Answer:
we need to factorise if imaginary number is in the denominator. no action is required if its in the numerator.
you can factorise an imaginary number by multiplying both the numerator and denominator by the conjuncate of the complex number
for instance,
we've given a complex number as follows
[tex] \frac{x}{3x + 4i} [/tex]
factorising
[tex] \frac{x}{3x + 4i} \times \frac{3x - 4i}{3x - 4i} [/tex]
as 3x -4i is the conjugate of 3x + 4i
and 4i is the imaginary number
[tex] \frac{ x(3x - 4i)}{9x {}^{2} - 4 {i}^{2} }[/tex]
and since i² = -1
[tex]\frac{ x(3x - 4i)}{9x {}^{2} + 4}[/tex]
hence factorised
Enter each intercept as an ordered pair (x, y). Use a comma to separate the ordered pairs of multiple intercepts. You may enter an exact answer or round to 2 decimal places. If there are no solutions or no real solutions for an intercept enter ∅.
Answer:
mm what the de une wtah boaim msua
PLEASE HELP ME WILL MARK YOU JF YOU HELP ME PLEASE!!!
Answer:
2, 3, 4, 7, 8, 10 I hope
Answers
Congruent by AAS (shown in the example)Congruent by SASCongruent by SSSCongruent by ASANot enough info (shown in the second example)Congruent by AASCongruent by SASCongruent by SSSCongruent by AASNot congruent=================================================
Explanations:
As the example shows, we have two pairs of congruent angles and a pair of congruent sides. The side are not between the angles in question. So AAS is slightly different from ASA.We have two pairs of congruent sides, and a pair of congruent angles. The angles are between the sides. So we use SAS which is a valid congruence theorem. Recall that SSA is not a valid theorem, so the order matters.We have three pairs of congruent sides, so we go with SSS. The order doesn't matter here.Similar to problem 1, but now the sides are between the angles. So we go with ASA this time instead of AAS.We unfortunately don't have enough info to determine if the triangles are congruent or not. We need to know something about the side lengths to determine congruency.As the hint suggests, marking the vertical angles will produce the other pair of congruent angles. So that's why we go for AAS (the side is not between the angles).This is similar to problem 2, as both use SAS. Note the unmarked vertical angles which are congruent.This is similar to problem 3. We use SSS here because we have 3 pairs of congruent sides as indicated by the tickmarks.The unmarked vertical angles can get double arcs to show they are congruent. We have a pair of congruent sides that are not between the two pairs of congruent angles, so we go for AAS (problems 1 and 6 also use AAS).For the triangle on the left, the arc is between the tickmarked sides. The triangle on the right has the arc not between the tickmarked sides. So there's no way the triangles are the same. The arc needs to be between the marked sides for each triangle, if we wanted them to be congruent (using SAS).---------------
Acronyms
SSS = side side side
SAS = side angle side
ASA = angle side angle
AAS = angle angle side
Suppose you take a survey of all the schools in your state. What would you expect the relationship between the number of students and the number of teachers in each school to be?
Answer:
25 students:1 teacher
Step-by-step explanation:
in ever class in my school there is 1 teacher and we have between 20 and 30 students therefor 20 + 30 / 2 is 25
What number is 18% more than 1257 Round your answer to two decimal places needed,
Differentiate the function. y = (2x - 5)^2 (5 - x)?
