Answer with Step-by-step explanation:
We are given that
[tex]a+ib=\sqrt{\frac{1+i}{1-i}}[/tex]
We have to prove that
[tex]a^2+b^2=1[/tex]
[tex]a+ib=\sqrt{\frac{(1+i)(1+i)}{(1-i)(1+i)}}[/tex]
Using rationalization property
[tex]a+ib=\sqrt{\frac{(1+i)^2}{(1^2-i^2)}}[/tex]
Using the property
[tex](a+b)(a-b)=a^2-b^2[/tex]
[tex]a+ib=\sqrt{\frac{(1+i)^2}{(1-(-1))}}[/tex]
Using
[tex]i^2=-1[/tex]
[tex]a+ib=\frac{1+i}{\sqrt{2}}[/tex]
[tex]a+ib=\frac{1}{\sqrt{2}}+i\frac{1}{\sqrt{2}}[/tex]
By comparing we get
[tex]a=\frac{1}{\sqrt{2}}, b=\frac{1}{\sqrt{2}}[/tex]
[tex]a^2+b^2=(\frac{1}{\sqrt{2}})^2+(\frac{1}{\sqrt{2}})^2[/tex]
[tex]a^2+b^2=\frac{1}{2}+\frac{1}{2}[/tex]
[tex]a^2+b^2=\frac{1+1}{2}[/tex]
[tex]a^2+b^2=\frac{2}{2}[/tex]
[tex]a^2+b^2=1[/tex]
Hence, proved.
rotation 180 degrees about the origin.
Answer:
Take the picture you uploaded.
Click the rotate button twice.
Done
A man walked 5km then traveled a certain distance by Nissan urban bus and twice as far by train. if the whole journey was 104km, how far did he traveled?
Answer:
33km
Step-by-step explanation:
Let the distance traveled by bus be x, then distance traveled by train would be 2x
Therefore,
5 + x + 2x = 104
5 + 3x = 104
3x = 104 - 5
3x = 99
x = 33
NEED ANSWER QUICK
Timmy and Tommy are two boys whose ages add up to 23. Timmy is 5
years older than Tommy. How old are they?
Answer:
Tommy's age is 9 years old.
Timmy's age is 14 years old.
Step-by-step explanation:
Take Tommy's age to be x and Timmy's age to be x+5
x+x+5=23
2x+5=23
2x=23-5=18
x=18÷2=9
x+5=9+5=14
What is 70% less than 55?
Answer:
100-70=30 so
55*0.3=16.5
Hope This Helps!!!
Answer:
Answer :
70% less than 55 is
16.5
The probability that a 38-year-old white male will live another year is .99813. What premium would an insurance company charge to break even on a one-year $1 million term life insurance policy
Answer:
The insurance company should charge $1,873.5.
Step-by-step explanation:
Expected earnings:
1 - 0.99813 = 0.00187 probability of the company losing $1 million(if the client dies).
0.99813 probability of the company earning x(price of the insurance).
What premium would an insurance company charge to break even on a one-year $1 million term life insurance policy?
Break even means that the earnings are 0, so:
[tex]0.99813x - 0.00187(1000000) = 0[/tex]
[tex]0.99813x = 0.00187(1000000)[/tex]
[tex]x = \frac{0.00187(1000000)}{0.99813}[/tex]
[tex]x = 1873.5[/tex]
The insurance company should charge $1,873.5.
