[tex]2-11i \text{ is the standard form of given expression }[/tex]
Solution:
The standard form of complex number is: a + bi
where a is the real part and bi is the imaginary part
Given expression is:
[tex](2-i)^3[/tex]
Expand the above expression using algebraic identity
[tex](a-b)^3=a^3-b^3-3ab(a-b)[/tex]
[tex]\text{For } (2-i)^3 \text{ we get, a = 2 and b = i}[/tex]
Thus on expanding using the above algebraic identity we get,
[tex](2-i)^3=(2)^3-(i)^3-3(2)(i)(2-i)[/tex]
Simplify the above expression
[tex](2-i)^3=8 -i^3-6i(2-i)\\\\(2-i)^3=8 -i^3-12i+6i^2[/tex]
We know that,
[tex]i^2 = -1\\\\i^3 = -i[/tex]
Substituting in above simplified expression, we get,
[tex](2-i)^3=8-(-i)-12i+6(-1)\\\\(2-i)^3=8 + i -12i -6\\\\\text{Combine the like terms }\\\\(2-i)^3=8 - 6 + i -12i\\\\(2-i)^3=2-11i[/tex]
Thus the given expression is expressed in standard form
A rectangular garage is 6 meters long and 5 meters wide. What is its area?
Answer:
30 meters
Step-by-step explanation:
You MUST multiply 5 and 6 to get 30 to find area you have to multiply length times width
Answer: 30 Meters
Step-by-step explanation: You find area by multiplying length by width. 6 times 5 is 30.
X^-x^4-5x^3+4x-4
Please I need help and please show the steps.
Answer:
1-5x^4x+3 +4x^4x+1 -4x^4x/ x^4x
Step-by-step explanation:
Find the steps in the app photomath it helps.
Write a system of two equations.
A system of linear equation consists of two or more linear equations with the two or more same variables. Such equations are called system of equations (or) simultaneous equations (or) a pair of equations.
Example:
x + y = 5 is one linear equation.
2x – y = 4 is another linear equation.
But x + y = 5, 2x – y = 4 together they form system of linear equation.
The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.
Answer:
A liner equation is an equation between two variables that gives a straight line when plotted on a graph.A system of linear equation consists of two or more linear equations with the two or more same variables.
Step-by-step explanation:
x + y = 5 and 2x – y = 4 together they form a linear equation.
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At a restaurant, bill and his four friends decided to divide the bill evenly. If each person paid $12, what was the total bill?
Answer:
total=$60
Step-by-step explanation:
Including bill there's a total of 5 people
take what each person paid, $12, and multiply by the number of people
$12(5)=$60
The total bill at the restaurant was $60, calculated by multiplying the amount each person paid ($12) by the number of people (5).
Explanation:In this Mathematics problem, Bill and his four friends, for a total of five people, decided to equally divide the restaurant bill. Each person paid $12. In order to find the total bill, we must multiply the amount each person paid by the number of people. This means, we multiply $12 by 5, which gives us a total bill of $60.
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Tomorrow I have a math midterm at 11:45a.m. and it is 9:30 p.m. I am going over the material and I really don't know it. What should I do? ( I only have to be at school for the test so 2 hours)
Answer: don't be scared to ask your teacher for help.
Step-by-step explanation:
You should try the best you can with whatever you got. Start with what you know and build from that to study in areas you aren't familiar with. Given the time constraints, you won't be able to get everything; however, you should be able to learn a few things, which is better than nothing. For any specific math questions you have, make a new post and I'll come take a look (or another helper will be able to help).
evaluate x+6 when x=7
Therefore, the solution of the given equation is [tex]13[/tex].
What is the simplification?
Simplification is reducing the expression/fraction/problem in a simpler form. It makes the problem easy with calculations and solving.
Here given equation is
[tex]x+6[/tex]
when [tex]x=7[/tex]
So, it would be
[tex]x+6=7+6\\=13[/tex]
Hence, the solution of the given equation is [tex]13[/tex].
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Lulu is taking a road trip to visit family. Her car has a 20-gallon gas tank and the car uses 12 gallons to travel 216 miles.
