The given expression is a complex expression and we can prove the given expression equal to 1 by using definition.
What is i in complex number?a+ib, often known as the generic form of complex numbers, is how complex numbers are expressed. In the complex numbers a+ib form, a represents the real component of the number, b represents the imaginary part, and i is defined as√(-1). Complex numbers can take a variety of shapes.
Write the general form of complex number.z=a+bi is the general form of complex number
As by definition
i^2=-1
So
i^4=(i^2)^2
=(-1)^2
=1
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2. Is she right or wrong? Explain. If she is wrong, tell how much carpet she needs. (
Michele is buying carpet for a room with the dimensions shown. 10 ft 8 ft 12 ft 4 ft 15 ft Michele calculates that the area she will cover with carpet is 180 square feet.
Answer:
She is wrong. She needs 140 square feet.
Explanation:
(8×10)+(4×15) = 140
The parent function of a quadratic equation is vertically stretched by a factor of 2, then translated 4 units left and one unit down
Answer:
[tex]f"'(x) = 2(x-4)^2 - 1[/tex]
Step-by-step explanation:
Given
[tex]f(x) = x^2[/tex] --- the quadratic function
Vertically stretched by 2
Translation: [tex]4\ units[/tex] left and [tex]1\ unit[/tex] down
Required
Determine the new function
[tex]f(x) = x^2[/tex]
The rule for vertical stretch is:
[tex](x,y) \to (x,ay)[/tex]
In this case:
[tex]a = 2[/tex]
So, we have:
[tex]f(x) = x^2[/tex]
[tex]f'(x) = a * f(x)[/tex]
[tex]f'(x) = a * x^2[/tex]
Substitute: [tex]a = 2[/tex]
[tex]f'(x) = 2 * x^2[/tex]
[tex]f'(x) =2x^2[/tex]
Translation: 4 units left
The rule is:
[tex](x,y) \to (x - c,y)[/tex]
In this case: [tex]c =4[/tex]
So, we have:
[tex]f"(x) = 2(x - 4)^2[/tex]
Translation: 1 unit down
The rule is:
[tex](x,y) \to (x,y-d)[/tex]
In this case, [tex]d=1[/tex]
So, we have:
[tex]f"'(x) = f"(x) - 1[/tex]
[tex]f"'(x) = 2(x-4)^2 - 1[/tex]
If 5x-3=3x+5, what is the value of 2X-8? 5
Answer:
5x-3=3x+5
5x-3x=5+3
2x=8
x=8/2
x=4
Therefore,
Value of 2x-8
Substitute the value of x
2(4)-8
8-8=0
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A XYZ is an equilateral triangle.
X
2
3
Z
Y
What is the measure of Z 2?
HURRY AND NO LINKS
Answer:
The value of the angle is 60 degrees
Step-by-step explanation:
Here, we want to find the value of the angle marked 2
From the question, we can see that we have three marked interior angles
These are the angles 1, 2 and 3
Mathematically, the interior angles of an equilateral triangle are equal
This means that each of the interior angle of an equilateral triangle measures 60 degrees
Hence, this means that the value of the angle marked 2 is 60 degrees
if your not good with percentages, i suggest you should go...
25% of ______ is 15
70% of 30 is ______
What % is 15 of 50?
15% of ______ is 6
40% of 30 is _____
LAST ONE!!!
What % is 40 of 50?
BONUS! (I'm good at these so its oppional)
3 / 1 1/6 =
Using the graph, determine the coordinates of the vertex of the parabola
The circumference of a circle is 20.724 yards. What is the circle's diameter?
Answer:
approximately 6.6 yards :)
Step-by-step explanation:
Answer:
6.6
Step-by-step explanation:
take pi as 3.14
formula for circumfurence is 2*pi*r
so 2r=20.724/pi
2r=6.6
since diameter is 2 radius, the diameter is 6.6
The retangular prism shows is made from cubs.Each cube is 1 cubic unit. What is the volume in cubic units
Answer:
72 square units
Step-by-step explanation:
To get these, we will use the attached diagram as a case study
Since each cube is 1cubic unit, hence the length of the side of a cube is 1unit
From the diagram
Length = 6units
Width = 3 units
Height = 4units
Volume of the prism = Length * Width * Height
Volume of the prism = 6 * 3 * 4
Volume of the prism = 18 * 4
Volume of the prism = 72 sq.units
Hence the volume of the prism is 72 square units
HELP URGENT PROBLEM IS IN THE PICTURE || SHOW YOUR WORK PLS ILL ADWQARD BRAINLEST
Answer:
19.550
Step-by-step explanation:
Sorry if I am wrong.....
What’s the answer?
Needed now
The Johnson family is taking a road trip that is 575 miles long. On the first day,
they drove 2/5 of the miles. How many miles did they travel?
