The graph which correctly shows the point A as the sum of the complex numbers z₁ and z₂ is graph number 4.
What is complex number?A complex number is the combination of real and imaginary number. In a complex number, real part and imaginary part of the number are written together. For example,
a+bi
Here, (a) is the real part while (b) is the imaginary part.
To add the two complex number on the graph, the addition as transition method is used.
In this one complex number is translated to the tip of the other graph. The resultant of addition is equal to the distance between them.
On the graph 4, the transition method of addition is applied.Thus, the graph which correctly shows the point A as the sum of the complex numbers z₁ and z₂ is graph number 4.
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Find the domain of the inverse
The domain of the inverse of the function f(x) = 5e^x + 3 is found being all real numbers > 3. Or, we can write this symbolically as: D( f^(-1)(x)) = (3,∞)
What is domain and range of a function?Domain is the set of values for which the given function is defined.
Range is the set of all values which the given function can output.
What is inverse of a function?Suppose that the given function is
[tex]f:X\rightarrow Y[/tex]
Then, if function 'f' is one-to-one and onto function (a needed condition for inverses to exist), then, the inverse of the considered function is
[tex]f^{-1}: Y \rightarrow X[/tex]
such that:
[tex]\forall \: x \in X : f(x) \in Y, \exists \: y \in Y : f^{-1}(y) \in X[/tex]
(and vice versa).
It simply means, inverse of 'f' is undo operator, that takes back the effect of 'f'
The domain of the inverse of a function (if it exists) is the range of the function it is inverse of. Similarly range of the inverse of that considered function is the domain of that considered function.
The function given is:
[tex]f(x) = 5e^x + 3[/tex]
The domain of the inverse of this function is this function's range.
Assuming only real values are allowed, for any real number x, we have:
[tex]e^x > 0[/tex]
And therefore, we get:
[tex]5e^x > 0 \: \forall x \in \mathbb R\\5e^x + 3 > 3 \: \forall x \in \mathbb R\\[/tex]
Also, since the function [tex]f(x) = 5e^x + 3[/tex] is strictly monotonically increasing and continuous, it touches all the values as its output from any real number > 3 till any finitely large number.
Thus, its range is (3, ∞) (it is an interval consisting of all the real numbers > 3)
This is the domain of its inverse function.
Thus, the domain of the inverse of the function f(x) = 5e^x + 3 is found being set of all real numbers > 3. Or, we can write this symbolically as: D( f^(-1)(x)) = (3,∞)
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PLEASE I REALLY NEED HELP FAST
A batch of 5500 computers is produced by a company. Four random samples of 35 computers per sample are
tested. The numbers of defective computers found in the fou samples are shown in the table.
Sample of 35
Computers
Number of
Defective
Computers
А
1
B
3
с
1
D
2.
Based on these results, how many defective computers should be expected in the entire batch of 5500 computers?
It's around 1 to 3
So
From 35 it's 1,2,3
From 5500 samples of 35
5500/35≈157Now
If 1 comes from each
157(1)=157 detectsIf 2
157(2)314detectsIf 3
157(3)471 detectsLast year direct marketing had $122,222 in sales. This year direct marketing's sales are down by 9%. What are direct marketings sales this year
Answer:
$111222.02
Step-by-step explanation:
This year = Last year * (100%-9%)
This year = 122222 * 91% = 111222.02
The first rule is to add 10, then divide by 2 starting from 2. The second rule is to multiply by 3, then subtract 2 starting from 2. What are the first four ordered pairs using the two sequences?
Answer: [tex](2, 2), (6, 4), (8, 10), (9, 28)[/tex]
Step-by-step explanation:
The first four ordered pairs using the two sequences are:[tex](2, 2), (6, 4), (8, 10), (9, 28)[/tex]
The first rule is to add 10, then divide by 2 starting from 2
Add/Divide:
[tex]10=2+10=12[/tex]
[tex]2=12[/tex]÷[tex]2=6[/tex]
Add/divide again:
[tex]10=6+10=16[/tex]
[tex]2 = 20[/tex]÷[tex]2 = 10[/tex] [tex]2=16[/tex]÷[tex]2=8[/tex]
Add/divide again:
[tex]10=8+10=18[/tex]
[tex]2=18[/tex]÷[tex]2=9[/tex]
Which number added to -1 gives the sum of 0?
