Answer:
564643
Step-by-step explanation:
Answer:
In the real number system, there is no solution to the equation x^2=-1x
2
=−1x, squared, equals, minus, 1. In this lesson, we will study a new number system in which the equation does have a solution.
The backbone of this new number system is the number iii, also known as the imaginary unit.
i^2=-1i
2
=−1i, squared, equals, minus, 1
\sqrt{-1}=i
−1
=isquare root of, minus, 1, end square root, equals, i
By taking multiples of this imaginary unit, we can create infinitely many more new numbers, like 3i3i3, i, i\sqrt{5}i
5
i, square root of, 5, end square root, and -12i−12iminus, 12, i. These are examples of imaginary numbers.
However, we can go even further than that and add real numbers and imaginary numbers, for example 2+7i2+7i2, plus, 7, i and 3-\sqrt{2}i3−
2
i3, minus, square root of, 2, end square root, i. These combinations are called complex numbers.
Defining complex numbers
A complex number is any number that can be written as \greenD{a}+\blueD{b}ia+bistart color #1fab54, a, end color #1fab54, plus, start color #11accd, b, end color #11accd, i, where iii is the imaginary unit and \greenD{a}astart color #1fab54, a, end color #1fab54 and \blueD{b}bstart color #11accd, b, end color #11accd are real numbers.
\begin{array}{ccc} \Large\greenD a&\Large+&\Large \blueD bi \\ \uparrow&&\uparrow\phantom{i} \\ \text{Real}&&\text{Imaginary} \\ \text{part}&&\text{part} \end{array}
a
↑
Real
part
+
bi
↑i
Imaginary
part
\greenD aastart color #1fab54, a, end color #1fab54 is called the \greenD{\text{real}}realstart color #1fab54, start text, r, e, a, l, end text, end color #1fab54 part of the number, and \blueD bbstart color #11accd, b, end color #11accd is called the \blueD{\text{imaginary}}imaginarystart color #11accd, start text, i, m, a, g, i, n, a, r, y, end text, end color #11accd part of the number.
The table below shows examples of complex numbers, with the real and imaginary parts identified. Some people find it easier to identify the real and imaginary parts if the number is written in standard form.
Complex Number Standard Form \greenD a+\blueD b ia+bistart color #1fab54, a, end color #1fab54, plus, start color #11accd, b, end color #11accd, i Description of parts
7i-27i−27, i, minus, 2 \greenD {-2}+\blueD 7i−2+7istart color #1fab54, minus, 2, end color #1fab54, plus, start color #11accd, 7, end color #11accd, i The real part is \greenD{-2}−2start color #1fab54, minus, 2, end color #1fab54 and the imaginary part is \blueD 77start color #11accd, 7, end color #11accd.
4-3i4−3i4, minus, 3, i \greenD 4 + (\blueD{-3})i4+(−3)istart color #1fab54, 4, end color #1fab54, plus, left parenthesis, start color #11accd, minus, 3, end color #11accd, right parenthesis, i The real part is \greenD{4}4start color #1fab54, 4, end color #1fab54 and the imaginary part is \blueD{-3}−3start color #11accd, minus, 3, end color #11accd
9i9i9, i \greenD 0+\blueD9i0+9istart color #1fab54, 0, end color #1fab54, plus, start color #11accd, 9, end color #11accd, i The real part is \greenD{0}0start color #1fab54, 0, end color #1fab54 and the imaginary part is \blueD 99start color #11accd, 9, end color #11accd
-2−2minus, 2 \greenD {-2}+\blueD0i−2+0istart color #1fab54, minus, 2, end color #1fab54, plus, start color #11accd, 0, end color #11accd, i The real part is \greenD{-2}−2start color #1fab54, minus, 2, end color #1fab54 and the imaginary part is \blueD 00start color #11accd, 0, end color #11accd
Step-by-step explanation:
plz brian list and allways happy to help.
Given the function: f (x) = (3 x + 4) minus (2 minus x) Evaluate for f (5). a. 22 b. 15 c. 16 d. 30 Please select the best answer from the choices provided A B C D
Answer:
A.22 is the answer
Step-by-step explanation:
When it says "f(5)", it is basically saying that what is the y-value if the x-value is 5. To find the y-value, we need to substitute 5 in for the variables. I have provided you with the steps.
Blaine's take-home pay is $2,500 each month, and he has created a monthly budget to become more aware of where his money goes. His budget is shown below. Blaine finds that he can join a cheaper gym for $40/month, reduce his spending money to $200, and find a phone and internet package for $175. How much will these choices save him each month?