Please help this is due tommorw
When given the picture using what you know find the answer. What is m
Answer:
40 degrees
Step-by-step explanation:
Answer:
Angle E = 25 deg because of reflective
Angle C = 115 degree because 180 - 65
Since triangle = 180 deg
Angle D = 180 - 115 - 25
= 40 deg
Step-by-step explanation:
Baking Brownies
A brownie recipe needs one cup of sugar for every 1⁄2 cup of flour to make a batch of cookies. To make multiple batches, we represent the relationship between flour and sugar with the function f = 1⁄2 s where f is the number of cups of flour and s the number of cups of sugar. What graph represents this relationship?
Answer:
A
Step-by-step explanation:
A because it is the only one the recipe calls for 1 cup of sugar and 1/2 cup of flour, the point is in the middle but also on one.
What is the Y-intercept of the line shown above
WILL GIVE BRAINLIEST!!!
Michelle weighs 90 pounds, which is 120% of what she weighed two years ago. How much did she weigh two years ago?
A) 108 pounds
B) 75 pounds
C) 175 pounds
D) 88 pounds
B. Michelle weighed 75 pounds two years ago
Someone plz help!! Plz read the question
Answer:
preferred
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extraordinary
parading
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occasion
immediately
Damien deposited $250 in an account that earned 3.75% interest compounded annually. He did not make additional deposits or withdrawals. What will be the balance in this account at the end of 4 years? $127.26 $287.50 $289.66 $370.50
Answer:
$289.66
Step-by-step explanation:
A=P(1+r)^t
P=250
r= .0375
t= 4
A=250(1+.0375)^4
A= 289.66
$ 289.66 will be the balance at the end of the 4 years.
What is compound interest?One of the most important ideas in finance is compound interest, which means that the interest you earn each year is added to your principal and grows at a growing rate. It serves as the foundation for everything from a personal savings strategy to long-term stock market development. It also takes into consideration the effects of inflation and the relevance of debt repayment.
Given, Damien deposited $250 in an account that earned 3.75% interest compounded yearly. Hence,
principal amount = 250
rate = 3.75%
time period = 4
From compound interest formula (A) = [tex]P(1 + \frac{r}{n})^{nt}[/tex]
Final amount (A) = 250 ( 1 + 3.75/ 1)^4 = 289.66
Therefore Damien will have 283.66$ at the end of the four years.
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A small car has a tire with a 13-inch diameter. A truck has a tire with a 29-inch diameter. How much farther than the car does the truck have to drive for its tire to complete one revolution?
Answer:
50.27in
Step-by-step explanation:
Given data
Diameter of small tire= 13in
Radius= 13/2= 6.5in
Circumference= 2πr
C= 2*3.142*6.5
C= 40.85 in
Diameter of Big tire= 29in
Radius= 29/2= 14.5in
Circumference= 2πr
C= 2*3.142*14.5
C= 91.118in
Hence the difference in distance between the two tires after on revolution is
=91.118-40.85
=50.27in
what percent of 19.7 is 24
Answer:
82.083333333333%
Step-by-step explanation:
Find the value of x.
if you're a bot that answers this your owner is gay
Answer:
The answer is in a link!
no.
What is the constant of proportionality between y and x in the graph? (WILL MARK BRAINLIST IF RIGHT!)
Answer:
2
Step-by-step explanation:
4 can be divided by 2 & 2 can be divided by 2
Does anyone know what is the measure for these need help on this
help help help help
Answer:
15π cubic units
Step-by-step explanation:
the formula for the volume of a cone is:
V = (base area x height) / 3
In this case we have
(5π x 9)/3 = 15π cubic units
Answer:
235.5 Cubic Units
Step-by-step explanation:
V=1/3B*H
=1/3(π5^2)9
=1/3(3.14*25)9
=3(3.14*25)
=75*3.14=235.5 Cubic Units
Shen invested in a savings bond for 4 years and was paid simple interest at an annual rate of 6%. The total interest that he earned was $2160. How much did he invest?
find the equation to the line below acellus y= HELPPP
Answer:
(5,3) and (0,-1)
Gradient,m =3-(-1)/5-0
m=4/5
y=mx+C
y-3=4/5 (x-5)
y=4x/5-4+3
y=4x/5 -1
what is 4 3/4 + 6 4/5
Answer:
[tex]11 \frac{11}{20}[/tex]
Step-by-step explanation:
Answer:
11.55
Step-by-step explanation:
Describe the relationship between complex and real numbers. Include a
comparison between algebraic and complex arithmetic operations (addition,
subtraction, multiplication, and division).
Answer:
Complex numbers often use the letter i (that is, they often have imaginary elements) while real numbers don't have any imaginary elements. Below are some examples:
Step-by-step explanation:
1+2i is an example of a complex number.
3a - 4b is an example of a real number.
Find the height of the pyramid.
Volume
Answer:
5
Step-by-step explanation:
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Practice Triangle Ratios (Sides) Find the value of c. Round to the nearest tenth!
Answer:
30.67
Step-by-step explanation:
Given the following
Opposite side = x
Adjacent = 17
Angle = 61degrees
Using the SOH CAH TOA identity
tan theta = opp/adj
tan 61 = x/17
x = 17tan61
x = 17(1.8040)
x = 30.67
Hence the value of x is 30.67