By applying knowledge on complex analysis, the complex numbers that satisfy the three conditions defined in the statement are z₁ = 4 - i 3 and z₂ = 5 + i 12.
How to determine two complex numbers based on their norms and a given operation
In this question we must derive two complex numbers such that the following conditions are fulfilled:
a² + b² = 5² (1)
c² + d² = 13² (2)
13 · (a + i b) - 5 · (c + i d) = 27 - i 99 (3)
If we assume that a, b, c, d are integers, then we can suppose that (a, b) = (4, -3) and (c, d) = (5, 12) and we check if these values satisfy (3):
13 · (4 - i 3) - 5 · (5 + i 12)
52 - i 39 - 25 - i 60
27 - i 99
By applying knowledge on complex analysis, the complex numbers that satisfy the three conditions defined in the statement are z₁ = 4 - i 3 and z₂ = 5 + i 12.
To learn more on complex numbers: https://brainly.com/question/10251853
#SPJ1
If f(x) = x² - 2x, find:
f(5) = [?]
Answer:
[tex]15[/tex]
Step-by-step explanation:
if [tex]f(x) = x^2 -2x[/tex], then that means that [tex]f(5) = (5)^2 - 2(5)[/tex] which equals [tex]15[/tex].
Step-by-step explanation:
A function f is defined by f (x) = 2x - 5. Write down the values of In mathematics, a function means a correspondence from one value x of the first set to another value y of the second set. NCERT Solutions Class 11 Math's Chapter 2 Exercise 2.3 Question 3 A function f is defined by f (x) = 2x - 5.
Which associations best describe the scatter plot?
Select each correct answer.
Positive association
Negative association
Linear association
Nonlinear association
♡♡♡ ▲ ▲ ▲ ▲ Ratio of hearts to triangles in simplest form.
3 hearts
4 triangle
H:T
3:4
So, ratio of hearts to triangles in simplest form is 3:4
(we can't simplify any further - HCF of 3 & 4 is 1)
Hope this helps!
A country has two political parties, the Reds and the Blues. The 100-member senate has 44 Reds and 56 Blues. How many ways are there to pick a 10 member committee of senators with the same number of Reds as Blues
There are 4.15E12 ways to select the members of the committee to have the same number of Reds as Blues
How to determine the number of ways?The given parameters are:
Reds = 44
Blues = 56
Committee member = 10
To have the same number of Reds as Blues, the committee must have 5 reds and 5 blues.
So, the number of ways is;
Ways = 44C5 * 56C5
Evaluate the combination expressions:
Ways = 1.086008 E+6 * 3.819816 E+6
Evaluate the product
Ways = 4.15E12
Hence, there are 4.15E12 ways to select the members of the committee
Read more about combination at:
https://brainly.com/question/11732255
#SPJ4
You and your family are going on a
family cruise this summer! WOO HOO!
Your parents had to put down a $250
deposit. Then, the cruise costs $500
per person on top of that. There are 5
people in your family. How much will
the entire cruise cost? Okay
What is f(x) + f(x) + f(x)?
✔ 3f(x)
3f(x) =
✔ 3x²
Evaluate 3f(2) =
.
Answer:
12
Step-by-step explanation:
The problem statement tells us the definition of 3f(x). In order to find the value of 3f(2), we substitute 2 for x and do the arithmetic.
__
definition3f(x) = 3x² . . . . given
application3f(2) = 3·2² = 3·4 = 12 . . . . . substitute 2 for x
The value of 3f(2) is 12.
find the value of x in (2^2x)^3 = 64
Answer: x=12
Step-by-step explanation:
Answer:
x=1
Step-by-step explanation:
The equation can be simplified and solved using the rules of exponents and the usual inverse operations.
__
Interpreted according to the Order of Operations, your equation is ...