Answer:
Amount Blaine save = $250
Step-by-step explanation:
Total take home pay = $2,500
Original budget:
Rent + electricity bills = $990
Food/groceries = $525
Gas + insurance = $320
Spending money = $235
Cellphone + Internet = $250
Gym membership = $180
Total = $2,500
New budget:
Rent + electricity bills = $990
Food/groceries = $525
Gas + insurance = $320
Spending money = $200
Cellphone + Internet = $175
Gym membership = $40
Total = $2,250
How much will these choices save him each month?
Amount Blaine save = Total take home - new budget
= $2,500 - $2,250
= $250
Amount Blaine save = $250
Ryan has 10 quarters.
Kelly has exactly seven times as much money as Ryan.
They will combine their money to buy a game.
The game costs $27. How much more money do they need to
save?
Answer:
its b
Step-by-step explanation:
The sum of the measures of angle P and angle Q in 180°. The measure of angle P is (4x + 12)°. The measure of angle Q is (2x - 24)°. What is the value of x?
Answer:
32
Step-by-step explanation:
Given
m<P = 4x+12
m<Q = 2x-24
If the sum of P and Q is 180, then;
4x+ 12 + 2x - 24 = 180
4x+2x+12-24 = 180
6x - 12 = 180
6x = 180+12
6x = 192
x = 192/6
x = 32
Hence the value of x is 32
CODES Use the following information to solve. A bank gives each new customer a 4-digit code number which allows the new customer to create
their own password. The code number is assigned randomly from the digits 1, 3, 5, and 7, and no digit is repeated.
• What is the probability that the code number will start with 371?
a 1/3
b 1/4
с 1/12
d 1/24
=============================================================
Explanation:
There are 4 digits to pick from and 4 slots to fill, so there are 4! = 4*3*2*1 = 24 different codes possible.
If we want the code to start with 371, then that must mean 5 is the only thing left for that fourth slot. In short, there's only one code that starts with 371 and that code is 3715
We have one code we want (3715) out of 24 total, which is why the answer is 1/24 (choice D)
what is the answer to my problem
Sydney buys a new car for $24,000 and finances the car for 5 years at 2.5% interest compounded yearly. She estimates that the value of the car will decrease by 16% each year. If Sydney is able to sell the car on the day of her last car payment for the value she estimated, how much money will she have spent over the 5 years?
Answer:17,117
Step-by-step explanation:
x) sec’A + cosec?A
secA. cosecA
Answer:
(Sin A + Cos A)/Sin A. Cos A
Step-by-step explanation:
As we know
Sec A = 1/Cos A
and Cosec A = 1/Sin A
Given Equation
Sec A + Cosec A
Substituting the given values, we get -
1/cos A + 1/Sin A
(Sin A + Cos A)/Sin A. Cos A
PLEASE HELP ASAP WILL GIVE POINTS AND BRAINLIEST! TY BESTIES! Factor using GCF 20x^2+10x please show work
Answer:
10x(2x+1)
Step-by-step explanation:
20x^2+10x
2*10*x*x + 10 *x
Factor out the common terms
10x(2x+1)
The line passes through the points (0, 2) and (-2, 2) is parallel to the line:
Answer:
Undefined
Step-by-step explanation:
you can't divide by 0
(-2-0)/(2-2)
I need some help plz
Answer:
B : both containers are 50
Step-by-step explanation:
Since water in container 2 is in higher temp, it will transfer some of its heat to container 1 until both the containers reach same temperature. This is the concept of equilibrium that mother nature abides by.
Given k > 3 and
( +
2x+2) dx = 10k
show that k3 – 10k2 + ak + b = 0
where a and bare constants to be found.
Answer:
See Below.
Step-by-step explanation:
We are given that:
[tex]\displaystyle \int_3^k\left(2x+\frac{6}{x^2}\right)\, dx = 10k, k>3[/tex]
And we want to show that:
[tex]k^3-10k^2+ak+b=0[/tex]
Integrate the definite integral:
[tex]\displaystyle x^2-\frac{6}{x}\Big|_{3}^{k}=10k[/tex]
Evaluate:
[tex]\displaystyle \left(k^2-\frac{6}{k}\right)-((9)-(2))\right)=10k[/tex]
Simplify:
[tex]\displaystyle k^2-\frac{6}{k}-7=10k[/tex]
Multiply both sides by k:
[tex]k^3-6-7k=10k^2[/tex]
Rewrite:
[tex]k^3-10k^2-7k-6=0[/tex]
Hence, a = -7 and b = -6.
rite 4 and 5 as a percentage
Answer:
4/5 as a percentage is 80%
if you want to write 4 and 5 as a percentage . . .
You can't do that
Identify the slope of the line
y=-4- 1/6x
Solve the equation below. Show all your steps
5x−8=17
Answer:
x=5
Step-by-step explanation:
Add 8 on both sides first. Then divide both sides by 5 to isolate the variable.
