Answer:
Let be a rational complex number of the form [tex]z = \frac{a + i\,b}{c + i\,d}[/tex], we proceed to show the procedure of resolution by algebraic means:
1) [tex]\frac{a + i\,b}{c + i\,d}[/tex] Given.
2) [tex]\frac{a + i\,b}{c + i\,d} \cdot 1[/tex] Modulative property.
3) [tex]\left(\frac{a+i\,b}{c + i\,d} \right)\cdot \left(\frac{c-i\,d}{c-i\,d} \right)[/tex] Existence of additive inverse/Definition of division.
4) [tex]\frac{(a+i\,b)\cdot (c - i\,d)}{(c+i\,d)\cdot (c - i\,d)}[/tex] [tex]\frac{x}{y}\cdot \frac{w}{z} = \frac{x\cdot w}{y\cdot z}[/tex]
5) [tex]\frac{a\cdot (c-i\,d) + (i\,b)\cdot (c-i\,d)}{c\cdot (c-i\,d)+(i\,d)\cdot (c-i\,d)}[/tex] Distributive and commutative properties.
6) [tex]\frac{a\cdot c + a\cdot (-i\,d) + (i\,b)\cdot c +(i\,b) \cdot (-i\,d)}{c^{2}-c\cdot (i\,d)+(i\,d)\cdot c+(i\,d)\cdot (-i\,d)}[/tex] Distributive property.
7) [tex]\frac{a\cdot c +i\,(-a\cdot d) + i\,(b\cdot c) +(-i^{2})\cdot (b\cdot d)}{c^{2}+i\,(c\cdot d)+[-i\,(c\cdot d)] +(-i^{2})\cdot d^{2}}[/tex] Definition of power/Associative and commutative properties/[tex]x\cdot (-y) = -x\cdot y[/tex]/Definition of subtraction.
8) [tex]\frac{(a\cdot c + b\cdot d) +i\cdot (b\cdot c -a\cdot d)}{c^{2}+d^{2}}[/tex] Definition of imaginary number/[tex]x\cdot (-y) = -x\cdot y[/tex]/Definition of subtraction/Distributive, commutative, modulative and associative properties/Existence of additive inverse/Result.
Step-by-step explanation:
Let be a rational complex number of the form [tex]z = \frac{a + i\,b}{c + i\,d}[/tex], we proceed to show the procedure of resolution by algebraic means:
1) [tex]\frac{a + i\,b}{c + i\,d}[/tex] Given.
2) [tex]\frac{a + i\,b}{c + i\,d} \cdot 1[/tex] Modulative property.
3) [tex]\left(\frac{a+i\,b}{c + i\,d} \right)\cdot \left(\frac{c-i\,d}{c-i\,d} \right)[/tex] Existence of additive inverse/Definition of division.
4) [tex]\frac{(a+i\,b)\cdot (c - i\,d)}{(c+i\,d)\cdot (c - i\,d)}[/tex] [tex]\frac{x}{y}\cdot \frac{w}{z} = \frac{x\cdot w}{y\cdot z}[/tex]
5) [tex]\frac{a\cdot (c-i\,d) + (i\,b)\cdot (c-i\,d)}{c\cdot (c-i\,d)+(i\,d)\cdot (c-i\,d)}[/tex] Distributive and commutative properties.
6) [tex]\frac{a\cdot c + a\cdot (-i\,d) + (i\,b)\cdot c +(i\,b) \cdot (-i\,d)}{c^{2}-c\cdot (i\,d)+(i\,d)\cdot c+(i\,d)\cdot (-i\,d)}[/tex] Distributive property.
7) [tex]\frac{a\cdot c +i\,(-a\cdot d) + i\,(b\cdot c) +(-i^{2})\cdot (b\cdot d)}{c^{2}+i\,(c\cdot d)+[-i\,(c\cdot d)] +(-i^{2})\cdot d^{2}}[/tex] Definition of power/Associative and commutative properties/[tex]x\cdot (-y) = -x\cdot y[/tex]/Definition of subtraction.
8) [tex]\frac{(a\cdot c + b\cdot d) +i\cdot (b\cdot c -a\cdot d)}{c^{2}+d^{2}}[/tex] Definition of imaginary number/[tex]x\cdot (-y) = -x\cdot y[/tex]/Definition of subtraction/Distributive, commutative, modulative and associative properties/Existence of additive inverse/Result.