Answer:
+1
Step-by-step explanation:
Positive 1
I WILL GIVE 20 POINTS TO THOSE WHO ANSWER THIS QUESTION RIGHT NOOOO SCAMS AND EXPLAIN WHY THAT IS THE ANSWER
Use natural logarithms to solve the equation. Round to the nearest thousandth.
7e3x − 4 = 14
Answer:
0.315 to nearest thousandth.
Step-by-step explanation:
7e^3x − 4 = 14
7e3x = 18
e^3x = 18/7
3x = ln(18/7)
x = ln(18/7) / 3
= 0.31482.
Find the range of the given numbers. {41 , 43 , 52 , 25 , 96 , 19 , 72}
Answer: 77
Step-by-step explanation:
[tex]$$Find the range of the list:$$(41,43,52,25,96,19,72)$$The range of a list is given by:(largest element) - (smallest element) \\$(41,43,52,25,\bold{96},19,72)$ We see that the largest element is $96:$ $-(($ smallest element $))+96$\\$(41,43,52,25,96,\bold{19},72)$ We see that the smallest element is $19:$ $96-19$\\$$96-19=77$$Therefore, the range of the set is 77[/tex]
Karen is applying for the nursing school at the University of Davis. Before applying, she received a breakdown of the tuition and fees from the university.
Tuition: $676 per semester plus $200 per class
Books: $86 per class
Nursing School Fee: $19 per class
Parking: $66 per semester
Facilities Fee: $54 per semester
The total cost of a semester for c classes is represented by the following expression. $305c + $796
Which statement best describes the coefficient of c?
A.
It is the sum of the cost of books and the nursing school fee.
B.
It is the total semester cost of c classes at the university.
C.
It is the sum of the additional cost of tuition, books, and nursing school fee.
D.
It is the sum of the tuition, parking, and facilities fee.
Answer:
A
Step-by-step explanation:
Step-by-step explanation:
Does anyone know the correct answer?
Step-by-step explanation:
using indices..
(7.2x 10³)/(1.2x10^5)
7.2/1.2 = 6
10³/10^5 = 10-²
answer = 6x 10-2
(c)
write an explicit formula for An, the nth term of the sequence 40,33,26,…
Answer:
an = 40 -7(n -1)
Step-by-step explanation:
The given sequence has terms with a common difference, so it is an arithmetic sequence. The formula for the general term of an arithmetic sequence applies:
an = a1 +d(n -1)
__
The first term of the given sequence is ...
a1 = 40
The common difference for this sequence is ...
d = 33 -40 = -7
Using these values in the equation for the n-th term, we have ...
an = 40 -7(n -1) . . . . . explicit formula for the n-th term
Find the value of x.
Answer:
x = 27
Step-by-step explanation:
because the angles are on a line that means they add up to 180
18 + x + 5x = 180
then combine like terms
18 + 6x = 180
then you subtract 18 from both sides
6x = 162
lastly divide both sides by 6
x = 27
Angie mixes 7 2/3 pints fruit juice and 3 1/4 pint sprite to make punch far a party. she has 6 pints left at the end of the party. How much punch did Angie serve at the party?
Answer:
16 11/12
Step-by-step explanation:
7 2/3 + 3 1/4 =
7 8/12 + 3 3/12 =
10 11/12 + 6
16 11/12
What is the median of the data set below?
59, 76, 18, 5, 2, 10, 8, 14, 18, 14, 8, 2
O 10
O 12
O 8
O 19.5
Angelica uses the point to represent the location of her house and uses the point to represent the location of a gas station. Each unit on the graph represents 1 mi. How far is the gas station from Angelica’s house? Show your work.
Answer:
Distance for leg a? _____________________
Distance for leg b?______________________
Fill in the distances below and use the formula to solve for c. a^2+b^2=c^2
C=____________________________
Will give brainliest if you answer all questions with work shown!