Answer:
[tex]\displaystyle y' = -(2x - 5)(6x - 25)[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightDistributive Property
Algebra I
Terms/CoefficientsFactoringCalculus
Derivatives
Derivative Notation
Derivative of a constant is 0
Basic Power Rule:
f(x) = cxⁿ f’(x) = c·nxⁿ⁻¹Derivative Rule [Product Rule]: [tex]\displaystyle \frac{d}{dx} [f(x)g(x)]=f'(x)g(x) + g'(x)f(x)[/tex]
Derivative Rule [Chain Rule]: [tex]\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)[/tex]
Step-by-step explanation:
Step 1: Define
Identify
y = (2x - 5)²(5 - x)
Step 2: Differentiate
Derivative Rule [Product Rule]: [tex]\displaystyle y' = \frac{d}{dx}[(2x - 5)^2](5 - x) + (2x - 5)^2\frac{d}{dx}[(5 - x)][/tex]Chain Rule [Basic Power Rule]: [tex]\displaystyle y' = [2(2x - 5)^{2 - 1} \cdot \frac{d}{dx}[2x]](5 - x) + (2x - 5)^2\frac{d}{dx}[(5 - x)][/tex]Simplify: [tex]\displaystyle y' = [2(2x - 5) \cdot \frac{d}{dx}[2x]](5 - x) + (2x - 5)^2\frac{d}{dx}[(5 - x)][/tex]Basic Power Rule: [tex]\displaystyle y' = [2(2x - 5) \cdot 1 \cdot 2x^{1 - 1}](5 - x) + (2x - 5)^2(1 \cdot -x^{1 - 1})][/tex]Simplify: [tex]\displaystyle y' = [2(2x - 5) \cdot 2](5 - x) + (2x - 5)^2(-1)[/tex]Multiply: [tex]\displaystyle y' = 4(2x - 5)(5 - x) - (2x - 5)^2[/tex]Factor: [tex]\displaystyle y' = (2x - 5)[4(5 - x) - (2x - 5)][/tex][Distributive Property] Distribute 4: [tex]\displaystyle y' = (2x - 5)[20 - 4x - (2x - 5)][/tex][Distributive Property] Distribute negative: [tex]\displaystyle y' = (2x - 5)[20 - 4x - 2x + 5][/tex][Subtraction] Combine like terms (x): [tex]\displaystyle y' = (2x - 5)[20 - 6x + 5][/tex][Addition] Combine like terms: [tex]\displaystyle y' = (2x - 5)(25 - 6x)[/tex]Factor: [tex]\displaystyle y' = -(2x - 5)(6x - 25)[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Derivatives
Book: College Calculus 10e
You earn $36 for washing 6 cars. How much do you earn for washing 3 cars?
Answer:
18$
Step-by-step explanation:
36 divided by 6 is 6 dollars. this means you earn 6 dollars per car. multiply that by 3 cars and you get 18$.
Answer:
You earn $18 for washing 3 cars.
$36➗ 6= $6
$6x3= $18
16. Using divisibility tests, check whether the number 240720 is divisible by
2, 3, 4, 5, 6, 8, 9, 10 and 11. (Give reason)
The name of the circle pictured is circle C
A. True
B. False
Answer:
TRUE IS THE ANSWER
Step-by-step explanation:
The name of the circle pictured is circle C is True statement.
What is Circle?A circle is a collection of points in a plane that are all equally spaced apart from one another. The radius is the distance from the centre, while the centre is the location of the point. The diameter is defined as twice the radius. A complete angle, which is equal to or radians, is the angle that a circle subtends from its centre.
we have a graph for a circle.
We know a circle many parts such as Center, Radius, Diameter, Chord, etc.
A circle usually know from its Center.
Also, the center of circle shows the point of circle.
Thus, the given statement is True.
Learn more about Circle here:
https://brainly.com/question/29142813
#SPJ2
A stamp collection is purchased for $1,000. Twenty years later, the owner is told that the collection is worth quite a bit of money! If the rate of return on the stamp collection is 4% per year, what is the current value of the stamp collection? In your final answer, include all of your calculations.
Answer:
The current value of the stamp collection is of $2,191.
Step-by-step explanation:
Compound interest:
The compound interest formula is given by:
[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]
Where A(t) is the amount of money after t years, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per year and t is the time in years for which the money is invested or borrowed.
A stamp collection is purchased for $1,000.
This means that [tex]P = 1000[/tex]
The rate of return on the stamp collection is 4% per year
This means that [tex]n = 1, r = 0.04[/tex]
So
[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]
[tex]A(t) = 1000(1 + 0.04)^{t}[/tex]
[tex]A(t) = 1000(1.04)^{t}[/tex]
What is the current value of the stamp collection?
This is A(20). So
[tex]A(20) = 1000(1.04)^{20} = 2191[/tex]
The current value of the stamp collection is of $2,191.
