Perform the indicated operation and express the result as a simplified complex number.
6 + 7i
6-7i
Answers
The value of complex number 6 + 7i / 6-7i is -13 / 85 + 84i/85
What are complex numbers?Complex numbers are those that are represented as a+ib, where a and b are actual numbers and I is a fictitious number termed a "iota." I has the value (-1). As an illustration, the complex number 2+3i is made up of the real number 2 (Re) and the imaginary number 3i (Im).
Given the complex number is -
6 + 7i / 6-7i
⇒ 6 + 7i / 6 - 7i × 6 + 7i / 6 + 7i
⇒ (6+7i)² / 6² - 7²(i²)
Using (a+b)² = a² + b² + 2ab
⇒ 6² + (7i)² +2(6)(7i) / 36 - 49(-1)
⇒ 36 - 49 + 84i / 36 + 49
⇒ -13 + 84i / 85
⇒ -13 / 85 + 84i/85
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Related Questions
An equilateral triangle is inscribed in a circle of radius 2r. express the area a within the circle but outside the triangle as a function of the length 3x of the side of the triangle.
Answers
The expression for the area within the circle but outside the triangle as a function of the length 3x of the side of the triangle is [tex]\frac{88r^2}{7}-\frac{9\sqrt{3} }{2}x^2[/tex].
It is given that:-
Radius of circle = 2r
Length of side of equilateral triangle = 3x
We have to find the expression for the area within the circle but outside the triangle as a function of the length 3x of the side of the triangle.
We know that,
Area of circle = [tex]\pi R^2[/tex]
Where R is the radius of the circle.
We have R = 2r
Area of an equilateral triangle = [tex]\frac{\sqrt{3} }{2}a^2[/tex]
Where, a is the length of side of equilateral triangle.
a = 3x
Hence,
Expression = [tex]\pi R^2-\frac{\sqrt{3} }{2}a^2[/tex]
Expression = [tex]\frac{22}{7}*(2r)^2-\frac{\sqrt{3} }{2}*(3x)^2 = \frac{88r^2}{7}-\frac{9\sqrt{3} }{2}x^2[/tex].
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Find the volume of the solid.
The volume of the solid is
cubic centimeters.
Answers
Answer:
27
Step-by-step explanation:
4.5*3*2 = 27
hi,
You just have to multiply the three measures.
So :
2*3*4.5 = 27 cm³
Easy, is it not ?
Laila needs 6 1/4 feet of chain to complete a project an outdoor project. She has two small pieces measuring 1 1/4 feet and 2 1/2 feet. How many feet of chain does laila need to purchase?
Answers
First you want to make the fractions have equal denominators. So you want to convert 1/2 to 2/4. Now you can add 1 1/4 to 2 2/4. After adding that subtract it from 6 1/4. Whatever your answer is will be how much more she needs.
Arianna buys computer games from an online store. each game she orders costs $22 and shipping for her total is $9. arianna can spend no more than $75. how many computer games can arianna buy?
Answers
There are 3 computer games she can brought at $75.
Unitary method
Unitary method is defined as the process of finding the value of a unit and then the value of a required number of units.
Given,
Arianna buys computer games from an online store.
Each game she orders costs $22 and shipping for her total is $9.
Arianna can spend no more than $75.
Here we need to find how many computer games did Arianna Brought.
Let x be the number of computer games she brought.
We know that,
Cost for one game = $22
Shipping cost = $9.
She spent = $75.
So, it can be written as,
=> 22x + 9 = 75
=> 22x = 75 - 9
=> 22x = 66
=> x = 66/22
=> x = 3.
So, she can brought 3 computer games at $75.
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let f (t) be the population (in thousands of people) of math city, as a function the time t (in years), where t
Answers
The mean is the population of city in 2026.
What is the short definition of a linear equation?
An algebraic equation of the form y=mx+b is referred to as a linear equation. m is the slope, and b is the y-intercept, and all that is involved is a constant and a first-order (linear) term. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."a) From the meaning of title -
f(t) = 3000t + 34000 { from 2020 it will be increase by 300 people
per year}
b) f(b) = 3000 × 6 + 34000
= 18000 + 34000
= 52000
The mean is the population of city in 2026.
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The complete question is -
Let f(t) be the population (in thousands of people) of Math City, as a function the time t (in years), where t = 0 corresponds to the year 2020. In 2020, the population was 34000, and each year the population increases by 3000 people. (a) Model the population by finding a formula for f(t), using the appropriate choice of a linear, polynomial, power, trigonometric, or exponential function, or a piecewise combination thereof. (b) Evaluate the expression f(6), and write a sentence explaining what this means. (c) Solve the equation f(t) = 64, and write a sentence explaining what this means
15. On the cross-country team, 7th graders
are required to run x number of miles each
morning. 8th graders are required to run 15%
more than the 7th graders. Which expression
represents the number of miles an 8th grader
is required to run?