((2^2)x)^3 = 64
(4x)^3 = 64x^3 = 64 . . . . . . use (ab)^c = (a^c)(b^c)
x^3 = 1 . . . . . . . . . . . . . . divide by 64
x = ∛1 = 1
__
Perhaps you want x in the exponent:
(2^(2x))^3 = 64
2^(6x) = 2^6 . . . . . . . . . use (a^b)^c = a^(bc)
6x = 6 . . . . . . . . match exponents
x = 1 . . . . . . divide by 6
_____
Additional comment
Folks are often not careful about identifying exponents. It is helpful if you write the exponent in a way that leaves no ambiguity.
a rectangle mural measure 234 inches by 245 inches, rihanna created a mural 33 inches longer
Rhiannna needs 1024 inches longer bedspread if Rhiannna gets a new bedspread that is 33 in length.
What is a rectangle?It is defined as the two-dimensional geometry in which the angle between the adjacent sides are 90 degrees. It is a type of quadrilateral.
The question is incomplete.
The complete question is:
Rhiannna has a rectangular bedspread that measures 234 in. By 245 in. She wants to sew a fringe around the edge of the bedspread. What length of fringe does Rhiannna need to purchase. Rhiannna gets a new bedspread that is 33 in length. What length of the fringe does Rhiannna need for the longer bedspread?
We know perimeter of the rectangle = 2(length + width)
= 2(234 + 245 )
= 958 inches
Rihannon gets a new bedspread that is 33 in length:
New perimeter = 2(33) + 958 = 1024 inches
Thus, Rhiannna needs 1024 inches longer bedspread if Rhiannna gets a new bedspread that is 33 in length.
Learn more about the rectangle here:
https://brainly.com/question/15019502
#SPJ1
Given f(x) = x^4. if the function is transformed so that the inflection point is
(-2, 1). write the new function.
-34 + 2x divided by -8
Answer:
-34+x/4
Step-by-step explanation:
Answer:
x=17
Step-by-step explanation:
Since you did not specify, we will assume that your equation is equal to 0.
1. (-34+2x)/(-8) = 0 (multiply both sides by -8)
2. (-34+2x) = 0 (add 34 to both sides)
3. 2x = 34 (divide both sides by 2)
4. x = 17
(3x-2)(3x-2)(3x-2)(2x+1)
can anyone answer this pls!!!!!!!!!!
u₁₂ represents the amount of loan remaining after 12 years
How to interpret u₁₂?The function is given as:
u₀ = 8000
[tex]u_n = u_{n-1}(1 + 0.054) - 500[/tex]
Given that the subscript n in [tex]u_n[/tex] represents number of years and [tex]u_n[/tex] represents the amount left to be paid after n years.
We can conclude that:
u₁₂ represents the amount of loan remaining after 12 years
Read more about loan at
https://brainly.com/question/26011426
#SPJ1
Someone please help fast!
Simplify: in the picture
Answer:
-3ab
Step-by-step explanation:
-27/9= 3
(a^2)/a=a
(b^2)/b=b
What is the quotient if 4/15 of 40 is divided by 1/2 of 1/8?
Answer:
l
Step-by-step explanation:
LL
F
C
9
5
D
2x+3
E
What is the value of x and the length of segment DE?
1 5
9
9
2x + 3
2. 10x+15=9(9)
Length of DE=
units
Answer:
[tex]x=\boxed{6.6}[/tex]
[tex]\overline{\sf DE}=\boxed{13.2}\:\:\sf units[/tex]
Step-by-step explanation:
Geometric Mean Theorem - Altitude Rule
The altitude drawn from the vertex of the right angle perpendicular to the hypotenuse separates the hypotenuse into two segments. The ratio of one segment to the altitude is equal to the ratio of the altitude to the other segment:
[tex]\sf \dfrac{segment\:1}{altitude}=\dfrac{altitude}{segment\:2}[/tex]
From inspection of the given diagram:
altitude = FD = 9segment 1 = CD = 5segment 2 = DE = [tex]2x+3[/tex][tex]\begin{aligned}\sf \dfrac{segment\:1}{altitude} & = \sf \dfrac{altitude}{segment\:2}\\\\\implies \dfrac{5}{9} & = \dfrac{9}{2x+3}\\\\5(2x+3) & = 81\\\\10x+15 & = 81\\\\10x & = 66\\\\ \implies x & = 6.6\end{aligned}[/tex]
Substitute the found value of x into the expression for DE:
[tex]\begin{aligned}\sf \overline{DE} & = 2x+3\\\implies \sf \overline{DE} & = 2(6.6)+3\\& = 13.2+3\\& =16.2\:\: \sf units\end{aligned}[/tex]
What is the inverse of function f? A) B) C) D)
Plato
Answer:
(7x-3)/-1
Step-by-step explanation:
swap the x and y and then move the y by itself
x=(3-y)/7
7x=3-y
7x-3=-y
(7x-3)/-1=y
A table of values shown below represents a linear function which of these points could also be an ordered pair in the table and why?
