By using demovire's theorem to determine the complex numbers to simplify (1+i)^12 we get [tex]z^{12}=-2^6=-64[/tex]
first, we have to find the argument. As the complex number, z=1+i will be in the 4th quadrant
we proceed according to conditions in demovire's theorem
[tex]r=\sqrt{(1)^2+(1)^2}\\ \\r=\sqrt{2}[/tex]
so from this our angle becomes
[tex]\alpha =2\pi -tan^{-1}=- \frac{\pi }{4}[/tex]
so putting r and alpha in the formula of demovier's of complex numbers
[tex]z^{n}=r^{n}(cos\alpha +isin\alpha )\\\\z^{12}=(\sqrt{2} )^{\112} }(cos\((\frac{-\pi }{4}) +isin(\frac{-\pi }{4}) )\\\\z^{12}=2^6(-1-0)\\\\z^{12}=-2^6=-64[/tex]
we get z to the power 12 equals to negative times sixty-four.
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Angel Sum Theorem PLEASE HELP with explanation if possible
Answer:
y = 90°
Step-by-step explanation:
You want the value of y in the diagram showing y as the angle at the base where the isosceles triangle a.pex angle bisector meets the base.
Angle sum theoremThe angle sum theorem tells you the sum of angles in a triangle is 180°.
Consider the large outside triangle. The sum of its angles is ...
60° +2x +60° = 180°
2x = 60° . . . . . . . . . . . . subtract 120°
x = 30° . . . . . . . . . . divide by 2
Now, consider the left smaller triangle. The sum of its angles is ...
60° +x +y = 180°
60° +30° +y = 180° . . . . . . use the known value of x
y = 90° . . . . . . . . . . . . subtract 90°
__
Additional comment
The a.pex angle bisector of an isosceles triangle is always an altitude that meets the base at right angles. The meeting point is the midpoint of the base, so that segment is also a median.
The halves of the isosceles triangle are congruent right triangles, so the base angle is complementary to the angle marked x.
Find the Amount (A) (Principal Rs 50000 Time = 7 years interest = 3%.
Answer: Rs 60500
Step-by-step explanation:
Principal = Rs 50000 = p
Time = 7 years = t
Simple interest rate = 3% = r
Interest = p*t*r/100
using above formula,
50000*7*3/100=10500
So, final amount = principal + interest = 50000+10500 = Rs 60500
Can anyone solve these 2 questions they are very easy but i want to double check
Answer:
Corresponding angels:
a,f
h,b
e,d
c,g
y = 80 Vertical angles are congruent
x = 50 Sum of the interior angles of a triangle is 180
180 - 80 -50 = 50
Step-by-step explanation:
What statistical technique is used to make predictions of future outcomes based on present data? Analysis of variance Repeated measures Linear regression Correlational analysis
To be able to make predictions for future outcomes based on present data, a statistical technique called regression analysis is used .
It helps in developing prediction models.
Regression analysis is basically a tool to show a relationship between two or more variables. Usually expressed in a graph, the method tests the relationship between a dependent variable against independent variables.
It is a quantative method wherein the basic form of regression models includes unknown parameters (β), independent variables (X), and the dependent variable (Y). Regression allows researchers to predict or explain the variation in one variable (called the dependent variable) based on another variable( known as the independent variable).
The most common and simple form of regression is the Linear Regression model.
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if you use a different experimental photo-missive material, what would be the same on the graph? (5 points) the y-intercept the intercept the slope
The slope would be the same on the graph.
What is a slope?
A line's steepness is determined by its slope. In mathematics, slope is determined by "rise over run" (change in y divided by change in x).
The slope-intercept form of an equation is used to represent each time the equation of a line is stated as y = mx + b.
M represents the line's slope. Additionally, b is the b in the y-intercepting point (0, b). For instance, the y-intercept is at (0, 7) and the slope is 3 in the equation y = 3x - 7.
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Solve |2 +1| = 10x
{-9/2, 9/2}
{-11/2, 9/2}
{9/2, 11/2}
The solution to the equation |2 +1| = 10x is x = 3/10
How to determine the solution to the equationFrom the question, we have the following parameters that can be used in our computation:
|2 +1| = 10x
Evaluate the sum in the above equation
So, we have the following representation
|3| = 10x
Remove the absolute bracket in the above equation
So, we have the following representation
3 = 10x
Divide both sides by 10
This gives
3/10 = x
Rewrite as
x = 3/10
Hence, the solution is 3/10
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Complete the table of values below: x -2 -1 0 1 2 3 f(x)=(1/3)^x -2 ANSWER
-1 ANSWER
0 ANSWER
1 ANSWER
2 ANSWER
9, 3, and 1 are the values of a, b, and c using the exponential function g(x)=(1/3)∧x.
