The subtraction of complex numbers [tex]z_{1} -z_{2}[/tex] is cos(π)+i sin(π).
Given [tex]z_{1} =\sqrt{2}[/tex][cos(3π/4+i sin(3π/4) and [tex]z_{2}[/tex]=cos (π/2) +i sin(π/2)
We have to find the value of [tex]z_{1} -z_{2}[/tex].
A complex number is a number that includes real number as well as a imaginary unit in which [tex]i^{2} =1[/tex]. It looks like a+ bi.
We have to first solve [tex]z_{1} and z_{2}[/tex] and then we will be able to find the difference.
[tex]z_{1} =[/tex][tex]\sqrt{2}[/tex][ cos (3π/4)+i sin (3π/4)]
[tex]=\sqrt{2}[/tex][cos(π-π/4)+ i sin (π-π/4)]
=[tex]\sqrt{2}[/tex] [-cos(π/4)+sin (π/4)]
=[tex]\sqrt{2}[/tex](-1/[tex]\sqrt{2}[/tex]+1/[tex]\sqrt{2}[/tex])
=[tex]\sqrt{2} *0[/tex]
=0
[tex]z_{2} =[/tex]cos(π/2)+i sin (π/2)
=0+i*1
=1
Now putting the values of [tex]z_{1} and z_{2}[/tex],
[tex]z_{1} -z_{2} =0-1[/tex]
=-1
=-1+i*0
=cos (π)+i sin(π)
Hence the value of difference between [tex]z_{1} and z_{2}[/tex] is cos(π)+i sin(π).
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Select the correct answer.
Here's another plant stand. It has 2 rows, each holding 4 plants. Suppose this plant stand is turned upright.
Choose the number sentence that represents the plants on the upright plant stand.
8 × 1 = 8
4 × 2 = 8
2 × 2 = 4
4 × 4 = 16
The number sentence that gives the best representation of the plants on the upright stand is 8 × 1 = 8.
How to solve for the plant on the upright stand.Given that the plant is said to be upright, then the number of row would be seen as 1.
The rows of the plants are made up of 2 and the plants in them are said to be 4. Hence we would have 4 x 2 = 8
From here we would conclude that 8 × 1 = 8 is the plants on the upright stand.
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What method of matrixes would be used for this question? ( Inverse Matrices, Cramer's Rule, Gaussian Elimination, and Gauss-Jordan Elimination)
John had $24,500 to invest. He divided the money into three different accounts. At the end of the first year he had made a total of $1,300 in interest between the three accounts. If the first account earned 4% interest on its original amount for the year, the second account earned 5.5% interest on its original amount for the year, and the third account earned 6% interest on its original amount for the year. Also, the amount of money in the first account was 4 times the amount in the second account. How much had he originally placed in each account?
Answer:
The method of matrixes that would be used for this question is Gaussian Elimination.
Step-by-step explanation:
Gaussian Elimination is a method of solving linear equations by transforming them into upper triangular form. In this case, we want to solve for the original amount of money placed in each account, which can be represented by variables x, y, and z. We can set up the equations as follows:
4x + 5.5y + 6z = 1,300
x + y + z = 24,500
4x = y
We can then use Gaussian Elimination to solve for x, y, and z.
Henry begins a savings account with $500. The savings account accumulates 2.5% annual interest based on the equation Vh=500(1.025)^t , where Vh is the value of the account after t years. Andres begins a savings account three years later with the same initial amount of money at the same interest rate. Which equations represent the value of Andres’s account after t years?