prove the identity of
[tex] 4 sin^{2}x + 7sin^{2} = 4 + 3cos^{2} [/tex]
Answer:
7sin
2
x+3cos
2
x=4
4sin
2
x+3sin
2
x+3cos
2
x=4
4sin
2
x+3=4
4sin
2
x=1
sin
2
x=
4
1
sinx=
2
1
or sinx=−
2
1
Step-by-step explanation:
TAKING THE POSITIVE ROOT x=
6
π
tan(
6
π
)=
3
1
You and a friend were invited to a
party. You both were asked to bring
pizzas and chips. Your friend brought
three pizzas and four bags of chips
and spent $48.05. You brought five
pizzas and two bags of chips and
spent $67.25. What is the cost of
each? Answer should be in (Pizza, Chips)
Answer:
Pizza = 12.35
Chips = 2.75
Step-by-step explanation:
Let :
Pizza = x
chips = y
3x + 4y = 48.05 - - - (1)
5x + 2y = 67.25 - - - (2)
Multiply (1) by 5 and (2) by 3
15x + 20y = 240.25
15x + 6y = 201.75
Subtract :
20y - 6y = 240.25 - 201.75
14y = 38.50
y = 38.50/ 14
y = 2.75
Put y = 2.75 in (1)
3x + 4(2.75) = 48.05
3x + 11 = 48.05
3x = 48.05 - 11
3x = 37.05
x = 37.05 / 3
x = 12.35
Pizza = 12.35
Chips = 2.75
Write the equation of the line that passes through the points ( – 3, 2) and ( - 1,6).
Answer:
the answer is y=2x+8
Step-by-step explanation:
2. The prices, in dollars per unit, of the three commodities X, Y and Z are x, y and z,
respectively
Person A purchases 4 units of Z and sells 3 units of X and 3 units of Y.
Person B purchases 3 units of Y and sells 2 units of X and 1 unit of Z.
Person C purchases 1 unit of X and sells 4 units of Y and 6 units of Z.
In the process, A, B and C earn $40, $50, and $130, respectively.
a) Find the prices of the commodities X, Y, and Z by solving a system of linear
equations (note that selling the units is positive earning and buying the units is
negative earning).
Answer:
Price of X is $24.81
Price of Y is $3.66
Price of Z is $11.36
Step-by-step explanation:
for person A, we know that earns $40, then we can write the equation:
-4*z + 3*x + 3*y = $40
For person B, we know that earns $50, then:
1*z + 2*x - 3*y = $50
For person C, we know that earns $130, then:
6*z - 1*x + 4*y = $130
Then we have a system of equations:
-4*z + 3*x + 3*y = $40
1*z + 2*x - 3*y = $50
6*z - 1*x + 4*y = $130
To solve the system, we need to isolate one of the variables in one of the equations.
Let's isolate z in the second equation:
z = $50 - 2*x + 3*y
now we can replace this in the other two equations:
-4*z + 3*x + 3*y = $40
6*z - 1*x + 4*y = $130
So we get:
-4*($50 - 2*x + 3*y) + 3*x + 3*y = $40
6*($50 - 2*x + 3*y) - 1*x + 4*y = $130
Now we need to simplify both of these, so we get:
-$200 + 11x - 9y = $40
$350 - 13*x + 28*y = $130
Now again, we need to isolate one of the variables in one of the equations.
Let's isolate x in the first one:
-$200 + 11x - 9y = $40
11x - 9y = $40 + $200 = $240
11x = $240 + 9y
x = ($240 + 9y)/11
Now we can replace this in the other equation:
$350 - 13*x + 28*y = $130
$350 - 13*($240 + 9y)/11 + 28*y = $130
Now we can solve this for y.
- 13*($240 + 9y)/11 + 28*y = $130 - $350 = -$220
-13*$240 - (13/11)*9y + 28y = - $220
y*(28 - (9*13/1) ) = -$220 + (13/11)*$240
y = ( (13/11)*$240 - $220)/(28 - (9*13/1) ) = $3.66
We know that:
x = ($240 + 9y)/11
Replacing the value of y, we get:
x = ($240 + 9*$3.66)/11 = $24.81
And the equation of z is:
z = $50 - 2*x + 3*y = $50 - 2* $24.81 + 3*$3.66 = $11.36
Then:
Price of X is $24.81
Price of Y is $3.66
Price of Z is $11.36
Question is in picture below
Answer:
The obove picture the rule is SSA
in a school project you need to provide a blueprint of the schools rectangular playground .the blueprint dimensions of the playground are 23/147 yd x 3/14 yd after reducing them by the factor of 2/147 what are the original dimensions if the playground in yards
Answer:
L = 0.16 yd, W = 0.22 yd
Step-by-step explanation:
Dimensions of play ground 23/147 yd x 3/14 yd
reducing factor 2/147
Let the original length is L.