Which linear equation represents the number of gallons of gas, G, left in the tank after driving m miles?
A. G = 360 - 18m
B. G = 20 - 18m
c. G=20 - 1gm
D. G=360 - 16"
Answer:
The answer is G = 20 - m/18, but none of the answers given is correct.
Step-by-step explanation:
1. Let's review the information given to us to help Lulu to answer the question correctly:
Capacity of the gas tank of Lulu's car = 20 gallons
Lulu can travel 216 miles using 12 gallons
2. Which linear equation represents the number of gallons of gas, G, left in the tank after driving m miles?
G = number of gallons left in Lulu's car
m = Miles driven by Lulu
miles per gallon = 216/12 = 18 miles per gallon
Now, we can write the linear equation, this way:
G = Capacity of the gas tank of Lulu's car - miles driven/miles per gallon
Replacing with the values we know:
G = 20 - m/18
Let's assume Lulu drives 180 miles, using our linear equation, we have:
G = 20 - 180/18
G = 20 - 10 = 10 gallons left
Let's assume Lulu drives 54 miles, using our linear equation, we have
G = 20 - 54/18
G = 20 - 3 = 17 gallons left
determine the 6th tern for the sequence: 4, 0.4
4 0 4 0 4 0 Answer is 0
Step-by-step explanation:
Mathaway
Sarina made $42,000 in the calendar year. How much does she owe in federal taxes?
Applying the 2020 US tax brackets, Sarina would owe $4,842.50 in federal taxes on her $42,000 income.
Explanation:The amount of federal taxes that Sarina owes on her $42,000 income can be determined by referring to the tax brackets provided by the IRS. In 2020, the federal income tax rates for individuals are as follows:
10% on income up to $9,875 12% on income over $9,875 to $40,125 22% on income over $40,125 to $85,525 And so on to a maximum rate of 37%
According to these brackets, Sarina would pay 10% on her first $9,875 and 12% on the remaining amount up to $40,125. Any income she earned over that up to $85,525 would be taxed at 22%. Given that Sarina made $42,000, she falls into the second tax bracket. Therefore, her tax would be calculated as follows:
10% of $9,875 is $987.50 12% of ($42,000 - $9,875) is $3,855
By adding these amounts together, we can conclude that Sarina would owe $4,842.50 in federal taxes for that year.
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Sarina, a single filer earning $42,000 annually, would first deduct the standard deduction to calculate taxable income. Her taxable income of $28,350 would be taxed at 10% for the first $11,000 and at 12% for the next $17,350. The total federal tax owed by Sarina would be $3,182.
The amount Sarina owes in federal taxes depends on the tax rates applied to income brackets. For a single taxpayer earning $42,000 a year, we look at the given tax brackets to calculate the tax owed based on the progressive tax system in the United States.
Since Sarina's income is within the second bracket ($11,001-$44,725), her income will be taxed at different rates for different portions of her income.
First, we subtract a single filer's standard deduction to determine her taxable income. Let's assume the current standard deduction is similar to the $13,650 mentioned.
Calculate taxable income:
Total Income: $42,000
Standard Deduction: $13,650
Taxable Income: $42,000 - $13,650 = $28,350
Now, we split the taxable income according to the tax brackets:
First $11,000 are taxed at 10%: $1,100
Next $17,350 ($28,350 - $11,000), taxed at 12%: $2,082
Total tax owed = $1,100 + $2,082 = $3,182.
The complete question is:
Sarina made $42,000 in the calendar year. How much does she owe in federal taxes?
Rate : 10% , 12% , 22% , 24% , 32% , 35% 37%
Single : Up to $11.000 , $11,001-$44.725 , $44,726-$95,375 , $95,376-$182,100 , $182,101-$231.250 , $231.251-$578-125 , $578-126 or more , standard deviation: $13,650
Married Filing Jointly : Up to $22.000 , $22-001-$89,450 , $89-451-$192,750 , $192,751-$364,200 , $364,201-$462,500 , $462,501-$693,750 , $6933.751 or more , standard Deduction: $27,700
Which of the following is equivalent to the expression i^22?