Answer:
(18,27) , because the rate of change of the function is 4/3
Step-by-step explanation:
our cell phone costs $50 a month plus $0.25 for each text message, t. How much would your monthly bill be if you sent 40 text messages? our cell phone costs $50 a month plus $0.25 for each text message, t. How much would your monthly bill be if you sent 40 text messages? our cell phone costs $50 a month plus $0.25 for each text message, t. How much would your monthly bill be if you sent 40 text messages? our cell phone costs $50 a month plus $0.25 for each text message, t. How much would your monthly bill be if you sent 40 text messages? our cell phone costs $50 a month plus $0.25 for each text message, t. How much would your monthly bill be if you sent 40 text messages? our cell phone costs $50 a month plus $0.25 for each text message, t. How much would your monthly bill be if you sent 40 text messages? our cell phone costs $50 a month plus $0.25 for each text message, t. How much would your monthly bill be if you sent 40 text messages?
Answer:
$60
Step-by-step explanation:
cost = $50 + $0.25x
Since x = 40
$(50 + 10) = $60
Answer:
$60/month
Step-by-step explanation:
So the equation would be 50 + (0.25 * 40), solve parenthesis 50 + 10, so answer would be $60.
Without using the formula, work out the gradient of the graph shown.
Answer:
1/3
Step-by-step explanation:
What is the answer (6√2)(-3√5)
Solution:
[tex] - 18 \sqrt{10} [/tex]
Step-by-step explanation:1. Apply rule : a(-b) = -ab
[tex] = - 6 \sqrt{2} \: \: • \: \: 3 \sqrt{5} [/tex]
2. Apply radical rule : [tex] \sqrt{a} \sqrt{b} = \sqrt{ab} [/tex] , [tex]a \geqslant 0[/tex], [tex]b[/tex]
[tex] = 6 \sqrt{2 \: • \: 5} \: • \: 3[/tex]
3.Multiply the numbers : 2 • 5 = 10=[tex]6 \sqrt{10} •3[/tex]
4.Multiply the numbers : - 6 • 3= - 18[tex] = - 18 \sqrt{10} [/tex]
Are the equations 4-5x=24 and 5x=20 equivalent?
Answer:
not equivalent
Step-by-step explanation:
solve for x
4-5x=24
-5x=20
x = - 4
5x=20
x = 4
no they are not equivalent
if you do 12 minutes of a 45 minute workout how many calories is it? (the 45 minutes is 1000 calories in total)
help!
Answer:
266[tex]\frac{2}{3}[/tex]
Step-by-step explanation:
if a 45 minute workout is 1000 calories, at the same rate, a 12 minute workout would be 266 calories and 2 thirds. [tex]\frac{12}{45}[/tex] x 1000 = 266[tex]\frac{2}{3}[/tex]
Solve system of equation using elimination by addition.
Will give brainliest!!
Answer:
x = -8
y = 0
Step-by-step explanation:
The two shown equations can be added together:
x + 4y = -8
+ ( x - 4y = -8 )
The two x's would combine to make two x, the 4y and -4y cancel out to zero, and -8 added to -8 is -16:
2x = -16
Therefore, x = -8. We can plug this into the first equation to get:
-8 + 4y = -8
Subtracting 8 on both sides yields:
4y = 0
Now divide by 4 on both sides to get
y = 0
We can check these values by plugging them into the second equation:
(-8) - 4(0) = -8
-8 - 0 = -8
-8 = -8
Since -8 always equals -8, the answer is correct.