Answers
If we know the distance of an object from earth, we can determine the size of the object by measuring its parallax. True or false?.
Answers
False, If we know the distance of an object from earth, we can determine the size of the object by measuring its parallax.
The size of an object can be calculated by measuring its parallax if we know how far it is from Earth. According to the heliocentric theory of the universe, Earth is the center of the universe, and everything else revolves around it. A planet's speed is unaffected by the location of the planet within its orbit.
What is parallax explain?
Particularly: the angular difference in direction of a celestial body as measured from two places in the earth's orbit. the apparent displacement or the difference in apparent direction of an object as observed from two separate points that are not on a straight line with the object.Learn more about parallax
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Are f(x) = 2x+4, g(x) = x-2 inverse of each other?
Answers
Answer:
This problem has been solved! See the answer Show transcribed image text Expert Answer Transcribed image text: Decide whether or not the functions are inverses of each other. f (x) = 2x + 4, g (x) = x – 2 no yes The function fis one-to-one.
Step-by-step explanation:
[HELP] For j(x) = [tex]5^x^-^3[/tex], find j of the quantity x plus h end quantity minus j of x all over h period
the quantity x minus 3 end quantity times the quantity 5 to the power of h plus 1 end quantity all over h [tex]\frac{(x-3)(5^2+1)}{h}[/tex]
5 to the power of the quantity x minus 3 end quantity times the quantity 5 to the power of h end quantity all over h [tex]\frac{5^x^-^3(h^h)}{h}[/tex]
5 to the power of the quantity x minus 3 end quantity times the quantity 5 to the power of h plus 1 end quantity all over h [tex]\frac{5^x^-^3(5^h+1)}{h}[/tex]
5 to the power of the quantity x minus 3 end quantity times the quantity 5 to the power of h minus 1 end quantity all over h [tex]\frac{5^x^-^3(5^h-1)}{h}[/tex]
Answers
The difference quotient of the function that has been presented to us will turn out to be 5.
How can I calculate the quotient of differences?In this step, we wish to determine the difference quotient for the function that was supplied.
To begin, keep in mind that the difference quotient may be calculated by:
Lim h->0 [tex]\frac{f(x+h)-f(x)}{h}[/tex]
Now, for the purpose of the function, we need this:
Then we will have:
[tex]$$\begin{aligned}&\lim _{h \rightarrow 0} \frac{j(x+h)-j(x)}{h} \\&\lim _{h \rightarrow 0} \frac{5 *(x+h)-3-5 * x+3}{h} \\&\lim _{h \rightarrow 0} \frac{5 x+5 h-3-5 x+3}{h} \\&\lim _{h \rightarrow 0} \frac{5 h}{h}=5\end{aligned}$$[/tex]
j(x) = 5x - 3
Then the following will be true:
Therefore, 5 is the value of the difference quotient for j(x) is %
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How is solving an equation with the variable on both sides of the equation the same as and different from solving an
equation with the variable on one side of the equation?
Answers
Answer:
when the variable is on both sides of the equation first collect the same variable in one side end evaluate it,
Step-by-step explanation:
when solving the them, we collect like term and put the same term in one side to other
Simplify m7m−4.
please please helpppp
Answers
Answer:
[tex]m^8-4[/tex]
Step-by-step explanation:
[tex]Rule: a^b\cdot \:a^c=a^{b+c}\\=m^7m=m^{7+1}\\=m^{7+1}-4\\=m^8-4[/tex]
Without making any calculations, which data set has the smallest standard deviation? 1, 1, 2, 2, 3, 3 1, 3, 5 0, 1, 5, 6, 9, 10 1, 1, 1, 1, 2, 2, 2, 2
Answers
Answer: 0
Step-by-step explanation:
Answer:
The answer is A
Step-by-step explanation:
What am I doing wrong here? Please help!
Answers
Answer:
If there are dotted lines available then use dotted lines for the range where its only greater than or less than, when there is no equals to sign then you use dotted lines
Step-by-step explanation:
Find the value of sin c
Answers
Check the picture below.
[tex]\textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies c=\sqrt{a^2 + b^2} \qquad \begin{cases} c=hypotenuse\\ a=\stackrel{adjacent}{7}\\ b=\stackrel{opposite}{\sqrt{95}}\\ \end{cases} \\\\\\ c=\sqrt{7^2~~ + ~~(\sqrt{95})^2}\implies c=\sqrt{49+95}\implies c=\sqrt{144}\implies c=12 \\\\[-0.35em] ~\dotfill\\\\ sin(C )=\cfrac{\stackrel{opposite}{\sqrt{95}}}{\underset{hypotenuse}{12}}\implies sin(C)\approx \text{\LARGE 0.81}[/tex]
Evaluate 2d+32 when d=8.