What are exponential functions?A mathematical function with the formula f (x) = an x is an exponential function.
Where x is a variable, and an is a constant called the basis of the function.
The most typically seen exponential-function base is the transcendental number e, which is equivalent to about 2.71828.
So, the exponential function:
g(x) = (1/3)∧x
From the table, we are also to find out the value of a, b and c
If x = -2
g(-2) = a = (1/3)⁻²
a = 1/3⁻²
a = 9
Accordingly,
If x = -1
g(-1) = b = (1/3)⁻¹
a = 1/3⁻¹
b = 3
Hence,
If x = 0
If x = -1
g(0) = c = (1/3)⁰
c = 1
Therefore, 9, 3, and 1 are the values of a, b and c using the exponential function g(x) = (1/3)∧x.
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Complete question:
Complete the table of values for the function.
f(x) = ( 1/3) ^x
a=
b=
c=
How can I solve this ? What is the angle whose tangent is 456/321?
The angle whose tangent is 456/321 is 54.85°
The tangent of an angle in trigonometry is the ratio of the lengths of the adjacent side to the opposing side. In order for the value of the cosine function to not be 0, it is the ratio of the sine and cosine functions of an acute angle.
The Tangent Formula is given as:
Tan A = Opposite Side/Adjacent side
In terms of sine and cosine, tangent may be represented as:
Tan A = Sin A / Cos A
We know that the sine of an angle is equal to the length of the opposite side divided by the length of the hypotenuse side whereas the cosine of the angle is the ratio of the length of the adjacent side to the ratio of the hypotenuse side.
That is, Sin A = Opposite Side/ Hypotenuse Side
Cos A = Adjacent Side/ Hypotenuse Side
Therefore, tan A = Opposite Side/ Adjacent Side
[tex]tan^{-1} (1.42056)[/tex] =54.85°
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If f(7) = 22, then f^-1(22) = [?]
The required value of the given inverse function f⁻¹(22) will be 7.
What is an inverse function?The inverse function is defined as a function obtained by reversing the given function.
Given that f(7) = 22
To determine the value of the given inverse function f⁻¹(22)
An inverse function's main objective is to show the value that occurs in a specific function value. Which means :
If we have f(x) and f⁻¹(x), then
if f(a) = b then f⁻¹(b) = a
As per the given question, we have
⇒ f(7) = 22 then f⁻¹(22) = 7
Therefore, the required value of the given inverse function f⁻¹(22) will be 7.
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a better understanding of how I can solve for 1/2d-3/4d+3f-2f
The simplified form of the given expression is, 1/4d + f.
What is simplified form of the expression?
To simplify an expression, create an equivalent expression without any terms that are similar.
The expression will then be rewritten using the fewest terms possible.
Mathematical operations can be made much simpler by using the right order of operations. Exponents, terms in parentheses, multiplication, division, addition, and finally subtraction are the correct order of operations.
Consider the given expression,
1/2d - 3/4d + 3f - 2f
Here the like terms are '1/2d and 3/4d' and '3f and 2f'.
To simplify the expression,
1/4d + f
Hence, the simplified form of the given expression is, 1/4d + f.
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As mentioned in the chapter, opinion-polling organizations contact their respondents by sampling random telephone numbers. Although interviewers can reach about 76% of U.S. households, the percentage of those contacted who agree to cooperate with the survey fell from 58% in 1997 to only 38% in 2003. Each household, of course, is independent of the others. Using the cooperation rate from 2003, a) what is the probability that the next household on the list will be contacted but will refuse to cooperate? b) what is the probability of failing to contact a house hold or of contacting the household but
a)The probability that the next household on the list will be contacted but will refuse to cooperate will be 0.38
b)The probability of failing to contact a household or of contacting the household but will refuse to cooperate is 0.62.
We are given the information that interviewers can reach about 76% of U.S. households, the percentage of those contacted who agree to cooperate with the survey fell from 58% in 1997 to only 38% in 2003. To calculate these probabilities, we use the cooperation rate from 2003. Since the cooperation rate is 38%, this means that 38% of the people will cooperate and 62% will not cooperate. Therefore, the probability of the next household on the list not cooperating is 0.62 and the probability of the next household on the list cooperating is 0.38.