A) Va=500(1.025)^t-3 and Va=464.30(1.025)^t
B) Va=500(1.025)^t+3 and Va=538.45(1.025)^t
C)Va=500(1.025)^t-3 and Va=538.45(1.025)^t
D)Va=500(1.025)^t+3 and Va=464.30(1.025)^t
The exponential function that represents the value of Andres’s account after t years is:
A) Va=500(1.025)^t-3 and Va=464.30(1.025)^t
What is the equation for the value of Andres's account?For Henry, it is given by:
[tex]Vh = 500(1.025)^t[/tex]
Andres starts 3 years later than Henry, hence the equation is:
[tex]Va = 500(1.025)^{t - 3}[/tex]
Applying an exponential simplification, we have that:
[tex]Va = 500\frac{1.025^t}{1.025^3} = 464.3(1.025)^t[/tex]
Hence option A is correct.
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You are 22 years old and are starting a savings plan and will deposit $200 every 2 months until you retire. The account will give you 7% interest. How much do you expect your account to be worth when you retire at 67 years old?
Answer:
Formulae can be searched for confirmation : compounding interest with regular payments
Step-by-step explanation:
Calculations do it by yourself
Answer:
clchjtdjgdtklgdlnajajhbshsjzsnnjdndmqjsnsn him
Taylor earned the following scores on her first ten quizzes. What would she need to earn on the eleventh test in order to have a mean score of 87? 78, 92, 98, 87, 86, 72, 92, 81, 86, 92
A mean is an arithmetic average of a set of observations. The score that Taylor needs to make in her eleventh test for the average to be 87 is 93.
What is Mean?A mean is an arithmetic average of a set of observations. it is given by the formula,
Mean = (Sum of observations)/Number of observations
The score earned by Taylor in her first 10 test are 78, 92, 98, 87, 86, 72, 92, 81, 86, 92. Also, she wants the average to be 87, therefore, we can write,
(78 + 92 + 98 + 87 + 86 + 72 + 92 + 81 + 86 + 92 + x)/11 = 87
864 + x = 957
x = 93
Hence, The score that Taylor needs to make in her eleventh test for the average to be 87 is 93.
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Simplify the expression: 2 * | 12 - 14 | =
[tex]2 \times |12-14|=2 \times |-2| =2\times 2=\boxed{4}[/tex]
Divide. Write the quotient in lowest terms.
Answer:
11/12
Step-by-step explanation:
2 3/4 ÷ 3
11/4 ÷ 3
11/4 × 1/3
11/12
Answer:
Hello! The answer is 11/12.
Step-by-step explanation:
Convert improper fractions:
[tex]2\frac{3}{4} \\= \frac{11}{4}[/tex]
Change 3 to its reciprocal:
[tex]\frac{1}{3}[/tex]
Multiply:
[tex]\frac{11}{4} * \frac{1}{3} \\= 11/12[/tex]
If 12 +22+ 32 +
+ 5122
= m, then 22 +42 +62+ 10242 is
equal to:
4m
2m
3m
M2
M4
Answer:
m2
Step-by-step explanation:
the 2nd equation is double the first one and the first one is 1
!!HELP!! PLEASE I NEED THIS DONE IN AN HOUR IF ANYONE CAN HELP
Answer:
the 1st answer is x = 5, the 2nd answer is x = 7, the 3rd answer is x = 4, the 4th answer is: x = 4, the 5th answer is the exact form: x = - 1/3 but the decimal form is: x = - 0.3, the 6th answer is x = 3.
Brainliest?
Do you know the answer to 8+(10-4)-3*2 and how to solve it?
Answer:
8
Step-by-step explanation:
10 minus 4 goes first because of BODMAS so thats 6
then 3 times 2 because again bodmas to thats 6
so then its 8 + 6 - 6
can be done in any order not affected by bodmas
6-6 cancels out so the answer is 8
comment if you want an in depth explanation on bodmas lol
A landscaping company is hired to mow the grass for several large properties. The total area of the properties combined is 1,345 acres. The rate at which one person can mow is as follows:
ŷ = 1350 – 1.2x where x is the number of hours and ŷ represents the number of acres left to mow.
How many acres will be left to mow after 20 hours of work?
How many acres will be left to mow after 100 hours of work?
How many hours will it take to mow all of the lawns? (When is ŷ = 0?)
