I’m very confused with this question, I tried to do it but I just have slight feeling I got this wrong and I want to double check make sure my answer is correct. Would you please me help me thank you very much
Answers
The powers of the imaginary number i have four possible values: 1, i, -1, and -i. Let's see some examples:
i⁰ = 1 (any number with the exponent 0 equals 1)
i¹ = i (any number with the exponent 1 is the number itself)
i² = -1 (this follows from the definition of the imaginary number, the square root of -1)
i³ = i² * i = -1 * i = -i
Now, the results start to repeat from 1 to -i:
i⁴= i² * i² = (-1) * (-1) = 1
i⁵ = i⁴ * i = 1 * i = i
i⁶ = i * i⁵ = i * i = i² = -1
i⁷ = i⁶ * i = -1 * i = -i
From that, we can follow the steps below to find the value of a power of i:
• divide the exponent by 4;
,• if the rest of the division is 0, then the power equals ,i⁰ = 1,;
,• if the rest of the division is 1, then the power equals ,i¹ = i,;
,• if the rest of the division is 2, then the power equals ,i² = -1,;
,• if the rest of the division is 3, then the power equals ,i³ = -i,.
So, for the power i⁶⁴⁹, the exponent is 649. Following the steps above, we find:
• 649/4, has a quotient of 162 and the, rest 1,. Therefore:
i⁶⁴⁹ = i¹ = i
Thus, i⁶⁴⁹ equals i.
Related Questions
ross is camping 4 miles west and 11 miles north (-4,11)
Answers
Using the equation for the distance between two points, the distance between Ross and Rachel is given by the following option:
D. 19 miles.
What is the distance between two points?Suppose that we have two points with coordinates [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]. The shortest distance between them is given by the equation presented as follows:
[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
This formula is derived from the Pythagorean Theorem, as the points form a right triangle in the xy-plane, and the hypotenuse represents the distance between them.
Their coordinates in this problem are as follows:
Ross: (-4, 11).Rachel: (8, -4).Each unit on the plane represents a mile, hence their distance is given as follows:
[tex]D = \sqrt{(8 - (-4))^2+(-4 - 11)^2}[/tex]
D = 19.2 miles.
Rounded to 19 miles, hence option D is correct.
Missing informationThe complete problem is given by the image at the end of the answer.
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Which of the following is not a condition necessary to create a valid probability distribution?
Answers
Given
different choices
Find
Which of the following is not a condition necessary to create a valid probability distribution?
Explanation
Each discrete outcome can have different probability of occuring
Hence the option stating each discrete outcome hsould have equal probability of occuring is not necessary
Final Answer
option (a) is correct option
Jane wants to save $500 to purchase a new television. She earns $10.50 an hour at her job. The function M(h) = 8h represents the amount of money Jane earns in dollars, M(h), for each hour h that she works. Find M(60).
*Type in your answer.
M(60) =$.
Answers
The amount that Jane would earn for working for 60 hours is $630.
What is M(60)?The given function is a linear function. A linear function is a function that changes at a constant rate. When a linear graph is drawn on a coordinate graph, it can slope either upward or downward.
The linear function that represents the total amount she earns is:
Total earnings = cost per hour x total number of hours worked
Total earnings = $10.50 x h
Total earnings = $10.50 x 60 = $630
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Does anyone know the answer to this question ?? PLS HELP.
Only answer if you know the answer !!!!
Answers
Polynomial function of least degree having real coefficient with given leading coefficient 1 and having zeros 3, 4 +i is equal to x³ -11x² +41x -51.
As given,
Standard form of the polynomial function:
f(x) = r(x-a)(x-b)(x -c)
r : leading coefficient
a, b, c are zeros
Polynomial function of least degree having real coefficient with given leading coefficient 1 and having zeros 3, 4 +i is given by
f(x) = 1(x -3) (x -(4+i))(x - (4-i))
⇒ f(x) = (x -3) (x-4 -i)(x -4 +i)
⇒ f(x) = (x-3) [(x-4)² -i²]
⇒f(x) = (x-3)(x² -8x +16+1)
⇒f(x) =(x-3)(x² -8x+17)
⇒f(x) = x³-11x² +41x-51
Therefore, polynomial function of least degree having real coefficient with given leading coefficient 1 and having zeros 3, 4 +i is equal to
x³ -11x² +41x -51.