Answer:
Step-by-step explanation:
[tex]i^{22}=i^{2*11}=(i^{2})^{11}=(-1)^{11}=-1[/tex]
Answer:
i^22 = -1.
Step-by-step explanation:
i^22 = (i^4)^5 * i^2
Now i^2 = -1 ( by definition)
and i^4 = i^2 * i^2 = -1 * -1 = 1
So i^22 = 1^5 * -1
= 1 * -1
= -1.
i need to know the factors that will get me 10x squared - 25x equals 0
Answer:
10x² - 25x = 0 ⇔ 5x(2x-5) = 0
the factors are 5x and 2x-5
Diagram 1 shows a triangle with feet of length 4y cm and height (y + 5) cm. Diagram 2 shows a square with a length of y cm. Given the area of the triangle exceeds the rectangle by 39 cm². Calculate the perimeter of the two diagrams.
Answer:
Step-by-step explanation:
Diagram 1
Area = b*h/2 = 4y*(y+5)/2 = 2y*(y+5)= 2y² + 10y
Diagram 2
Area = side*side = y * y = y²
the area of the triangle exceeds the rectangle by 39 cm².
2y² + 10y - y² = 39
y² + 10y = 39
y² + 10y -39 = 0
y² +13y - 3y - 3*13 = 0
y(y+13) -3(y+13)=0
(y+13)(y-3) = 0
y + 13 = 0 will not come as length couldn't be in negative
y - 3 = 0
y = 3 cm
Diagram 2:
Perimeter = 4*side = 4*y = 4*3 = 12 cm
The camera was $824.99 but I had to pay the additional 10% tax. What did I pay in total for my camera?
Answer:
$907.489
Step-by-step explanation:
Cost of camera : $824.99
Tax = 10%
tax on camera = 824.99 x 10 /100 = 82.499
total amount to be paid = cost + tax
$824.99 + $82.499 = $907.489
Answer:
$907.49
Step-by-step explanation:
Figure out what 10% of 824.99 is. You should get 82.499 which you round up to the nearest hundredth because this is money which gives you 82.50.
824.99+82.50=907.49
What type of number can be written as a fraction a over b where a and b are integers and b is not equal to zero ?
What type of number can be written as a fraction a over b where a and b are integers and b is not equal to zero ?
The answer is integers.
Examples of integers: 5, -8, 6/9, 100, -4/2
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HURRY ANSWER 16 POINTS
What percent of the volleyball players on Monday afternoon were counselors?
Answer: 10%
Step-by-step explanation: If there is a total of 20 volleyball players, but only 2 were counselors so, you have to divide 2 into 20 which would be .10 .
What is -2+5(4+3r) equal to?
Answer:
18+3r
Step-by-step explanation:
-2+5(4+3r)
-2+5×4+3r
-2+20+3r
=18+3r
The perimeter of the square can be represented by the expression 36x+44 robin wants to write an equivalent expression for the perimeter that shows the side length of the square
Answer:
4 (9 x + 11) is an equivalent expression for the perimeter that shows the side length of the square is (9 x + 11).
Step-by-step explanation:
Here, given The perimeter of the square = (36 x+44)
Now,as we know :
PERIMETER OF SQUARE = 4 x ( SIDES)
Simplifying the perimeter expression.
Take 4 common out of the expression (36 x+44), we get:
(36 x+44) = 4 (9 x + 11)
⇒ Perimeter of the square = 4 x (9 x + 11)
⇒4 x ( SIDES) = 4 x (9 x + 11)
⇒ Each Side = (9 x + 11)
Hence, 4 x (9 x + 11) is an equivalent expression for the perimeter that shows the side length of the square is (9 x + 11).
What is the algebric expression for
Multiply x by 3
Add 6
Raise to the second power
Answer:
[tex] {(3x + 6)}^{2} [/tex]
Solve the inequality -24 < x - 3 - 8x.