I am going to assume that leg a:
⇒ is the horizontal distance between the house and the gas station
⇒ Distance for leg a: 6 miles
I am also going to assume that leg b
⇒ is the vertical distance between the house and gas station
⇒ Distance for leg b: 5 miles
Thus using the Pythagorean theorem: [tex]a^2+b^2=c^2[/tex]
⇒ (look at diagram attached for further explanation)
[tex]a^2+b^2=c^2\\\\6^2+5^2=c^2\\c=\sqrt{6^2+5^2} \\c=\sqrt{61} =7.81[/tex]
Answer: 7.81
Hope that helps!
A cylinder, cone, and sphere all have the same radius of 5 cm. The cone and cylinder have the
same height of 6 cm.
Find the volume of each shape. Show your work or explain your work.
Which shape would hold them most?
The volume of the cylinder is 471.43 cm³.
The volume of the cone is 157.14 cm³.
The volume of the sphere is 523.81 cm³.
The shape that would hold the most volume is the sphere.
What is the volume of a cylinder?A cylinder is a three-dimensional object. It is a prism with a circular base.
Volume of a cylinder = πr²h
Where:
π = 22/7
r = radius
22/7 x 5² x 6 = 471.43 cm³
What is the volume of a cone?Volume of a cone = 1/3 x volume of a cylinder
1/3 x 471.43 cm³ = 157.14 cm³
What is the volume of a sphere?
Volume of a sphere = 4/3 x pi x r³
4/3 x 5³ x 22/7 = 523.81 cm³
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please answer this question
Answer:
-ln(| x - 1 |) + -ln(| x - 2 |) + C
Step-by-step explanation:
[tex]\displaystyle \int \dfrac{1}{x^2 -3x +2} dx\\\\\\=\displaystyle \int \dfrac{dx}{x^2 -3\cdot \dfrac 32 \cdot x + \left(\dfrac 32 \right)^2 -\left( \dfrac 32 \right)^2 +2}\\\\\\=\displaystyle \int \dfrac{dx}{\left(x- \dfrac 32 \right)^2 +2- \dfrac 94}\\\\\\=\displaystyle \int \dfrac{dx}{\left(x - \dfrac 32 \right)^2-\dfrac 14 }\\\\\\=\displaystyle \int \dfrac{du}{u^2-\left( \dfrac 12 \right)^2} ~~~~~~~~~~~~~~~~~~;\left[u = x - \dfrac32\implies du= dx\right]\\[/tex]
[tex]=\dfrac{1}{2\cdot\tfrac 12} \ln \left| \dfrac{u-\dfrac 12 }{u+\dfrac 12 } \right|+C~~~~~~~~~~:\left[ \displaystyle \int \dfrac {dx}{x^2 -a^2} = \dfrac 1{2a} \ln \left| \dfrac{x-a}{x+a} \right| +C\right]\\\\\\=\ln\left|\dfrac{x- \dfrac 32 - \dfrac 12}{x-\dfrac3 2 + \dfrac 12 } \right|+C~~~~~~~~~~~~;\left[\text{Substitute back}~u =x- \dfrac 32 \right]\\\\\\=\ln\left|\dfrac{x-2}{x-1} \right|+C[/tex]
The circumference of a circle is 25 units. What is the area of the circle in terms of pie?
Answer:
49.7359 units²
Step-by-step explanation:
Area = πr²
Circumference = 2πr
2πr = 25
πr = 12.5
r = 12.5 / π = 3.97887
π(3.97887)² = 49.7359 units²
Hope this helps
Find the surface area of the barn, brainiest will be given (urgent)
The surface area of the barn is 2040 square feet.
What is a rectangle?A rectangle is a plane shape with four sides and four right angles.
Analysis:
The barn is composed of:
Two straight long rectangles with dimensions = 10ft x 40ft
Two slant rectangles with dimensions = 10.6ft x 40ft
Two short rectangles with dimensions = 10ft x 14ft
Two triangles, height 8ft and base 14feet
The surface area of barn = 2(10x40) + 2(10.6 x 40) + 2(1/2 x 14 x 8) + 2(10 x 40) = 800 + 848 + 112 + 280 = 2040 square feet
In conclusion, the surface area of the barn is 2040 square feet.
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During the editing step, what function helps spot errors in your writing and helps you to fix them?