5x-8=17
add 8 to both sides
5x=25
divide by 5 on both sides
x=5
The topic is about secant tangle anges
The secant is the reciprocal of the cosine. It is the ratio of the hypotenuse to the side adjacent to a given angle in a right triangle.
What is the domain of the function
Answer:
third answer is correct
Step-by-step explanation:
find the product.
enter your answer in simplest form.
6x2/3 = _=_
A spinner is divided into 10 equal parts and numbered 1-10. Four of the parts are colored blue, four parts are colored red, and two parts are colored green.
What is the probability of spinning a 6? Write your answer as a decimal.
theres a slight chance of spinning a 6 0.06
The top of a storage container is a hemisphere with a diameter of 28 feet. What is the volume of the storage container? Round your answer to the nearest tenth
Answer:
5749.3 cubic feet
Step-by-step explanation:
The volume of the storage container would be defined by the volume of the shape; a hemisphere
The volume V of a hemisphere is given as
V = 2/3 π r^3
where r is the radius of the hemisphere
Given that the diameter is 28 feet, the radius = 14 feet
hence the volume
= 2/3 * π * 14^3
= 5749.333333
To the nearest tenth
= 5749.3 cubic feet
a cylindrical tinfull of engine oil has a diameter of 12cmand the height of 14cm.the oil is poured into a rectangular tin 16cm long and 11cm wide,what is the depth of the oil in the tin?
Find the volume of the cylinder using the formula v = pixr^2 x height
V= 3.14 x 6^2 x 14 = 1,582.56 cubic cm
Area of of the rectangle = 16 x 11 = 176 square cm
The height will be the volume divided by the area
Height =1582.56/176 = 8.99 cm
The height is 8.99 cm ( round off as needed)
ASAP
-WILL MARK BRIANIST
Answer:
part A: 83-8=75
part B: b represents chocolate bars so the answer would be 75 chocolate bars. good luck with the test and have a nice day!
Step-by-step explanation:
I am in need for help please
Answer:
x = 12
Step-by-step explanation:
Exterior angles thm:
8x - 10 + 5x - 12 = 134
13x - 22 = 134
13x = 134 + 22
13x = 156
x = 12
Write the missing terms (in the given order of missing):
3x-___+ ____+5y = 5x - y
A. 2x and 4y
B. 4y and 5x
C. 6y and 2x
D. 2x and 6y
C. 6y and 2x
_____________________________
3x - 6y + 2x + 5y =
3x + 2x + 5y - 6y =
( 3 + 2 )x + ( 5 - 6 )y =
5x - y
please help with this one
Answer:
1st and 2nd to last
Step-by-step explanation:
Answer:
x< -3 is correct answer...........
What is the answer if you Factor 4x^2-256
Answer:
4(x + 8)(x - 8)
Step-by-step explanation:
We can start by finding the GCF of both terms. We can notice that both terms are divisible by 4, so we can factor it out:
4(x^2 - 64)
Now, we can notice that x^2 - 64 resembles the special product a^2 - b^2 which factors to (a + b)(a - b). In this case, a^2 = x^2 and b^2 = 64.
So,
a = x
b = 8
We can substitute:
(a + b)(a - b)
(x + 8)(x - 8)
We can add the 4 from the beginning in to get:
4(x + 8)(x - 8)
Answer:
x = -8 and 8
Step-by-step explanation:
1st we can factor out a 4 so we get
0 = 4(x^2 - 64)
now can either factor it out some more or just solve for x.
if we factor it out more we get
0 = 4(x + 8)(x - 8)
we got x + 8 and x - 8 because 64 is a perfect root and it was negative. now we solve for x.
x = 8, x = -8
Which could be the missing data item for the given set of data if the median of the complete data set is 15?
11, 23, 12, 18, 11, 10, 19, 15, 19, 21, 13, 17, 24, 14
A: 16
B: 18
C: 20
D: 11
Answer:
A: 16
Step-by-step explanation:
its in between
Can someone help me do this like the equation?!.
Answer:
36$
Step-by-step explanation:
what is the local maximum over the interval [-3, 1.5] for the graphed function?
A) 0
B) 56
C) -11.4
D) 2
Answer:
56
Step-by-step explanation:
It's tempting to use the local maximum at the point (2, 0), but x = 2 is outside the interval given in the question!
Answer:
B) 56
Step-by-step explanation:
Find the missing number to make these fractions equal.
2/8 = ?/4
Answer:
?= 1
Step-by-step explanation:
Answer:
Step-by-step explanation:
let the missing number be x
2/8=x/4(do cross multiplication)
8*x=4*2
8x=8
x=8/8
x=1