1. write it on a piece of paper
[tex]\\ \sf\longmapsto 1\dfrac{1}{2}+2\dfrac{3}{4}[/tex]
[tex]\\ \sf\longmapsto \dfrac{3}{2}+\dfrac{11}{4}[/tex]
[tex]\\ \sf\longmapsto \dfrac{6+11}{4}[/tex]
[tex]\\ \sf\longmapsto \dfrac{17}{4}[/tex]
2:-
[tex]\\ \sf\longmapsto 4\dfrac{3}{7}+6\dfrac{1}{5}[/tex]
[tex]\\ \sf\longmapsto \dfrac{31}{7}+\dfrac{31}{5}[/tex]
[tex]\\ \sf\longmapsto \dfrac{155+225}{35}[/tex]
[tex]\\ \sf\longmapsto \dfrac{380}{35}[/tex]
[tex]\\ \sf\longmapsto 12[/tex]
3:-
[tex]\\ \sf\longmapsto 4\dfrac{2}{5}+5\dfrac{2}{6}[/tex]
[tex]\\ \sf\longmapsto \dfrac{22}{5}+\dfrac{32}{6}[/tex]
[tex]\\ \sf\longmapsto \dfrac{132+160}{30}[/tex]
[tex]\\ \sf\longmapsto \dfrac{292}{30}[/tex]
4:-
[tex]\\ \sf\longmapsto 3\dfrac{7}{7}+3\dfrac{1}{3}[/tex]
[tex]\\ \sf\longmapsto \dfrac{28}{7}+\dfrac{10}{3}[/tex]
[tex]\\ \sf\longmapsto 4+\dfrac{10}{3}[/tex]
[tex]\\ \sf\longmapsto \dfrac{12+10}{3}[/tex]
[tex]\\ \sf\longmapsto \dfrac{22}{3}[/tex]
[tex] \bf \large \longrightarrow \: \: 1 \frac{1}{2} \: + \: 2 \frac{3}{4} \: = \: \\ [/tex]
[tex] \bf \large \longrightarrow \: \: \frac{3}{2} \: + \: \frac{11}{4} \\ [/tex]
[tex] \bf \large \longrightarrow \: \: \frac{6 \: + \:11 }{4} \\ [/tex]
[tex] \bf \large \longrightarrow \: \: \frac{17}{4} \\ [/tex]
2.[tex]\bf \large \longrightarrow \: \: 4 \frac{3}{7} \: + \: 6 \frac{1}{5} \\ [/tex]
[tex]\bf \large \longrightarrow \: \: \frac{31}{7} \: + \: \frac{31}{5} \\ [/tex]
[tex]\bf \large \longrightarrow \: \: \frac{155 \: + \: 217}{35} \\ [/tex]
[tex]\bf \large \longrightarrow \: \: \frac{372}{35} \\ [/tex]
3.[tex]\bf \large \longrightarrow \: \: 4 \frac{2}{5} \: + \: 5 \frac{2}{6} \\ [/tex]
[tex]\bf \large \longrightarrow \: \: \frac{22}{5} \: + \: \frac{32}{6} \\ [/tex]
[tex]\bf \large \longrightarrow \: \: \frac{132 \: + \: 160}{30} \\ [/tex]
[tex]\bf \large \longrightarrow \: \: \frac{292}{30} \\ [/tex]
4.[tex]\bf \large \longrightarrow \: \: 3 \frac{7}{7} \: + \: 3 \frac{1}{3} \\ [/tex]
[tex]\bf \large \longrightarrow \: \: \frac{28}{7} \: + \: \frac{10}{3} \\ [/tex]
[tex]\bf \large \longrightarrow \: \: \cancel\frac{28 ^{4} }{7 \: ^{1} } \: + \: \frac{10}{3} \\ [/tex]
[tex]\bf \large \longrightarrow \: \: \frac{4}{1} \: + \: \frac{10}{3} \\ [/tex]
[tex]\bf \large \longrightarrow \: \: \frac{12 \: + \: 10}{3} \\ [/tex]
[tex]\bf \large \longrightarrow \: \: \frac{22}{3} \\ [/tex]
The Chesapeake Bay holds about 18 trillion gallons of water. The bay covers 4,480 square miles or 2,867,200 acres. Each acre can hold 750,000 oysters. Each oyster can filter 50 gallons of water each day. Can there be enough oysters to filter the whole Chesapeake Bay in one day
Answer:
There are enough oysters
Step-by-step explanation:
Given
[tex]Volume = 18\ trillion\ gallon[/tex]
[tex]Area = 2867200\ acre[/tex]
[tex]1\ acre = 750000\ oysters[/tex]
[tex]1\ oyster = 50\ gallons[/tex]
Required
Determine if there is enough water for a day
We have:
[tex]1\ oyster = 50\ gallons[/tex]
Convert to oysters: multiply both sides by 750000
[tex]750000 * 1\ oyster = 50\ gallon *750000[/tex]
[tex]750000\ oysters = 37500000\ gallons[/tex]
Given that:
[tex]1\ acre = 750000\ oysters[/tex]
So, we have:
[tex]1\ acre= 37500000\ gallons[/tex]
Convert to acre: Multiply by 2867200
[tex]2867200 * 1\ acre= 37500000\ gallons * 2867200[/tex]
[tex]2867200\ acres= 107520000000000\ gallons[/tex]
By comparison:
[tex]18000000000000\ gallons < 107520000000000\ gallons[/tex]
i.e. the volume of water in the bay is less than the capacity of the oysters. Hence, there are enough oysters.