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Spoonhead's
heart beats 48 times
per minute. How many times will
his heart beat in two hours?
Answers
Answer:5760
Step-by-step explanation:
48 beats per min and its 120 min in 2 hours so multiply 120×48=5760
Select the value that make the inequality w≥6 true
Answers
Answer:
Every number that is greater than 6
Simplify the following radical
√175x^5
Answers
Simplified version of the given radical expression would be...
[tex]5x^2\sqrt{7x}[/tex]
Hope this helps!
the equation 2x-20/3=2x models temperature change, where x represents the difference in degrees in the last 24 hours. solve for x
a. x = -5
b. x = -2
c. x = 2
d. x= 13
Answers
The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions.
The answer is x = -5 for the following equation (2x - 20) /3 = 2x.A formula for the question at hand is 2x minus 20 divided by 3 Equals 2x, or (2x - 20) /3 = 2x.
The difference in degrees over the last 24 hours is represented by x in this equation, which predicts temperature change.
We must find x in the given equation.
(2x - 20) /3 = 2x \s (2x - 20) = 3(2x) (2x) ...........(Multiply by 3 on both sides)
2x - 20 + 20 = 6x + 20 ...........(Add 20 to both sides)
2x - 6x = 6x + 20 - 6x ..........(Subtract 6x from both sides) (
-4x = 20 \s x = -5 ..........(Divide by - 4 on both sides)
As a result, x = -5 for the given equation (2x - 20) /3 = 2x.
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triangle ABC has coordinates A(1,4) B(3.-2) and C(4,2) . Find the coordinates of the image ABC after a reflection over the x axis.
Answers
The given vertices are A(1,4), B(3,-2), and C(4,2).
The reflection over the x-axis is expressed as
[tex](x,y)\rightarrow(x,-y)[/tex]This means we have to multiple each y-coordinate with -1. Let's do it!
[tex]\begin{gathered} A(1,4)\rightarrow A^{\prime}(1,-4) \\ B(3,-2)\rightarrow B^{\prime}(3,2) \\ C(4,2)\rightarrow C^{\prime}(4,-2) \end{gathered}[/tex]Therefore, the vertices of the new triangle are A'(1,-4), B'(3,2), and C'(4,-2)the area of a right angled triangle is 96cm^2if the two shaded sides of the triangle differ by 2 what is the length of the shorter sides
Answers
The triangle have shorter sides of 12.9 and 14.9 cm, respectively
How to determine the lengths of the shorter sides?From the question, the given parameters are:
Triangle type = Right-angled triangleArea of triangle = 96 cm^2Also, from the question, we have:
Two shaded sides of the triangle differ by 2
In this case, the shaded sides of the triangle are
Opposite and Adjacent
This can also be interpreted as
Base and Height
So, we have
Base - Height = 2
The area is calculated as
Area = 0.5 * Base * Height
So, we have
0.5 * Base * Height = 96
This gives
0.5 * (Height + 2) * Height = 96
Divide by 0.5
(h + 2) * h = 192
Using a graphing calculator, we have
h = 12.9
Substitute h = 12.9 in Base - Height = 2
Base - 12.9 = 2
Evaluate
Base = 14.9
Recall that the Opposite and Adjacent are the shorter sides of a right triangle
Hence, the shorter sides are 12.9 and 14.9 cm
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Hello! I think I have this correct but want to make sure.
Answers
Solution;
y=5x
Explanation;
[tex]\begin{gathered} y\propto x \\ y=kx \\ k=\frac{y}{x} \\ when\text{ x=1 and y=5;} \\ k=\frac{5}{1}=5 \\ Therefore; \\ y=5x \end{gathered}[/tex]Find 3 ratios that are equivalent to 6:15
Answers
Answer:12:30,2:5 and 18:45
Step-by-step explanation:
suppose that you were trying to predict house price based on square footage, distance from the beach, and lot size for miami, florida. run a multiple regression predicting price based on square footage, and lot size. assume you are trying to determine if the slope of lot size is different than 0, and you find a p value 0.5677. what conclusion can you make?
Answers
The slope for lot size is not different from 0.