A. Spell check
B. Internet
C. Dictionary
D. Thesaurus
Answer:
The answer is A: Spell check
A group of friends wants to go to the amusement park. They have $318.50 to spend on parking and admission. Parking is $17, and tickets cost $33.50 per person, including tax. How many people can go to the amusement park?
Answer:
9 people
Step-by-step explanation:
The amount spent on tickets
318.5 - 17 = 301.5
If 301.5 was for tickets alone, the number of tickets can buy
301.5/33.5 = 9
Now
our equation is
y=33.5x+17No of persons=x
318.5=33.5x+1733.5x=301.5x=9peopleSolve for x.
2/x^2−4 − 1/x+2=3/x−2
−32
−12
23
2
Answer:
x = -1/2.
Step-by-step explanation:
x^2 - 4 = (x - 2)(x + 2) so if we multiply each term by x^2 -4 we get:
2 - 1(x - 2) = 3(x + 2)
2 - x + 2 = 3x + 6
2 + 2 - 6 = 3x + x
4x = -2
x = -1/2.
Answer:
[tex]-\frac{1}{2}[/tex]
Step-by-step explanation:
1. Multiply both sides of the equation by the LCM (x - 2)(x + 2):
[tex]\frac{2}{x^{2} -4} (x-2)(x+2)[/tex]
factor x² - 4 by rewriting it as x² - 2²
x² - 2² = (x + 2)(x - 2)
now we have;
[tex]\frac{2}{(x+2)(x-2)} (x-2)(x+2)[/tex]
cancel the common factors (x - 2)(x + 2)
= 2
-------------------------------
[tex]\frac{-1}{x+2} (x-2)(x+2)[/tex]
cross cancel the common factor (x + 2)
[tex]\frac{-1}{x-2}=-(x-2)=-x+2[/tex]
-------------------------------
[tex]\frac{3}{x-2} (x-2)(x+2)[/tex]
cross cancel the common factor (x - 2)
3(x + 2)
distribute the 3
3x + 6
-------------------------------
combining all new values, we have;
2 + (-x) + 2 = 3x + 6
-x + 4 = 3x + 6
2. Isolate x:
-x + 4-4 = 3x + 6-4
-x = 3x + 2
-x-3x = 3x-3x + 2
-4x = 2
-4x/-4 = 2/-4
x = [tex]-\frac{1}{2}[/tex]
hope this helps!
What is 1 minus 2 times parentheses 3 minus 4 and closed parentheses.
Answer:
1
Step-by-step explanation:
because parentheses go first so 2 x 3 = 6 minus 1 = 5 minus 4 = 1
Find the probability that exactly four of them retake this test.
I believe it’s C, convert 0.188 into a fraction
solve for x～
[tex]x {}^{2} - 5x + 6 = 0[/tex]
thankyou! :)
Answer:
x=2,3
Step-by-step explanation:
[tex] {x}^{2} - 5x + 6 = 0 \\ {x}^{2} - 2x - 3x + 6 = 0 \\ x(x - 2) - 3(x - 2) = 0 \\ (x - 2)(x - 3) = 0 \\ either \: x = 2 \: \: \: \: \: or \: x = 3[/tex]
find the discriminantof 3x - 10x = -2
Answer:Here, a=3, b=-10 and c=2. Substitute the values, Therefore, the discriminant of is 76.
Step-by-step explanation:
how many fluid ounces is in 6 cups
Answer: 48
Step-by-step explanation: i know
Suppose a triangle has sides 3, 4, and 6. Which of the following must be true?
• A. The triangle in question may or may not be a right triangle.
•
B. The triangle in question is not a right triangle.
• C. The triangle in question is a right triangle.
Answer:
The answer would be B
Step-by-step explanation:
Hope this helps:)....if not then sorry for wasting your time and may God bless you:)
A right triangle with sides 3 and 4 would have a hypotenuse of 5.
The answer would be:
B. The triangle in question is not a right triangle.
this is my last problem for this it shouldn’t take long pls help.
Answer:
2
Step-by-step explanation:
i got 20/8 from multiplying same with 1/2
20/8 - 1/2 = 2
Enter the number 0.9 as hundredths in fraction form and decimal form.
Fraction:
Decimal:
Answer:
Below.
Step-by-step explanation:
0.9 = 90/100 fraction and
= 0.90 as a decimal.