Answer:
Step-by-step explanation:
y = 1000(1+0.04)^20
y = 1000(1.04)^20
Rounded to the nearest hundredth
y = 1000(2.19)
y = $2190
For each of the following, shade the portion of the Venn diagram that illustrates the set. ( A ∩ B ) ∪ ( A ∩ C )
Answer:
Here's what that would look like on a venn diagram
Step-by-step explanation:
The following data represent the maximum wind speed (in knots) and atmospheric pressure (in millibars) for a random sample of hurricanes that originated in the Atlantic Ocean.
Atmospheric Pressure (mb) Wind Speed (knots) Atmospheric Pressure (mb) Wind Speed (knots)
993 50 1006 40
995 60 942 120
994 60 1002 40
Required:
a. Find the y-intercept of the least-squares regression line, treating atmospheric pressure as the explanatory variable (round to four decimal places.)
b. Find the slope of the least-squares regression line, treating atmospheric pressure as the explanatory variable (round to four decimal places.)
c. Is it reasonable to interpret the y-intercept of the least-squares regression line, treating atmospheric pressure as the explanatory variable? Why or why not?
Answer:
Step-by-step explanation:
X Y X² Y² XY
993 50 986049 2500 49650
995 60 990025 3600 59700
994 60 988036 3600 59640
1006 40 1012036 1600 40240
942 120 887364 14400 113040
1002 40 1004004 1600 40080
[tex]\sum X: 5932[/tex] [tex]\sum Y : 370[/tex] [tex]\sum X^2 : 5867514[/tex] [tex]\sum Y^2 = 27300[/tex] [tex]\sum XY : 362350[/tex]
To determine the regression:
[tex]Mean \ (X) = \dfrac{\sum X }{n} \\ \\ = \dfrac{5932}{6} \\ \\ = 988.67[/tex]
[tex]Mean \ (Y) = \dfrac{\sum Y}{n} \\ \\ = \dfrac{370}{6} \\ \\ = 61.67[/tex]
Intercept [tex]b_o = \dfrac{\sum YX *\sum X^2 - \sum X \sum Y}{n(\sum X^2) - (\sum X)^2}[/tex]
[tex]=\dfrac{370(5867514) -(5932)(370)}{6(5867514) - (5932)^2}[/tex]
= 131760.9563
Slope [tex]b_1 = \dfrac{n(\sum XY) -(\sum X *\sum Y) }{n(\sum X^2)-(\sum X)^2}[/tex]
[tex]b_1 = \dfrac{6(362350) -(5932*370) }{6(5867514)-(5932)^2}[/tex]
[tex]b_1 = -1.2600[/tex]
The regression line equation [tex]Y = b_o +b_1X[/tex]
[tex]Y = 131760.96 -1.2600 X[/tex]
We then make a comparison of the slope of the equation to y = mx+c
slope of the equation = -1.2600
the y-intercept corresponds to when X = 0, thus:
y-intercept = 131760.9563
Yes, it is reasonable to interpret the y-intercept of the regression line, Using atmospheric pressure as an explanatory variable due to the fact that:
X is the independent variable and Y exists as the dependent variable.
what is 72 Times 27 equal
Answer:
1,944
Step-by-step explanation:
72x27=1,944
Have a wonderful day or night
Answer
1944
Step-by-step explanation:
72*27 = 1944
the image above should clarify how you're actually supposed to do it! couldn't submit this without 20 characters :,)
Simplify the expression
Answer:
6
Step-by-step explanation:
3 sqrt(20) / sqrt(5)
We know that sqrt(a) /sqrt(b) = sqrt(a/b)
3 sqrt(20/5)
3 sqrt(4)
3 *2
6
if f(x) = -3x - 5 and g(x) = 4x-2, find (f+g)(x)
Answer:
(f+g)(x) = x - 7
Step-by-step explanation:
it is simple - when adding 2 functions your simply add both expressions. and the result is then the function of the sum.
the same applies also to other arithmetic operations.
-3x -5 + 4x - 2 = x - 7
Do you guys know this
Answer:
Kindly check attached picture
Step-by-step explanation:
The expected graph is attached in the picture below :
Since additional fee is charged on only luggage exceeding 50 pound weight :
The inequality is :
Additional fee applied to :
Weight > 50
Hence x our arrows starts from 50 to the right of the number line
Sketch the region enclosed by the given curves and calculate its area.
y=4-x^2 ,y=0
The answer is 32/3. But how do I get to that answer?