We will let the slope of the size be β
So the hypothesis can be: β = 0 (Null Hypothesis) , β≠ 0 (Alternate Hypothesis)
If we consider a confidence level (the probability for which we can be confident that the null hypothesis is true) to be 95% (Probability = 0.95) then the level for which we are not confident that the null hypothesis is true will be (100 - 95)% = 5% (Probability = 0.05)
Thus, for this coefficient the P value is 0.5782.
As the p-value is more than the Probability for which we are not confident (0.05), so in this regard we can state then there is no such significance difference seen in this regard. Thus, we accept the null hypothesis here. This means that we can take the coefficient to be 0.
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Write a simplified expression for the right half of the equation that can be used to find the nth term in the sequence6,7,8 9,10
Answers
A recipe calls for 3 ⅜ cups of flour. How can you express that mixed number as a fraction?
Answers
To convert a mixed number to a fraction, you must multiply the denominator (8) by the number beside the fraction (3).
8 x 3 = 24.
Next, you add the numerator (3) to your answer!
24 + 3 = 27.
Lastly, put this number over your original denominator (8).
Therefore, the answer is 27/8!! I hope this helped!! <33
Forty years ago, uncle Luke was 5 times
as old as his
nephew. Today, Uncle Luke is 16 yeas older than his nephew. How
old is uncle Luke now?
Answers
Answer: Uncle Luke is at 50 years old
Step-by-step explanation: I went through trial and error first with simple t-charts. In the first one, I simply implemented the piece of info that Luke was 5 times older than the nephew. But then, I realized that Luke would always be 5 years older than his nephew. Here was the info for that t-chart:
[tex]\left \{ {{N=1} \atop {L=5}} \right. \left \{ {{N=2} \atop {L=6}} \right. \left \{ {{N=3} \atop {L=7}} \right.[/tex]
Next, I tried a chart starting with the nephew at 2 years of age, and got an age gap of 8. This helped me realize that I would have to start at 4 years of age in order to have an age gap of 16
[tex]\left \{ {{N=2} \atop {L=10}} \right.[/tex] | [tex]\left \{ {{N=4} \atop {L=20}} \right. \left \{ {{N=5} \atop {L=21}} \right.[/tex] (remember there are 1 increments)
Next, I realized that N=4, L=20 was 40 years ago, so if now the nephew was 44, we can increment 16 to get 50
44+16=50
Please only answer if you know the answer thank you.
Answers
Answer:
x = - 5;
y = 5;
Step-by-step explanation:
Identify the equation.
y = ( 2 / 3 )x + c;
Substitute a point.
5 = ( 2 / 3 )( - 2 ) + c;
5 = ( - 4 / 3 ) + c;
5 - ( - 4 / 3 ) = c;
5 + ( 4 / 3 ) = c;
19 / 3 = c;
y = ( 2 / 3 )x + ( 19 / 3 );
Substitute point A.
3 = ( 2 / 3 )x + ( 19 / 3 );
3 - ( 19 / 3 ) = ( 2 / 3 )x;
( 9 / 3 ) - ( 19 / 3 ) = ( 2 / 3 )x;
- ( 10 / 3 ) = ( 2 / 3 )x;
- ( 10 / 3 )( 3 / 2 ) = x;
( - 30 / 6 ) = x;
- 5 = x;
x = - 5;
Substitute point B. Use common sense and notice that point B is actually the same as the first point.
y = 5;
Answer:
x = -5
y = 5
Step-by-step explanation:
You could write the equation in the point slope form of a line
y - [tex]y_{1}[/tex] = m( x - [tex]x_{1}[/tex])
Use the slope they gave us 2/3. Use the point they gave us for [tex]x_{1}[/tex] ( -2 ) and [tex]y_{1}[/tex] ( 5)
y -5 = 2/3(x - -2)
y - 5 = 2/3(x + 2) Plug in 3 for y to solve for x
3-5 = 2/3(x + 2)
-2 = 2/3x + 4/3 subtract 4/3 from both sides of the equation
-2 - 4/3 = 2/3x
[tex]\frac{-6}{3}[/tex] - [tex]\frac{4}{3}[/tex] = 2/3x
[tex]\frac{-10}{3}[/tex] = 2/3 x Multiply both sides by [tex]\frac{3}{2}[/tex]
([tex]\frac{3}{2}[/tex])[tex]\frac{-10}{3}[/tex] = ([tex]\frac{3}{2}[/tex])([tex]\frac{2}{3}[/tex]) x
-5 = x
substitute in -2 for x to solve for y
y - 5 = 2/3(x + 2)
y - 5 = 2/3(-2+2)
y - 5 = 2/3(0)
y - 5 = 0 Add 5 to both sides
y = 5
Write the coordinates of the vertices after a reflection over the y-axis
Answers
The most appropriate choice for reflection will be given by-
After reflection over y-axis, coordinate of K will become K' (6, -1)
After reflection over y-axis, coordinate of L will become L' (0, -1)
After reflection over y-axis, coordinate of M will become M' (0, -2)
After reflection over y-axis, coordinate of J will become J' (6, -2)
What is reflection?