Using the given linear function, we have that:
After 20 hours, 1326 acres will be left to mow.After 100 hours, 1230 acres will be left to mow.It will take 1125 hours to mow all the lawns.What is the linear function?
The linear function for the number of acres left to mow after x hours is given as follows:
y = 1350 - 1.2x.
After 20 hours, the number acres is given as follows:
y = 1350 - 1.2(20) = 1326.
After 100 hours, the number acres is given as follows:
y = 1350 - 1.2(100) = 1230.
The time it takes to mow all the lawns is given by:
1350 - 1.2x = 0.
1.2x = 1350
x = 1350/1.2
x = 1125 hours
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En la feria el juego de gusano da 5 vueltas y equivale a 150 metros, calcula a cuento equivale lo siguiente: 8/4 de vuelta =_____3 4/6 de vuelta =_____1 4/6 de vuelta= _____3/4 de vuelta= ___4/6 de vuelta= ____7/9 de vuelta =___
las ecuaciones con fracciones dan:
8/4 de vuelta = 60m(3 + 4/6) de vuelta = 110m4/6 de vuelta = 20m3/4 de vuelta = 22.5m7/9 de vuelta= 23.33 m¿Cuanto vale cada una de las expresiones?Sabemos que 5 vueltas es igual a 150 metros, entonces cada vuelta es equivalente a:
v = 150m/5 = 30m
Es decir, cada vuelta equivale a 30 metros.
Ahora simplemente podemos resolver las ecuaciones con fracciones:
8/4 de vuelta = (8/4)*30m = 60m(3 + 4/6) de vuelta = (3 + 4/6)*30m = 110m4/6 de vuelta = (4/6)*30m = 20m3/4 de vuelta = (3/4)*30m = 22.5m7/9 de vuelta = (7/9)*30m = 23.33 mSi quieres aprender más sobre fracciones:
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pls help! i need an explanation and the steps that show how it’s solved too. tysm!
Answer:
true
Step-by-step explanation:
6(6(13x-2)
36(13x-2)
468x-72
please mark brainliest :D
Answer:
True
Step-by-step explanation:
Given functions:
[tex]\begin{cases}f(x)=3x-7\\g(x)=13x-2\\h(x)=6x\end{cases}[/tex]
[tex]h(h(g(x)))[/tex] is a composite function.
Composite functions are when the output of one function is used as the input of another.
Therefore, the given composite function means to substitute the function g(x) in place of the x in function h(x), then substitute this in place of the x in function h(x).
Step 1
Substitute the function g(x) in place of the x in function h(x):
[tex]\begin{aligned}h(x) & = 6x\\\implies h(g(x)) & =6(g(x))\\& = 6(13x-2)\\ & = 78x-12\\\end{aligned}[/tex]
Step 2
Now substitute the above in place of the x in function h(x):
[tex]\begin{aligned}h(x) & = 6x\\\implies h \left(h(g(x))\right) & =6(h(g(x)))\\& = 6(78x-12)\\& = 468x-72\end{aligned}[/tex]
Therefore, the statement is true.
To carry out the composite function in one step:
[tex]\begin{aligned}h(x) &=6x\\\implies h(h(g(x))) & = 6\:(h(g(x)))\\& = 6(6(g(x)))\\& = 6( 6(13x-2))\\& = 6(78x-12)\\& = 468x-72\end{aligned}[/tex]
Given: 1.1 1.2 1.3 f(x) = 8 +4 x-8
Write down the domain and range off.
Write down the equations of the asympotes of f
Sketch the graph of f clearly showing the intercepts with the axes and the asymptotes.
Answer:
Did you mean " f(x)=8+4^{x-8} ? " The function you entered was linear, meaning there would be no asymptote.