Alberto quiere envasar 32 toneladas de arroz en sacos de 15 kilogramos cada uno, ¿Cuántos sacos necesitarán?
Please help: 6m - m = 5/6(6m - 10)
Will mark brainliest!!
Answer:
No solution.
Step-by-step explanation:
[tex]6m-m=\frac{5}{6}(6m-10)\\5m=5m-\frac{25}{3}\\0\neq -\frac{25}{3}[/tex]
Therefore, there is no solution.
13 Water is pulled up from a well in a bucket on a rope. The rope winds on a cylindrical drum 15 cm in diameter. It takes 28 turns of the drum to pull the bucket up from the bottom of the well. How deep is the well? (Use the value 2 for m.)
Answer ASAP Please!
cos(13°) correct to four decimal places is:
A:0.2311
B:0.2312
C:0.9734
D:0.9735
E:0.9744
Answer:
E:0.9744
Step-by-step explanation:
Answer: E) 0.9744
Explanation:
This is something you'll need a calculator for. As far as I know, there isn't a clean formula that will allow you to compute this by hand, and get something like sqrt(3)/2. There is a way to find the decimal value by hand, but it will require knowledge of Taylor polynomials and it will take a very long while to compute the value. So again, it's better to use a calculator. When using a calculator, make sure it's in degree mode. You can check by computing cos(60) and you should get 0.5
Write the function for the graph.
Answer:
B)
Step-by-step explanation:
exponential function given by:
[tex] \displaystyle f(x )= a \cdot{b}^{x} [/tex]
where:
a is the y-interceptb can be any numbersince the function crosses y-axis at (0,4) point
[tex]a = 4[/tex]to find a we can consider (1,8) point it tells us when x is 1 then y is 8 thus:
[tex] \displaystyle 8= 4 \cdot{b}^{1} [/tex]
[tex] \displaystyle 8= 4 \cdot{b}^{} [/tex]
divide both sides by 4:
[tex] \displaystyle \boxed{b = 2}[/tex]
altogether substitute:
[tex] \displaystyle f(x)= 4 \cdot{2}^{x} [/tex]
hence our answer is B)
PLEASE HELP WILL GIVE BRAINLIEST!!!!
Answer:
wqhg
Step-by-step explanation:
its situated in u.s, in quahog , rhode island
Urgently need help step by step explanation needed
Answer:
p=8
Step-by-step explanation:
-5log(p+1)+2=-8
-5log(p+1)=-10
log(p+1)=2
p+1=9, p=8
HELP PLEASE BRAIN FOR CORRRECT
Answer:
1/6
Step-by-step explanation:
you divide y by x
y ÷ x
each column when you you divide y by x the answer is 1/6
PLZZZ HELPPP, IF NOT 100% SURE PLZ DONT ANSWER…BRAINLIEST TO FIRST AND CORRECT ANSWER, THX TO SECOND AND CORRECT ANSWER
=============================================================
Explanation:
1/2 = 4/8 after multiplying top and bottom by 8
So the mixed number 7 1/2 is the same as 7 4/8
We can convert to an improper fraction like so
7 4/8
7 + 4/8
7*(8/8) + 4/8
56/8 + 4/8
(56+4)/8
60/8
Notice how dividing 60 over 8 leads to 7 remainder 4. Think of it like having 60 cookies and you want to share them amongst 8 friends. Each friend gets 7 whole cookies (7*8 = 56 taken so far) and then we have 60-56 = 4 left over as the remainder.