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As mentioned in the chapter, opinion-polling organizations contact their respondents by sampling random telephone numbers. Although interviewers can reach about 76% of U.S. households, the percentage of those contacted who agree to cooperate with the survey fell from 58% in 1997 to only 38% in 2003. Each household, of course, is independent of the others. Using the cooperation rate from 2003, a) what is the probability that the next household on the list will be contacted but will refuse to cooperate? b) what is the probability of failing to contact a house hold or of contacting the household but will refuse to cooperate
Geometry- Can someone break this down for me in a simple way?
Answer:
z = 22
Step-by-step explanation:
Because we are given that angle measures TUW and VUW are the same, we can assume that both triangles are the same since they also have 90 degree angles and both their third angles are equal to 54. (I found that out by taking 180 degrees which is the total angle measure of all triangles, and subtracted it by 90 and 36).
Since they are the same, that means that side TW is the same length as side VW. With this information we can set up an expression:
2z = z + 22
Now, all we have to do is solve for z
2z = z + 22
-z - z
z = 22
If m<1=55, then find the value of m<3
The measure of angle 3 is given as follows:
m < 3 = 55º.
What are vertical angles?Vertical angles are angles that are opposite by the same vertex on crossing segments, hence they share a common vertex, thus being congruent, meaning that they end up having the same angle measure.
The vertical angles in this problem are listed as follows:
1 and 3.2 and 4.The measure of angle 1 is given as follows:
m < 1 = 55º.
Angle 1 and angle 3 are vertical angles, hence the measure of angle 3 is obtained as follows:
m < 3 = 55º.
As angle 3 is congruent to angle 1.
Angles 2 and 4 are also supplementary to angles 1 and 3, meaning that the sum of their measures is of 180º, hence m<2 = m<4 = 125º.
Missing InformationThe diagram is given by the image shown at the end of the answer.
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What is 16/64 simplified?
Answer:
1/2
Step-by-step explanation:
16/64 (divide the numerator and denominator by 4)
-> 4/8 (divide the numerator and denominator by 4)
-> 1/2
Ashley is going to invest in an account paying an interest rate of 5.6% compounded continuously. How much would Ashley need to invest, to the nearest dollar, for the value of the account to reach $2,080 in 16 years?
Rounding to the nearest dollar, Ashley would need to invest $1,062 to reach $2,080 in 16 years at an interest rate of 5.6% compounded continuously.
How can you figure out compound interest in mathematics?Compound interest (CI) is calculated as CI = P(1 + r/100)n - P. To calculate the compound interest value, first compute the amount and then deduct the principal from it.
To find the amount Ashley needs to invest, we can use the formula for continuously compounded interest:
A = P * e^(rt)
where A is the final amount, P is the principal (the initial investment), r is the interest rate, and t is the time in years.
We know that A = $2,080 and r = 5.6% = 0.056, and we want to solve for P. We can rearrange the formula to solve for P:
P = A / e^(rt)
Plugging in the values, we get:
P = $2,080 / e^(0.056 * 16)
The value of e^(0.056 * 16) can be calculated using a calculator or computer, and it is approximately 1.96. Plugging this in, we get:
P = $2,080 / 1.96 = $1062.24
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a special window has the shape of a rectangle surmounted by an equilateral triangle. see the figure. if the perimeter of the window is 16 feet, what dimensions will admit the most light?
A triangle whose sides are all equal is called an equilateral triangle and its area is given by A=[tex]\frac{\sqrt{3} }{4}[/tex] [tex]x^{2}[/tex], where x is the side of the triangle.
The area of a rectangle is found by using the formula
A=lw, where l is the length and w is the width.
The given figure can be split into two shapes: a rectangle and an equilateral triangle as shown in the diagram. Let l be the length of the rectangle.
Add all of the sides of the window and equate their result to 16. Then solve for l.
x + x + l + x + l = 16
3x + 2l = 16
2l = 16 - 3x
l = [tex]\frac{16-3x}{2}[/tex]
The total area of the window will be the sum of the area of the equilateral triangle ABE and the area of rectangle BCDE.
A = [tex]\frac{\sqrt{3} }{4}[/tex][tex]x^{2}[/tex] + lx
Subsitute [tex]\frac{16-3x}{2}[/tex] for l into the obtained equation and simplify.
A =[tex]\frac{\sqrt{3} }{4}[/tex][tex]x^{2}[/tex] + ( [tex]\frac{16-3x}{2}[/tex])x
A = [tex]\frac{\sqrt{3} }{4} x^{2}[/tex] + 8x - [tex]\frac{3}{2} x^{2}[/tex]
Differentiate the obtained equation with respect to x and equate the first derivative to 0 to calculate the critical point x .