You used $3000 of your budget for training your employees. each hour of training costs $40 per employee plus a one-time $200 fee. a. how many hours of training can your purchase? b. how many hours of training will each of your employees receive? remember how many employees do you have?
A. The number of hours of training that you can purchase with a $3,000 training budget at $40 per employee per hour and a one-time $200 fee is 70-employee-training-hours.
B. Each employee will get 7 hours of training, assuming your organization has 10 employees.
What is the cost of training employees?The training cost of employees varies from one organization to another.
The training cost also depends on the training provider and the number of hours of training being offered.
Data and Calculations:Training budget = $3,000
One-time fee = $200
Remainder after the one-time fee = $2,800 ($3,000 - $200)
Training costs per employer per hour = $40
Hours of training to purchase = 70 ($2,800/$40)
Thus, an organization with 10 employees can obtain 70 hours of training with the training budget.
Learn more about training needs and costs at https://brainly.com/question/26821802
#SPJ1
Consider 8x-4 = 8^10
n triangle ABC (see sketch), AD is the angle bisector of the angle A and BH is the height from side AC. The obtuse angle between BH and AD is four times the side of DAB. How big is the angle CAB?
A. 30 B.45 C.60 D.75 E.90
Answer: C
Step-by-step explanation:
We know that [tex]\angle AHB=90^{\circ}[/tex], and thus by the exterior angle theorem,
[tex]90^{\circ}+\alpha=4\alpha\\\\90=3\alpha\\\\\alpha=30^{\circ}[/tex]
Thus, [tex]\angle CAB=2\theta=\boxed{60^{\circ}}[/tex]
400 people were asked if they liked their school lunch.10% said yes. 32 of those that said yes were boys.152 of those that were surveyed were girls. Complete the table to display this data. How many boys said no to liking their school lunch?
Using proportions, considering the total number of students, it is found that 216 boys to linking their school lunch.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
In this problem, 400 - 152 = 248 boys were surveyed. 32 said they liked the school lunch and 248 - 32 = 216 said no liking their school lunch.
More can be learned about proportions at https://brainly.com/question/14398287
#SPJ1
Kian borrowed £1900 at a simple interest rate of 8% per year.
After a certain number of years, he owes a total of £2812 on this loan.
How many years have passed since he took out the loan?
[tex]~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \pounds 2812\\ P=\textit{original amount deposited}\dotfill & \$1900\\ r=rate\to 8\%\to \frac{8}{100}\dotfill &0.08\\ t=years \end{cases} \\\\\\ 2812=1900[1+(0.08)(t)]\implies \cfrac{2812}{1900}=1+0.08t\implies \cfrac{37}{25}=1+0.08t \\\\\\ \cfrac{37}{25}-1=0.08t\implies \cfrac{12}{25}=0.08t\implies \cfrac{ ~~ \frac{12}{25} ~~ }{0.08}=t\implies 6=t[/tex]
You have one cubic mile of water. you release it at 1000 gallons per
minute. how long will it take to empty??
It will take 764664.6875 days to empty the water
How to determine the time to empty?The given parameters are:
Volume = 1 cubic mileRate = 1000 gallons per minutesThe time is calculated as:
Time = Volume/Rate
So, we have:
Time = 1 cubic mile ÷ 1000 gallons per minute
Convert gallons to cubic mile
Time = 1 cubic mile ÷ (9.0817e-13 * 1000) cubic mile per minute
Divide
Time = 1.10111715 × 10^9 minute
Convert to days
Time = 764664.6875 days
Hence, it will take 764664.6875 days to empty the water
Read more about volumes at:
https://brainly.com/question/1972490
#SPJ1
Work out the value of 2⁰
Answer:
1
Key:
[tex]a^0=1,\:\quad \:a\ne \:0[/tex]Step-by-step explanation:
[tex]2^0=1[/tex]