Through similar steps, you should find that the mixed number 1 7/8 converts to the improper fraction 15/8.
-----------------------------
To rephrase the problem with improper fractions would be to say:
"The electrician needs to buy 60/8 feet of wire. There are 15/8 feet of wire in each spool. How many spools should the electrician buy?"
Let x be the answer to that question.
We multiply the number of spools (x) by the amount of feet of wire per spool (15/8) to get the expression (15/8)x
Set this equal to the target 60/8 and solve for x
(15/8)x = 60/8
15x = 60 .... multiply both sides by 8 to clear out the fractions
x = 60/15
x = 4
The electrician needs to buy exactly 4 spools
-----------------------------
A different approach could have us convert each mixed number into decimal form
7 1/2 = 7 + 1/2 = 7 + 0.5 = 7.5
1 7/8 = 1 + 7/8 = 1 + 0.875 = 1.875
So the electrician needs to buy 7.5 ft total and each spool has 1.875 ft of wire.
Using the same idea as before, we would then have,
1.875x = 7.5
x = (7.5)/(1.875)
x = 4
PLS HELP ME ON THIS QUESTION I WILL MARK YOU AS BRAINLIEST IF YOU KNOW THE ANSWER!!
The median of the lower half of the data set is the _____________.
A. Third quartile
B. First quartile
C. Fourth quartile
D. Second quartile
Answer:
B. First quartile
Step-by-step explanation:
The first quartile is the first 25% of a line graph, and the median of the lower half of a data set would be the median of the median, which means it would split the graph at 25%
What is the expected value?
Answer:
2.1
Step-by-step explanation:
The expected value of a probability is given by the formula:
E(x) = Σxp(x)
Therefore from the table showing the winnings of a game, the expected value of the probability distribution is:
E(x) = Σxp(x) = (0 * 0.5) + (2 * 0.2) + (4 * 0.15) + (6 * 0.1) + (10 * 0.05)
E(x) = 0 + 0.4 + 0.6 + 0.6 + 0.5 = 2.1
Hence we can conclude that the expected value of the winnings of the game is 2.1.
Find the value of x in the triangle shown below.
This is a isoceles triangle so base angles will be equal.
Therefore
ATQ
55 + 55 + x = 180
110 + x = 180 (Angle Sum Property)
x = 180 - 110
x = 70
Therefore x° = 70°
Answered by Gauthmath must click thanks and mark brainliest
Answer:x°=70°
Step-by-step explanation:
This is an isoceles triagle because the values on the sides of the figure are the same. Therefore the base angles will be equal.
55+55+x=180
110+x=180
Next, you will subtract 110 from both sides.
110+x=180
-110 -110
x°=70°
Sandra is 5 years old. When she asked her father about his age, he gave her this answer. "When you are my age, I will be 67." How old is her dad?
Step-by-step explanation:
Her father is 34 years old
What is the correct answer to this multiple choice question? Please help!
Answer:
[tex]\sqrt[3]{4}[/tex]
Step-by-step explanation:
To solve this we need to take the square root of both sides with a certain degree.
[tex]4^6 = a^{18}[/tex]
We can take the root of both sides with a degree of 18.
[tex]\sqrt[18]{4^6} = \sqrt[18]{a^{18}} \\(4^6)^{\frac{1}{18} } = a\\a = 4^{\frac{6}{18} } = 4^{\frac{1}{3} } = \sqrt[3]{4}[/tex]
It's helpful to understand that when a number has its square root taken with some degree n. The square root can be represented as just the value raised to the (1/n) power.
It's also helpful to understand that when you raise something to the power of another power, you can simply multiply the powers together. For instance (2^3)^5 = 2^15
In a random sample of 190 people, 151 said that they watched educational television. Find the 90% confidence interval of the true proportion of people who watched educational television. Round intermediate answers to at least five decimal places. Round your final answers to at least three decimal places.