D: (-∞, +∞)
R: (8, +∞)
Horizontal asymptote at y=8
No vertical asymptote
the cost c(x) for a taxi ride is given by c(x) =2x + 3.00, where x is the number of minutes. on a piece of paper graph c(x) =2x + 3.00. then determine which answer matches the graph you drew, including the correct axis
A function assigns the values. The correct option is D.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
The complete options of the question are mentioned in the below image.
The cost cost c(x) for a taxi ride is given by c(x) =2x + 3.00, where x is the number of minutes. Therefore, the graph of the equation can be drawn as shown below.
Hence, the correct option is D.
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if anyone knows how to answer this do so pleass
Answer:
x = 4.08
Step-by-step explanation:
As we now, from Trigonometric Identities
that [tex]tan(\alpha )=\frac{Opposite}{Adjacent}[/tex]So for our Problem , [tex]\alpha =27[/tex] , [tex]Opposite=x[/tex] , [tex]Adjacent = 8[/tex]
by substituting , then [tex]tan(27)=\frac{x}{8}[/tex]
by multiplying both sides by 8 , then [tex]x=8tan(27)=4.0762=4.08[/tex]
Which table matches the graph below
The table that matches the graph shown is the second table.
How to depict the table?It should be noted that in the graph, there's a quadratic equation. The form is given as ax² + bx + c.
When x = 0, y = 2. When x = 1, y is a number between 3 and 4. In the second table x we have y(1) = 7/2. This is in the range.
The graph is attached.
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using this diagram, find x and y
Answer:
x=13
y=11
Step-by-step explanation:
3y+5+52=90
3y=90-57
3y=33
y=33/3=11
4x=52
x=52/4=13
3y+5 and 52 are complementary
3y+5+52=903y+57=903(y+19)=90y+19=30y=11Apply angle sum property
4x+3(11)+5+90=1804x+33+5=904x+38=904x=52x=13The volume of a fish tank is 50 cubic feet. if the density is 0.2 fish over feet cubed, how many fish are in the tank? 5 10 125 250
Answer: 10
Step-by-step explanation:
I just took the test!! :)
Which linear inequality is represented by the graph?
Answer:
y>2/3+3
Step-by-step explanation:
Answer:
y<2/3x+3
Step-by-step explanation:
1. Find the slope, the slope is 2/3
2. Find the y-intercept, the y intercept is 3
3. Make an linear equation out of it, y=2/3x+3
4. Dotted or solid? Its dotted which means the answer has to be greater or less than, not equal or less than or equal or greater than
5. Test you have 2 answer choices y<2/3x+3 or y>2/3x+3, input the origin (0,0)
0<2/3(0)+3, 0<3 which is true
0>2/3(0)+3 0>3 which is false
So y<2/3x+3 is the right answer. :)
A boat is heading towards a lighthouse, whose beacon-light is 148 feet above
the water. The boat's crew measures the angle of elevation to the beacon, 8°.
What is the ship's horizontal distance from the lighthouse (and the shore)?
Round your answer to the nearest hundredth of a foot if necessary.
Answer:
feet
Submit Answer
attempt 1 out of 2 / problem 2 out of max 4
Answer:
x = 1053.07 ft
Step-by-step explanation:
So if you look at the diagram I drew it might become a bit more apparent what you have to do. For this problem you'll need to use one of the six trigonometric functions. In this case you know the angle and the opposite side of the angle, and you need the adjacent side. The trigonometric function tan is defined as [tex]\frac{oppposite}{adjacent}[/tex]. So let's plug in the known values:
[tex]tan(8) = \frac{148}{x}[/tex]
multiply both sides by x
[tex]tan(8) * x = 148[/tex]
Divide both sides by tan(8)
[tex]x=\frac{148}{tan(8)}[/tex]
Calculating tan of 8 degrees using a calculator
[tex]x=\frac{148}{0.141}[/tex]
Simplify
x = 1053.07 ft
The area of the parallelogram below is ____ square meters. A parallelogram with height labeled with 7 meters. The top horizontal side is labeled 6 meters. The base of the left triangle formed by the height is 2 meters. Numerical Answers Expected
The area of the parallelogram in the image given is: 42 m².