Reflection of a figure about a line is a transformation in which a mirror image of the figure can be obtained over the line.
The line is called the line of reflection.
Here,
After reflection over the y - axis, sign of x coordinate will be same.
Coordinate of K = (-6, -1)
After reflection over y-axis, coordinate of K will become K' (6, -1)
Coordinate of L = (0, -1)
After reflection over y-axis, coordinate of L will become L' (0, -1)
Coordinate of M = (0, -2)
After reflection over y-axis, coordinate of M will become M' (0, -2)
Coordinate of J = (-6, -2)
After reflection over y-axis, coordinate of J will become J' (6, -2)
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Write an equation of a line that goes through (4, 1) and has a slope of 2.
Answers
Answer this question for me
Answers
Answer:
3.97%
Step-by-step explanation:
You want to know the annual interest rate, compounded daily, that will result in $43,000 growing to $75,000 in 14 years.
FormulaThe formula for the account value is ...
A = P(1 +r/n)^(nt)
where P is the principal invested at annual rate r compounded n times per year for t years.
ApplicationFilling in the given values, we can solve for r.
75000 = 43000(1 +r/365)^(365·14)
75/43 = (1 +r/365)^5110 . . . . . divide by 43000 and reduce the fraction
Taking the 1/5110 power gives ...
(75/43)^(1/5110) = 1 +r/365 ≈ 1.00010886855
r/365 = 0.0010886855 . . . . subtract 1
r = 0.001086855·365 . . . . . multiply by 365
r ≈ 0.039737 = 3.9737%
The required interest rate is about 3.97%.
Does anyone have an answer or explanation? I kind of need it before 12pm (CDT)
A museum charges $10 for general admission and $2 for each special exhibit you attend.
What does f(0) = 10 represent in the context of this problem?
Answers
Answer:
i d k 20???????????
Step-by-step explanation:
Answer:
The visitor attended no special exhibits and so paid a total of $10 just to get in.
An equation to represent the cost of admission could look like this:
f(x) is the total cost.
x is the number of special exhibits attended.
f(x) = 2x + 10
If I see no special exhibits on my visit,
x = 0, then
f(0) = 2•0 + 10
f(0) = 10
I only pay $10.
What does do the congruence criterion mean.
Please explain what AAS, SSS, ASA, and HL mean.
Answers
AAS = Angle , angle and one side of 2 congruent triangles
SSS = All 3 sides are measure same of the 2 triangles.
ASA = 2 angles and the side between them are same
HL = A right triangle is congruent if its hypotenuse and one of its legs are congruent with the hypotenuse and one of its other legs.
What is meant by congruency?The dimensions of the triangles' sides and angles determine whether two or more triangles are congruent. A triangle's size is determined by its three sides, and its shape by its three angles. Pairs of corresponding sides and corresponding angles in two triangles are said to be equal if they are congruent. They share a similar size and shape. In triangles, there are numerous congruence conditions. For the two triangles to be congruent, they must be the same size and shape. It should be possible to superimpose the two triangles under examination. A triangle's position or appearance appears to change when we rotate, reflect, and/or translate it. In that situation, we must recognize the six components of a triangle.