O A.x2-3 B.X2-9 C.x23 D.xs3
Answer:
Step-by-step explanation:
-24 < x - 3 - 8x
-24 < -7x - 3
-24 + 3 < - 7x
-21 < - 7x ......divide by -7 and change ur sign
-21/-7 > x
3 > x <==== ur answer
** in an inequality, if u multiply or divide by a negative, u have to change the sign
:
Step-by-step explanation:
-24 < x - 3 - 8x
-24 + 3 < x - 8x
-21 < -7x
7x > 21
x > 21/7
x > 3
what is 17/27 as a decimal
Answer:
0.63
Step-by-step explanation:
Do the long division.
If Johnny hits 51 baseballs that are thrown to him and he has 73 pitches thrown
to him, what is his efficiency?
Answer:
0.699 (=69.9%)
Step-by-step explanation:
Efficiency = total hits / total attempted
given total hits = 51 and total attempted = 73
Efficiency = 51/73 = 0.699 (=69.9%)
To indicate that one's purpose for writing is to inform, an author would include clues such as
Answer:
Facts
Step-by-step explanation:
whats the radical form of 192????
Answer:
The radical form of [tex]192[/tex] is [tex]8\sqrt{3}[/tex].
Step-by-step explanation:
Given the number is [tex]192[/tex], we need to find its radical form.
We will do the factorization of [tex]192[/tex].
[tex]192=2\times2\times2\times2\times2\times2\times3=2^6\times3\\192=(2^3)^2\times 3\\192=8^2\times3\\[/tex]
Taking square root both sides we get,
[tex]\sqrt{192}=\sqrt{8^2\times 3}\\\sqrt{ab}=\sqrt{a}\times \sqrt{b}\\\sqrt{192}=\sqrt{8^2}\times \sqrt{3}\\\sqrt{192}=8\times\sqrt{3}\\\sqrt{192}=8\sqrt{3}[/tex]
So, the radical form of [tex]192[/tex] is [tex]8\sqrt{3}[/tex].
Khaleah has 35 pencils. She gave away 20% of her pencils to her friends. How
many pencils did she give away?
Answer:
7
Step-by-step explanation:
35 times .20 is 7
What is another name for 1
a single
a lone
a solitary
a unit of
Andrew and Elena knew that after 28 days they would have 2^28 coins, but they wanted to find out how many coins that actually is Andrew wrote: 2^28=2×28=56. Elena said, " No, exponents mean repeated multiplication. It should be 28×28, which works out to be 784." Do you agree with either of them? Explain your reasoning.
Both Andrew and Elena are wrong. The actual value of 2^28 equals 268,435,456.
Step-by-step explanation:
Elena was right when she said exponents mean repeated multiplication but she accidentally calculated the value of 28^2 instead of 2^28. 2^28 means that the number 2 should be multiplied with itself for 28 times.
2^2 means 2 multiplied by 2 equals 4. 2^3 means 2 multiplied by 2 and then multiplied by 2 again which equals 8. Similarly, if you multiply 2 with itself 28 times you will get a value of 268,435,456 (two hundred and sixty-eight million, four hundred and thirty-five thousand, four hundred and fifty-six). So Andrew and Elena will have 268,435,456 coins after 28 days.
The sum of two consecutive numbers is 501. What are the two numbers.
Answer:
250 + 251= 501
A store advertises a 35% discount on a $951 computer system.
Answer:
The computer system would be $332.85 less than the normal price, or $618.15 total.
AE = EC and BF = FC. EF = 8 and DF = 10. AB = [?]
Answer:
Therefore AB is 16 units.
Step-by-step explanation:
Given:
AE = EC
BF = FC
EF = 8 and DF = 10
To Find:
AB = ?
Solution:
Mid Point Theorem:
The Midpoint Theorem states that "the segment joining two sides of a triangle at the midpoints of those sides is parallel to the third side and is half the length of the third side".
AE = EC .....Given
Therefore E is the Mid Point of AC.
BF = FC .....Given
Therefore F is the Mid Point of BC.
Therefore,
EF || AB ........................Mid Point Theorem.
[tex]EF=\dfrac{1}{2}AB[/tex] ..............Mid Point Theorem.
Substituting the values we get
[tex]8=\dfrac{1}{2}AB\\\\AB=8\times 2=16\ units[/tex]
Therefore AB is 16 units.
Answer:
16
Step-by-step explanation:
explain why triangles LMN and NOP are similar
work out the length of MO