What is the Area of a Parallelogram?Area of a parallelogram = base × height
Given the parameters:
Base = 6 metersHeight = 7 metersArea of the parallelogram = (6)(7)
Area of the parallelogram = 42 m²
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If the cost of 5m of cloth is Rs 375,find the cost of 80m of cloth
Step-by-step explanation:
If the cost of 5m cloth is Rs.375
Then cost of 80m cloth is (80m× Rs 375)÷ 5m
then the cost of is 6000 Rs. you can use the criss cross method
5m = 375 Rs
80m = ?
80 × 375 = (30,000) ÷5
?= 6000
What fraction of this shape is shaded?
Time
Running
Give your answer in its simplest form.
Given: -2x^(2)-3x+4=0, use the quadratic formula to solve for the roots
The roots of the quadratic equations are -4 and -1
How to determine the roots-2x^(2)-3x+4=0
Expand the equation first
[tex]-2(x^2 - 3x + 4) = 0[/tex]
Find two factor that are multiples of -8 and sum up to give -3, the facors are -4 and -1
Replace -3x with 4x and -x
[tex]-2(x^2 -4x + x + 4) = 0[/tex]
Factorize the equation
[tex]-2 (x (x + 4) + 1 (x + 4)[/tex]
We have
2(x + 1) = 0 and 2(x+ 4) = 0
2(x + 1) = 0
2x + 2 = 0
x = -1
2(x+ 4) = 0
2x + 8 = 0
x = -8/2
x = -4
Therefore, the roots of the quadratic equations are -4 and -1
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The price of an item has been reduced by 85%. The original price was $33.
Answer:
4.95
Step-by-step explanation:
85% of 33 = 28.5
33 - 28.5 = 4.5
Word problem involving conversion between compound units...
A business based in South Africa pays a consultant in the U.S. 1,570,000 rand per year. Assume that the conversion is 1 rand to 0.074 dollars. What is the
consultant's salary in dollars per month?
First fill in the two blanks on the left side of the equation using two of the ratios. Then write your answer rounded to the nearest hundredth on the right side o
the equation.
Ratios:
1 rand
0.074 dollars
1,570,000 rand
1 yr
0.074 dollars
1 rand
1 yr
12 mo
0
0
I need help with this math problem.
Using proportions, it is found that the consultant's salary in dollars per month is of $9,681.67.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
A business based in South Africa pays a consultant in the U.S. 1,570,000 rand per year. Considering the conversion rate, his salary in dollars per year is given as follows:
S = 1570000 x 0.074 = $116,180.
Since a year has 12 months, his salary in dollars per month is given by:
Sm = $116,180/12 = $9,681.67.
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Please answer all parts as I know the answers but need the work to go with them. Thus, I believe some answers are correct. Thank you!
The approximate 95 % confidence interval for p is found by the formula
p^ ± Z∝/2 √p^q^/n
The sample size n can be found by the
The formula
n= (Z∝/2)² p^q^/e²
The approximate 95 % confidence interval for p is 0.165; 0.243
This indicates 95 % confidence interval level.
A sample of 6239 nonprofits should be surveyed
Solution
Part a:
Sample Proportion p^= 84/412= 0.2038 ≅ 0.204
q^ = 1-p^= 1.0 -0.204= 0.796
The degree of confidence is 95% so z∝/2= 1.96
Putting the values
p^ ± Z∝/2 √p^q^/n
0.204 ± 1.96 √0.204(0.796)/ 412
0.204 ± 0.0389
0.1650 ; 0.2429
0.165; 0.243
The approximate 95 % confidence interval for p is 0.165; 0.243
Part B
This indicates 95 % confidence interval level.