[tex]\frac{dA}{dx}[/tex] = [tex]\frac{\sqrt{3} }{4}[/tex] (2x) + 8 - [tex]\frac{3}{2}[/tex] (2x)
0 = [tex]\frac{\sqrt{3} }{2}[/tex] x - 3x + 8
x (3 - [tex]\frac{\sqrt{3} }{2}[/tex]) = 8
x = [tex]\frac{16}{6-\sqrt{3} }[/tex]≈3.74887
Again, differentiate the equation
[tex]\frac{dA}{dx}[/tex] = [tex]\frac{\sqrt{3} }{2}[/tex]x - 3x + 8 with respect to x.
[tex]\frac{d^{2}A }{dx^{2} }[/tex] = [tex]\frac{\sqrt{3} }{2}[/tex] - 3
The value of the second derivative is [tex]\frac{\sqrt{3} }{2}[/tex]−3, which is negative. This implies that the area will be maximum at the critical point.
Subsitute x = 3.74887 into the equation
l = [tex]\frac{16-3x}{2}[/tex] and simplify
l = [tex]\frac{16-(3)(.74887)}{2}[/tex] ≈ 2.3767
The maximum light will enter through the window when the triangular portion will have the side length of 3.74887 feet and the dimensions of the rectangular portion will be 3.74887-ft-by-2.3767-ft.
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Gravitational potential energy depends on which two of the following
Gravitational potential energy depends on which two of the following weight and height.
What is Gravitational potential energy ?The energy that an object can possess or acquire when its position changes as a result of a gravitational field is known as gravitational potential energy. The energy connected to gravity or gravity is what is known as gravitational potential energy.
What exactly does GCSE Gravitational Potential Energy mean?The motion, position, and deformation of an object can all contribute to its energy storage. Gravity affects you constantly on Earth. There is a latent (stored) energy present in everyone on Earth's surface. the gravitational potential energy of this.
Answer is - The gravitational potential energy of an object depends upon its weight and height.
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The correct question is -
What two things does gravitational potential energy depend on?
decide whether enough information is given to prove that $\triangle abc\cong\triangle dbe$ using the sss congruence theorem. explain. two triangles, triangle a c b and triangle d e b that share a common vertex b. point b is on the segment a d. in triangle a c b, side a c is marked with single tick, side b c is marked with double ticks and side a b is marked with three ticks. in triangle d e b, side d e is marked with single tick, side b e is marked with double ticks and side b d is marked with three ticks.put responses in the correct input to answer the question. select a response, navigate to the desired input and insert the response. responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. responses can also be moved by dragging with a mouse.you are given that $\overline{ab}\cong$ response area, $\overline{bc}\cong$ response area, and $\overline{ac}\cong$ response area. so, the triangles response area be proven congruent using the sss congruence theorem.
No, enough information is not given to prove that triangles are congruent using the SSS congruence theorem.
The SSS congruence theorem expresses that assuming in two triangles, three sides of one are consistent to three sides of the other, then, at that point, the two triangles are said to be congruent.
Now, we are given that triangle ACB and triangle DEB that share a common vertex b. So, both triangles share a common side. So, one side is same for both of triangles.
From the diagram, we can see that both triangles opposite side are equal. So, second side is equal for both of triangles.
Now, from the diagram, we can see that both triangles vertically opposite angles are equal. So, we have two sides equal and one angle is equal.
So, given triangle is proved to congruent by SAS congruency not by SSS congruency.
Hence, enough information is not given.
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5pages in a book have pictures and if there are 40pages in the book what percent of the book has pictures
Answer:
12.5%
Step-by-step explanation:
First,
take 5 page and divide by total amount in book 40 pages.
5/40 = 0.125.
Second,
To get percent multiply by 100.
0.125*100 = 12.5%
Y=-3x²+26x–46
x+y = 8
Answer:
-3x^2--20x+(y-8)=0
The value of x is the equation X + 5 = 12 is
Answer:
x+5=12
or,x=12-5
or,x=7
When archeologists excavate a site, they mark it off with a coordinate grid so that they can easily
identify where artefacts are found and keep a record of the site forever. At the West Kennet Long
Barrow in England, a grave site back to 3600 BCE was found. There are three chambers at the
coordinates (7,9), (17, 33) and (-36,41). It has been said that they form an isosceles triangle with
height twice the length of its base.
Determine whether the statement is true. Justify your answer. Hint: An isosceles triangle has at
least two sides of equal side lengths.
What is the measure of angle B in this triangle?