Answer:
Step-by-step explanation:
1.) we need to find the bounds of integration which is just the points of intersection
here is it (-2,0) and (2,0)
which means we will integrate from -2 to 2
next, we take the upper equation and subtract that from the lower one
kind of confusing but it would look like (sketch it out if you're not sure)
(4-x²)-0= 4-x²
then we can integrate
[tex]\int\limits^2_{-2} {4-x^2} \, dx =4x-\frac{x^3}{3}|_{-2}^{2}=(4*(2)-\frac{2^3}{3})-(4(-2)-\frac{-2^3}{3})=5.333333-(-5.3333333)= 10.666666667=\frac{32}{3}[/tex]
1)
Ay
X
1
A)
Nin
B) -2
2
C)
D) 2.
2
Answer:
A) -1/2
Step-by-step explanation:
the slope is defined by the ratio of y/x.
that means that for a change of a certain number of units in x, y changes this number of units.
e.g. a slope of 5/3 means, if x changes by 3 units, y changes by 5.
the graphic shows a line that goes "down" with increasing x.
that means the slope is negative.
that eliminates C and D.
and we see that when x increases by 2 units, y decreases by 1 unit.
that means the slope is -1/2.
When a factory operates from 6 AM to 6 PM, its total fuel consumption varies according to the formula f(t)=0.9t^3−0.6t^0.5+10, where t is the time in hours after 6 AM and f(t) is the number of barrels of fuel oil. Step 1 of 3 : How much fuel is consumed by 11 AM? Round your answer to 2 decimal places.
Step-by-step explanation:
the answer is in the image above
The amount of oil consumed in 5 hours is 120.5 barrels.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Given is an equation, of fuel consumption in a factory from 6 am to 6 pm,
The equation =
f(t) = 0.9t³-0.6[tex]t^{0.5}[/tex]+10
where t is the time in hours after 6 am and f(t) is the number of barrels of fuel oil.
We need to find the how much oil is consumed by 11 am,
So, the hours between 11 am to 6 am = 11-6 = 5 hours
So, we need to find the oil consumption in 5 hours, so for the same put t = 5, in the equation,
f(5) = 0.9(5)³-0.6[tex](5)^{0.5[/tex]+10
= 112.5-2+10
= 120.5
Hence, the amount of oil consumed in 5 hours is 120.5 barrels.
Learn more about equations, click;
https://brainly.com/question/29538993
#SPJ2
You deposit $10,000 in an account that pays 4.5% interest compounded quarterly. Find the future value after one year.
Answer:
11800
Step-by-step explanation:
4.5%=0.045
0.045x10,000=450
450x4(quarterly)=1800
10,000+1800= 11800
Answer:
After 1 year, $10,457.65
Step-by-step explanation:
P = $ 10, 000
r = 4.5% = 0.045
T = 1 year
n = 4 ( compounded quarterly )
[tex]A = P( 1 + \frac{r}{n})^{nt}[/tex]
[tex]= 10000( 1 + \frac{0.045}{4})^{4 \times 1}\\\\=10000 \times 1.01125^{4}\\\\= 10000 \times 1.04576508633\\\\= 10457.6508633\\\\= \$ 10, 457.65[/tex]
Write the equation of the line that passes through the points (8,-1) and (2,-5) in standard from, given that the point-slope form is y+1=2/3(x-8)
____x+____y=____
Answer: 2/3x-y=19/3
Step-by-step explanation:
Points are useless since we already know the point slope form and we can just simply that
y+1=2/3(x-8)
y+1=2/3x-16/3
y=2/3x-19/3
2/3x-y=19/3
mong moi nguoi giup do
Which one is this please help thank u
Answer:
isosceles
Step-by-step explanation:
Two sides are the same length as indicated by the lines on the sides.
This tells use that the triangle is isosceles
Answer:
Hi, this an isoceles triangle
Step-by-step explanation:
An isoceles triangle has 2 equal sides
A right angled one has a right angle (90 degrees)
An equilateral traingle has all of his sides equal
A scalene has all of his sides different.
So this must be an isoceles triangle because there is basically a proof of the two equal sides (the bars).
Hope its clear!