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1.39 to 1 decimal point
Answers
Answer: 1.4 or just 1
Step-by-step explanation:
But we are going to a decimal point then go to 1.4, cause the 9 makes the 3 round-up. :)
Answer: 1.4
Step-by-step explanation:
I believe you're asking what 1.39 rounded to the nearest tenths place is, in that case it is 1.4
-7/8u = -21 solve for u and simplify your answer as much as possible
Answers
Answer:
u = 24
Step-by-step explanation:
-7/8u = -21
Solve for u
Multiply each side by -8/7
-8/7 *-7/8u = -21 *-8/7
u =3*8
u = 24
Answer:
u = 1/24
Write the equation:
–7/8u = –21
Get rid of fraction:
–7/2^3 • u = –21
–7 = ( – (8u) ) 21
Solve:
–7 = –8u + 21
–7 + 8u = –8u + 8u + 21
–7 + 8u = 21
–7 + 7 + 8u = 21 + 7
8u = 21 + 7
8u = 28
u = 1/24
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Eli dug a trench
18
20
of a meter long. The next day he dug another 17
20
B
of a meter. What is a reasonable estimate of the total length of the trench?
Answers
The summation is the adding two quantities thus the reasonable estimate of the total length of the trench is 1 1/2 meters so option (C) is correct.
What is summation?A summation, also abbreviated as a sum, is the outcome of adding two or more numbers or quantities.
There could be only two terms, but there could be one hundred, a thousand, or a million.
Here are always an integer number of terms in a summation.
As per the given,
Length of the trench on the first day = 18/20 meters
Length of the trench on the second day = 9/20
Total length of the trench = 18/20 + 9/20
Take LCM as 20
⇒ (18 + 9)/20 = 27/20
⇒ 1.35 which is closest among the given option by 1 1/2 meters.
Hence "The summation is the adding two quantities thus the reasonable estimate of the total length of the trench is 1 1/2 meters".
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What is the slope of the line? ASAP.
Answers
Answer:
The slope would be 25/1 or 25.
Step-by-step explanation:
Use the formula y2-y1 over x2-x1. Or use rise over run.
Simplify the following expression
Answers
Answer:
y
-------------
x²¹ z⁵
Step-by-step explanation:
(x⁻⁹ y³ z⁻²)²
-------------------
x³ y⁵ z
x⁻¹⁸ y⁶ z⁻⁴
-------------------
x³ y⁵ z
y⁶
-------------------
x³ ⁺ ¹⁸ y⁵ z¹ ⁺ ⁴
y
-------------------
x²¹ z⁵
I hope this helps!
After simplification by rule of exponent solution is,
⇒ y / x²¹ z⁵
We have to given that;
The expression is,
⇒ (x⁻⁹ y³ z⁻²)² / x³ y⁵ z
Now, We can simplify by rule of exponent as;
⇒ (x⁻⁹ y³ z⁻²)² / x³ y⁵ z
⇒ x⁻¹⁸ y⁶ z⁻⁴ / x³ y⁵ z
⇒ y⁶ / x³ ⁺ ¹⁸ y⁵ z¹ ⁺ ⁴
⇒ y / x²¹ z⁵
Thus, After simplification by rule of exponent solution is,
⇒ y / x²¹ z⁵
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The graph shows g(x), which is a transformation of f(x)= 1x1. Write the function rule for
g(x).
Answers
The most appropriate choice for function will be given by -
g(x) = -|x| is the correct function
What is a function?
A function from A to B is a rule that assigns to each element of A a unique element of B. A is called the domain of the function and B is called the codomain of the function.
There are different operations on functions like addition, subtraction, multiplication, division and composition of functions.
f(x) = |x| is the given function.
f(x) has been transformed to g(x) according to the graph given in the figure
In the figure, the range is negative real number.
So the transformation g(x) = - |x|
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Hello I just need help with A and B on my homework I was able to complete C
Answers
ANSWERS
a) 58
b) 62.2
EXPLANATION
a) The median is the middle value. It separates the data set in two. To find the median we have to put the data in order, from least to greatest:
[tex]44,49,53,54,58,74,74,74,80[/tex]The number of data is odd, this means that the median will be one of the values of the data set and not a mean between two of them. If there are 9 values, the median is the 5th value - so we have 4 values to the left and 4 values to the right.
The first 4 values are 44,49,53,54, so the median is 58.
b) The mean is the sum of all values of the data set divided by the amount of data:
[tex]\bar{x}=\frac{44+49+53+54+58+74+74+74+80}{9}=\frac{560}{9}=62.2222\ldots[/tex]Rounded to one decimal place, the mean is 62.2
Please solve for y. There should be no actual numbers besides for 9.
Answers
Answer:
y= x/(n-9)
Step-by-step explanation:
Move 9 to the right side to get n-9
Take y over to get x=y(n-9)
Then shift n-9 over to other side to get y= x/(n-9)