Answers
Given [tex]2d+32[/tex]
[tex]d=8[/tex]
Put the value of d in the given equation
[tex]2d+32[/tex]
[tex]2(8)+32[/tex]
[tex]16+32[/tex][tex]= 48[/tex]
What we do in Evaluation in math?
The verb "evaluate" is used in mathematics to mean to discover or determine the worth of something. Finding the precise value of an algebraic expression or numerical computation is relevant here as well as financial mathematics.
In mathematics, the terms "evaluate" and "solve" are often used interchangeably. Consider the following basic multiplication problem: "Evaluate the cost of six tomatoes when the tomatoes are purchased at $2 each." The student would multiply 6 by 2 to get the result of $12. The term evaluate might also come before a list of inquiries, as a list of straightforward algebraic equations.
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One batch of brown paint uses 8 of yellow paint and 3 cups of purple paint Tyler made a large amount of brown paint using 40 cups of yellow paint
Answers
Answer:
not sure what you were asking, but its 15 cups of purple paint
Beginning with the graph of f(x) = x2, what transformations are needed to form g of x equals one half times the quantity x plus 4 end quantity squared minus 3 question mark
The graph of g(x) is narrower than f(x) and is shifted to the right 4 units and down 3 units.
The graph of g(x) is narrower than f(x) and is shifted to the left 4 units and down 3 units.
The graph of g(x) is wider than f(x) and is shifted to the left 4 units and down 3 units.
The graph of g(x) is wider than f(x) and is shifted to the right 4 units and down 3 units.
Answers
Beginning with the graph of f(x) = x2, The transformations that are needed to form [tex]g(x)=\frac{1}{2}(x+4)^2-3[/tex] is
The graph of g(x) is wider than f(x) and is shifted to the left 3 units and down 3 units
This is further explained below.
What is transformations?Generally, A point, a line, or a geometric figure may undergo one of these four distinct transformations in order for the point's, line's, or figure's shape and/or location to be altered.
The shape of the item as it was before the transformation is referred to as the Pre-Image, while the shape and location of the object after the change make up the Image.
In conclusion, The necessary transformations may be found by beginning with the graph of the function f(x) = x2.
[tex]g(x)=\frac{1}{2}(x+4)^2-3[/tex]
The graph of g(x) is bigger than the graph of f(x), and it is displaced 3 units to the left and 3 units down from its original position.
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Answer:
The graph of g(x) is wider than f(x) and is shifted to the left 4 units and down 3 units.
Step-by-step explanation:
I got it right.
Point S is located at -10. Points T and U are each 5 units away from point S. Where are T and U located?
Answers
2/14 in simplist form
Answers
Answer: 1/7 or 0.142857
Step-by-step explanation:
Answer:
1/7 :)
Step-by-step explanation:
Which equation represents a linear function? Iready- Understand functions, Level H.
Answers
Answer:
y = 4x + 5
Step-by-step explanation:
y = 4x + 5 is the only one that graphs a straight line
Find the value of |-4 + 3| · 8.
-8
56
8
-56
?
Answers
The value of expression |-4 + 3| · 8 is 8.
What is Modulus function?
A modulus function is a function which gives the absolute value of numbers or variable.
The expression is given as;
| -4 + 3 | * 8
Now, Solve the expression as;
⇒ | -4 + 3 | * 8
⇒ | - 1 | * 8
⇒ 1 * 8
⇒ 8
Since, Modulus of a negative number gives the positive of that number.
Hence, The value of expression |-4 + 3| · 8 is 8.
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Each leg of an isosceles triangle is twice as long as its base. Express the perimeter in terms of the length of the base.
Answers
The perimeter of the triangle in discuss expressed in terms of the length of the base as required in the task content is; Perimeter= 5x.
What is the perimeter of the isosceles triangle in terms of the length of the base?According to the task content, it follows that the perimeter of the triangle in terms of the length of the base is to be determined.
Let x = length of the base
Therefore, length of each leg = 2x.
Therefore, since the perimeter of the triangle is the sum of all sides; it follows that we have;
Perimeter = x + 2x +2x
Perimeter = 5x.
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Match the imaginary solutions with the correct simplified forms:
Answers
Answer:
See the picture below.
Step-by-step explanation:
Answer:
[tex]\sqrt{-63}=3i\sqrt{7}[/tex]
[tex]\sqrt{-156}=2i\sqrt{39}[/tex]
[tex]6\sqrt{-12}=12i\sqrt{3}[/tex]
[tex]-5\sqrt{-75}=-25i\sqrt{3}[/tex]
Step-by-step explanation:
An imaginary number is a non-zero real number multiplied by the imaginary unit [tex]i[/tex].