Enter your answer in the box.
m∠B=
By using the fact that the sum of all internal angles must be equal to 180°, we will see that the measure of angle B is 70°.
How to find the measure of angle B?Remember that the sum of the internal angles of a triangle is always equal to 180°, then we can write the linear equation:
40° + (2x - 30°) + (x + 20°) = 180°
(2x - 30°) + (x + 20°) = 180° - 40°
2x + x - 30° + 20° = 140°
3x = 140° + 30° - 20°
3x = 150°
x = 150°/3
x = 50°
Then the measure of angle B is (2x - 30°) = (2*50° - 30°) = 70°.
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The correct answer is 70
Which of the following system of equations has no solution?
O 3x - y = 2,9x - 3y = 6
O 4x - 7y + 28 = 0,5y - 7x + 9 = 0
O 3x - 5y - 11 = 0,6x - 10y - 7 = 0
O None of these
4x - 7y + 28 = 0,5y - 7x + 9 = 0 is the system of equation that has no solution.
What is meant by system of equation?A group of equations comprising one or more variables is known as a system of equations. The variable mappings that satisfy each component equation, or the points where all of these equations cross, are the solutions of systems of equations.
Name three types of system of equation.Dependent, Independent and inconsistent are the three types of system of equation.
If we solve this system of equation we will get complex roots that means it has no solution.
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Question
Find the range of the function represented by the list of ordered pairs below.
((-9, 4). (-0,3). (-8,0). (-2, -4))
Answer: {4,3,0,-4}
Step-by-step explanation:
The range is the set of all the values of y
Range {4,3,0,-4}
distance formula definition
The distance formula is a mathematical equation that can be used to calculate the distance between two points in a coordinate system. It is typically expressed as d = √(x2−x1)2+(y2−y1)2, where (x1,y1) and (x2,y2)
The distance formula is an equation used to calculate the distance between two points in a coordinate system. To use it, you must know the x- and y-coordinates of each point. The equation is expressed as d = √(x2−x1)2+(y2−y1)2, where (x1,y1) are the x- and y-coordinates of the first point, and (x2,y2) are the x- and y-coordinates of the second point. The result, d, is the distance between the two points. To calculate the distance, you must first subtract the x-coordinate of the first point from the x-coordinate of the second point, then square the result. Next, subtract the y-coordinate of the first point from the y-coordinate of the second point and square the result. Finally, add the two squared numbers and take the square root of the sum. The result is the distance between the two points.
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There were 900 freshwater fish at an aquarium 212 fish are in the large tank there are 16 fish in each smaller tank How many smaller tanks are there
Answer: 43 small tanks
Step-by-step explanation:
First, take 900 - 212 = 688 fish in small tanks
Then take 688 divided by 16 fish in each tank = 43
So there are 43 smaller tanks
Please help, giving thanks and brainliest:) (Please give an explanation if possible and please dont give a fake answer)
Answer: h = 92
Step-by-step explanation:
148 - 180 = 32
32 + 56 = 88
88 - 180 = 92
1. Noah placed an empty bowl on a scale. He added different amounts of a liquid to the bowl, recording the amount of liquid added, in tablespoons, and the total weight of the bowl and liquid, in grams, each time on a scatter plot. He fit the line
y = 14.75x+861.82 to the data in his scatter plot, where x represents the amount
of the liquid, in tablespoons, and y represents the total weight of the bowl and the
liquid, in grams. Determine the weight, in grams, when 18 tablespoons on the liquid are placed in the bowl. determine the approximate number of tablespoons of the liquid noah needs to add so that the total weight is 1,200 grams
1. The weight for 18 tablespoons is 1127.32 grams.
2. The number of tablespoons of the liquid noah needs to add so that the total weight is 1,200 grams is 23 tablespoon.
What is the weight when 18 tablespoons on the liquid are placed in the bowl?It's vital to note that an equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario.
From the information, Noah placed an empty bowl on a scale and the equation is given as:.
y = 14.75x + 861.82
x = the amount of the liquid, in tablespoons
y = the total weight
The weight for 18 tablespoons will be:
y = 14.75x + 861.82
y = 14.75(18) + 861.82
y = 1127.32
The liquid that Noah needs to add so that the total weight is 1,200 gram will be:
y = 14.75x + 861.82
14.75x + 861.82 = 1200
Collect like terms
14.75x = 1200 - 861.82
14.75x = 338.18
Divide
x = 138.18 / 14.75
x = 23
The tablespoons is 23.
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Kenneth drove 187.6 miles in 1.85 hours. What was his average speed?