Part C
With ± 0.01 of 0.95 Confidence interval gives range 0.94 to 0.96
For 0.96 interval Z∝/2 = 2.054
For 0.94 interval Z∝/2 = 1.8808
and error e= 0.01
For solving n the formula is
n= (Z∝/2)² p^q^/e²
and e= 0.01
Putting the values
n= 1.96²(0.204)(0.796)/ 0.01²
n= 6238.1437≅ 6238.14
A sample of 6239 nonprofits should be surveyed.
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The data below represents the relationship between the number of incidences of UFO sightings in late 1930s and early 1940s. Draw a scatter plot for the data.
Year of Incidence
1936
1937
1938
1939
1940
1941
1942
1943
1944
1945
1946
Number of Incidences (percent)
0.9
0.8
0.8
1.3
1.4
1.2
1.7
1.8
1.6
1.5
1.5
a.
A graph has years of incidence on the x-axis from 1932 to 1948, and incidence on the y-axis, from 0 to 10. Points are around (1936, 0.9), (1937, 0.8), (1938, 0.8), (1939, 1.3), (1940, 1.4), (1941, 1.2), (1942, 1.7), (1943, 1.8), (1944, 1.6), (1945, 1.5), (1946, 1.5).
c.
A graph has years of incidence on the x-axis from 1932 to 1948, and incidence on the y-axis, from 0 to 10. Points are around (1936, 0.9), (1937, 0.8), (1938, 0.8), (1939, 1.3), (1940, 1.4), (1941, 1.2), (1942, 1.7), (1943, 1.8), (1944, 1.6), (1945, 1.5).
b.
A graph has years of incidence on the x-axis from 1932 to 1948, and incidence on the y-axis, from 0 to 10. Points are around (1936, 0.9), (1937, 1.7), (1938, 0.8), (1939, 1.3), (1940, 1.4), (1941, 1.2), (1942, 1.7), (1943, 1.8), (1944, 1.6), (1945, 1.5), (1946, 1.5).
d.
A graph has years of incidence on the x-axis from 1932 to 1948, and incidence on the y-axis, from 0 to 10. Points are around (1936, 0.9), (1937, 0.8), (1939, 1.3), (1940, 1.4), (1941, 1.2), (1942, 1.7), (1943, 1.8), (1944, 1.6), (1945, 1.5), (1946, 1.5).
The description of graph of the data about relationship of UFO sightings in late 1930s and early 1940s will be :A graph has years of incidence on the x-axis from 1932 to 1948, and incidence on the y-axis, from 0 to 10. Points are around (1936, 0.9), (1937, 0.8), (1938, 0.8), (1939, 1.3), (1940, 1.4), (1941, 1.2), (1942, 1.7), (1943, 1.8), (1944, 1.6), (1945, 1.5), (1946, 1.5).
Given:
Year of incidence percent
1936 0.9
1937 0.8
1938 0.8
1939 1.3
1940 1.4
1941 1.2
1942 1.7
1943 1.8
1944 1.6
1945 1.5
1946 1.5
We have been given the percentages of different years. The points will be (1936,0.9) , (1937,0.8) , (1938,0.8) , (1939,1.3) , (1940,1.4) , (1941,1.2) , (1942,1.7), (1943,1.8) , (1944,1.6) , (1945,1.5) , (1946,1.5).
We have to just plot the points on the graph to find scatter plot. It is called scatter plot as the points are not in line but they are scattered.
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What is the inverse of
F(x) =5x/3+ 5
The inverse function of f(x) = 5x/3 + 5 is f-1(x) = 3x/5 - 3
How to determine the inverse?The function is given as:
f(x) = 5x/3 + 5
Rewrite as:
y = 5x/3 + 5
Swap x and y
x = 5y/3 + 5
Subtract 5 from both sides
x - 5 = 5y/3
Multiply through by 3
3x - 15 = 5y
Divide through by 5
y = 3x/5 - 3
Express as inverse function
f-1(x) = 3x/5 - 3
Hence, the inverse function of f(x) = 5x/3 + 5 is f-1(x) = 3x/5 - 3
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