[tex]\boxed{\begin{minipage}{4 cm}\begin{center}\underline{Imaginary Number Rule}\end{center}\\\begin{center}$\sqrt{-1}=i$\end{center}\end{minipage}}[/tex]
[tex]\boxed{\begin{minipage}{4 cm}\begin{center}\underline{Radical Rule}\end{center}\\\begin{center}$\sqrt{a \cdot b}=\sqrt{a} \sqrt{b}$\end{center}\end{minipage}}[/tex]
[tex]\begin{aligned}\sqrt{-63} & = \sqrt{9 \cdot -1 \cdot 7}\\& = \sqrt{9}\sqrt{-1}\sqrt{7}\\& = 3i\sqrt{7}\end{aligned}[/tex]
[tex]\begin{aligned}\sqrt{-156} & = \sqrt{4 \cdot -1 \cdot -39}\\& = \sqrt{4} \sqrt{-1} \sqrt{39}\\& = 2i\sqrt{39}\end{aligned}[/tex]
[tex]\begin{aligned}6 \sqrt{-12} & = 6 \sqrt{4 \cdot -1 \cdot -3} \\& = 6 \sqrt{4} \sqrt{-1} \sqrt{3} \\& = 6 \cdot 2 i \sqrt{3} \\& = 12i \sqrt{3}\end{aligned}[/tex]
[tex]\begin{aligned}-5 \sqrt{-75} & = -5 \sqrt{25 \cdot -1 \cdot -3} \\& = -5 \sqrt{25} \sqrt{ -1 } \sqrt{3} \\& = -5 \cdot 5i \sqrt{3} \\& = -25i \sqrt{3}\end{aligned}[/tex]
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Fatima is selling cookies in a bake sale. She packages 20 cookies in 4 minutes. Describe the relationship between the amount of cookies and the time it takes to package them.
Answers
Based on the number of cookies that Fatima was able to package in a certain amount of time, the relationship between the cookies and the time it takes to package them is a single cookie is packaged in 12 seconds.
How long does it take to package the cookies?To find the amount of time it takes to package the cookies, the formula is:
= Number of minutes / Number of cookies
= 4 / 20
= 1/5
= 0.20 minutes
When converted to minutes, this is:
= 0.20 x 60 seconds per minute
= 12 seconds
In conclusion, it takes 12 seconds to package a cookie on average.
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If a person with an hourly pay of $9.50 per hour gets a 20$ raise, what is the new hourly pay?
Percent formula, show your work
Answers
======================================================
Work Shown:
20% of $9.50 = 0.20*9.50 = 1.90
You earn an extra $1.90 on top of the $9.50 already there. So the new wage is 9.50 + 1.90 = 11.40 dollars per hour
-----------
Shortcut:
1.20*9.50 = 11.40
Think of 1.20 as 100% + 20% = 1 + 0.20 = 1.20, and this represents an increase of 20%
PLEASE HELP!!!!! please? :D
Answers
Answer:
9
Step-by-step explanation:
→ Substitute in the values
2³ +√64 ÷ 8
→ Simplify
8 + 8 ÷ 8
→ Calculate
8 + 1 = 9
Answer:
9
Step-by-step explanation:
2 to the power of 3 is 8
8 + 64 = 72
72 ÷ 8 = 9
What is the price of a perpetuity that has a coupon of $55 per year and a yield to maturity of 2.5%? the price of the perpetuity is $?
Answers
The price of the perpetuity is $2200
What is price of the perpetuity?The present value of a perpetuity is determined by simply dividing the amount of the regular cash flows by the discount rate. A growing perpetuity includes a growth rate that increases the cash flows received each period going forward.
Given:
coupon=$55
yield to maturity=2.5%
As, we know price of the perpetuity is determined by dividing the coupon by the yield to maturity.
So,
price=coupon/yield to maturity
price=$55/2.5%
price=$2200
Hence, the price of the perpetuity is $2200
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____Is used for examining data with more than two variables, and it includes a different vertical axis for each variable.
Answers
A Scatter plot is used for examining data with more than two variables, and it includes a different vertical axis for each variable.
What is the Scatter plot?The variables in the scatter plot made from the data are described by the independent variable, time, which is graphed along the horizontal axis. The independent variable will be time, and the dependent variable will be the number of calories provided.
When analyzing data with more than two variables, a scatter plot is used, which has a separate vertical axis for each variable.
Therefore, a scatter plot is used for examining data with more than two variables, and it includes a different vertical axis for each variable.
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In FGH, g = 140 inches, f= 980 inches and to the nearest degree.
Answers
Answer:
1204.7 in
Explanation:
(3x^3)^3 is equivalent to
Answers
Answer: (3x^3)^3 = 3^3 (x^3)^3 = 27 (x^3)^3 = 27^3x3 = 27^9
27^9
Answer:
27x^9
Step-by-step explanation:
Distribute.
3^3 (x^3)^3
27 (x^3)^3
Power of a power.
27x^3 times 3
Multiply.
27x^9
