2=-7-i\sqrt2[/tex]