Liner equation with a rapid change over time
Answer:
y=130(2.5) ^(x-1)
Step-by-step explanation:
This should give you an exponential growth curve. I'm assuming this is what you meant by "rapid change over time".
7. You are mixing some concrete for a home project, and you've calculated according to the
directions that you need six gallons of water for your mix. But your bucket isn't calibrated, so you
don't know how much it holds. On the other hand, you just finished a two-liter bottle of soda. If you
use the bottle to measure your water, how many times will you need to fill it?
Answer:
11.4 bottles for US gal.
13.6 bottles for Imperial gal.
Step-by-step explanation:
1 US gallon = 3.8 L
6 US Gallons = 6*3.8 L = 22.8 L = 11.4 bottles
1 Imperial gallon = 4.54 L
6 Imperial gallons = 6*4.54 L = 27.24 L = 13.6 bottles.
I got 7 to go :( help plz
Answer:
I think the second one is the answer ; 2√b
서울기업(주)는 2X20년 7월 5일에 장기간 보유 목적으로 원주기업(주)의 주식 1,200주를 1주당 15,000원에 매수하고 수표를 발행하여 매수대금을 지급하였다. 취득 부대비용은 없다. 이 1,200주는 원주기업(주)이 발행한 주식의12%에 해당하고, 서울기업(주)은 이를 FVOCI 측정 추자주식으로 분류하였다. 서울기업(주)은 원주기업(주) 주식 외에는 다른 회사 주식을 보유하고있지 안다. 다음은 원주기업(주) 주식에 대한 자료이다.
(1) 2X20년 말에 원주기업(주) 주식의 1주당 주가는 14,000원이었다.
(2) 2X20년 3월 25일에 원주기업(주)으로부터 배당금 150만원을 현금으로 받았다.
(3) 2X21년 말에 원주기업(주) 주식의 1주당 주가는 18,000원이었다.
(4) 2X22년 4월 20일에 서울기업(주)은 원주기업(주) 주식을 주당 17,500원에 전부 매각처분하고 처분대금을 현금으로 받았다.
물음: 서울기업(주)의 2X21년 말 재무상태표에 표시되는 장기투자주식 금액과, 기타포괄손익누계액 금액 그리고 포괄손익계산서에 표시되는 기타포괄손익(평가손익)은 각각 얼마인가?
Answer:
ディーズナッツ
Step-by-step explanation:
What is the probability of spinning a natural number and a number less than 5?
Answer:
The probability of spinning a 5 or less is 1/8 or, you can say ⅛
Really Hope I helped! ♡♡♤♤♧♧
The probability of spinning a natural number and a number less than 5 would be 2/3.
What is probability?The probability exists the branch of mathematics involving numerical descriptions of how likely an event is to happen, or how likely it exists that a proposition is true. The probability of an event exists in a number between 0 and 1, where, roughly speaking, 0 demonstrates the impossibility of the event and 1 demonstrates certainty.
No of total outcomes =6
No of favorable outcomes=4 {1,2,3,4}
Therefore, Probability of getting a number less than 5 is= 4/6 = 2/3.
To learn more about probability refer to:
https://brainly.com/question/13604758
#SPJ2
Given: x - 8 > -3.
Choose the solution set.
Answer:
X=-2,-1,0,1,2,3,4,5,6,
Step-by-step explanation:
IF 8 IS LARGER THAN -3 YOU COULD GET THE FOLLOWING ANSWER
Answer:
x>5
Step-by-step explanation:
move -8 to the right side, change the sign and solve:
x > - 3 + 8
x > 5
There are twelve empty rooms in the office of Acme Softwares, inc. Alif and Laila joins the company. How many ways can they be assigned a room each from these twelve
Answer:
132.
Step-by-step explanation:
That would be the number of permutations of 2 from 12.
12P2 = 12! / (12-2)!
= 132.
if marvin bought 490 soda cans and candy bars, where the ratio is 3:4, respectively, how many of each did marvin buy?
9514 1404 393
Answer:
210 soda cans280 candy barsStep-by-step explanation:
The 3+4 = 7 ratio units represent the total of 490 snacks, so each ratio unit represents 490/7 = 70 snacks.
The number of soda cans is 3·70 = 210.
The number of candy bars is 4·70 = 280.
Marvin bought 210 soda cans and 280 candy bars.