Answer:
(0.7465 , 0.8429 )
Step-by-step explanation:
Confidence Level - "P" values
90% 1.645
Confidence Interval - "P" values
(0.7465 , 0.8429 )
Which of the following illustrates the truth value of the given conditional statement?
If 3.2 = 5, then 6 <0.
OFF-T
OTT →T
OTEF
OFT →T
Answer:
OTT →T.................
................... ............
Find the value of x-8 when x=16.
Answer:
8
Step-by-step explanation:
x=16
x(16)-8=8
NEED some HElp please
Explain why the amount of money in the account at the end of the first year is given by the formula with n as the exponent:
P = P∨0 (1 + r/n)^n
Answer:
Is this answer correct.Does the anwer help you
The numbers 8,x,9 and 36 are in proportion.Find x
If you can give the proportion then it would be better.
I am asuming
8:x::9:36
Then 8:x::1:4
So x = 32
Answered by Gauthmath must click thanks and mark brainliest
Answer:
x = 32
Step-by-step explanation:
[tex]\frac{8}{x}[/tex] = [tex]\frac{9}{36}[/tex] = [tex]\frac{1}{4}[/tex] ( cross- multiply )
x = 8 × 4 = 32
Elias made a polyhedron with 9 edges and 5 faces. Which solid could he have made?
The polyhedron that Elias could have made is a TRIANGULAR BASED PRISM.
Triangular based prism are as described below:
A triangular-based prism is known to consists of 9 edges and 5 faces as shown in the diagram below.
It is a three-sided prism and also a polyhedron made of a triangular base, a translated copy, and 3 faces joining corresponding sidesThe edges are made up of lines and these lines are the ones that intersect to form facesLearn more here: https://brainly.com/question/16682058
Answer: c
Step-by-step explanation:
Hunter pushed a couch across the room. He did 800 J of work in 20 seconds. The couch weighed 500 N. How much power did he have?
A . 40 W
B . 1.6 w
C. 16,000 w
D . 800 w
Find f(-3) if f(x) = x2 .
Type a numerical answer in the space provided. Do not type spaces in your answer.
Answer:
f(-3) = 9
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Functions
Function NotationStep-by-step explanation:
Step 1: Define
Identify
f(x) = x²
Step 2: Evaluate
Substitute in x [Function f(x)]: f(-3) = (-3)²Exponents: f(-3) = 9please help. people take my points without answering. 15 points left, please show work. and please dont just take my points
Answer:
Step-by-step explanation:
Reference angle in quadrant I,
θ' = θ
Reference angle in quadrant II,
θ' = 180° - θ
Reference angle in quadrant III,
θ' = θ - 180°
Reference angle in quadrant IV,
θ' = 360° - θ
13). θ = 315°
Since, the given angle is in the 4th quadrant,
Reference angle θ' = 360° - 315°
= 45°
14). θ' = (620° - 540°)
= 80°
Reference angle = 80°
15). θ' = 630° - θ
= 630° - 580°
= 50°
Reference angle = 50°
You are taking a survey on the heights of all your classmates. This is an example of categorical data.
True or false?
Answer:
trueeeeeeeeeeeeeeeeeee
write x²-y² in factorize form.
write (p+p) ²in expanded form.
Answer:
(x-y)^2
p^2+p^2
Step-by-step explanation:
^2 means square
Answer:
see explanation
Step-by-step explanation:
x² - y² ← is a difference of squares and factors in general as
a² - b² = (a - b)(a + b) , then
x² - y²
= (x - y)(x + y)
------------------------------
(p + p)²
= (2p)²
= 2p × 2p
= 4p²
The lengths of the diameters of two concentric circles are 6 and 8. What is the distance between the circles?
Answer: 1 unit
Explanation:
The diameters are 6 and 8, which cut in half to 3 and 4 respectively.
The difference in these radii values is 4-3 = 1.
This is the distance from one circle's edge to the other circle's edge, such that we're on the same line that goes through the center of the circles. This is the gap width or ring width so to speak.
How do you find the volume of this pyramid with what is given? pls
Answer:
373.3333... in^3
Step-by-step explanation:
V = lwh / 3
V = 10 * 8 * 14 / 3
V = 1120 / 3
V = 373.3333... in^3
I'm probably wrong, I haven't done volume in a looong time.
The football team loses 5 yards on first down.
a. Write an integer to represent this situation.
Answer:
-5
Step-by-step explanation:
since it is a lose, it is represented by a negative sign.