[tex]L - \frac{2L}{147} = \frac{23}{147}\\\\L\frac{143}{147} = \frac{23}{147}\\\\L=\frac{23}{143} yd[/tex]
L = 0.16 yd
Let the width is W.
[tex]W - \frac{2W}{147} = \frac{3}{14}\\\\W\frac{143}{147} = \frac{3}{14}\\\\W=0.22 yd[/tex]
If a procedure meets all of the conditions of a binomial distribution except the number of trials is not fixed, then the geometric distribution can be used. The probability of getting the first success on the xth trial is given by
P(x) = p(1−p)x−1
where p is the probability of success on any one trial. Subjects are randomly selected for a health survey. The probability that someone is a universal donor (with group O and type Rh negative blood) is 0.15. Find the probability that the first subject to be a universal blood donor is the fifth person selected.
Answer:
0.0783
Step-by-step explanation:
The probability of getting the first success on xtg trial ; this is a geometric distribution :
P(x) = p(1−p)^x−1
The probability of being a universal donor , p = 0.15
The probability of obtaining someone who is a universal donor on 5th trial will be :
P(5) = 0.15(1 - 0.15)^(5 - 1)
P(5) = 0.15(0.85)^4
P(5) = 0.15(0.52200625)
P(5) = 0.0783009375
P(5) = 0.0783
If P(E)=0.55, P(E or F)=0.65, and P(E and F)=0.20, find P(F).
P(F)=
(Simplify your answe
Answer:
.3
Step-by-step explanation:
let x= P(f)
.65= .55+x-.2
P(F)=.3
Explain the steps to find x- and y- intercepts of an equation of the form Ax + By = C
Step-by-step explanation:
For an equation of form Ax + By = C, we are given A, B, and C.
The x intercept is when the line/equation is on the x axis, or when y=0.
Therefore, if we plug y=0 into the equation Ax+By=C, and anything multiplied by 0 is equal to 0, we can say that
Ax + 0 = C
Ax = C
divide both sides by A
x = C/A
Therefore, the x intercept is equal to C/A
Similarly, for the y intercept, or when the line is on the y axis (or when x=0), we have
A*0 + By = C
By = C
divide both sides by B
y= C/B at the y intercept
Movie genres. The pie chart summarizes the genres of 120 first-run movies released in 2005. a) Is this an appropriate display for the genres
Answer:
Yes, it is appropriate
Step-by-step explanation:
Given
See attachment for pie chart
Required
Is the pie chart appropriate
The attached pie chart displays the distribution of each of the 4 genre. The partition occupied represents the measure of each genre.
A polygraph (lie detector) is an instrument used to determine if an individual is telling the truth. These tests are considered to be 90% reliable. In other words, if an individual lies, there is a 0.90 probability that the test will detect a lie. Let there also be a 0.045 probability that the test erroneously detects a lie even when the individual is actually telling the truth. Consider the null hypothesis, "the individual is telling the truth," to answer the following questions
a. What is the probability of a Type I error? (Round your answer to 3 decimal places.)
b. What is the probability of a Type II error? (Round your answer to 2 decimal places.
Answer:
A) P(Type I error) = 0.045
B) P(Type II) error = 0.1
Step-by-step explanation:
We are told that the reliability of the test is 90% reliable.
Also, we are told that the probability that the test erroneously detects a lie even when the individual is actually telling the truth is 0.045.
Thus;
A) To calculate the probability of type I error:
From statistics, in this question we can say that the probability of a type I error is the probability that the test will erroneously detect a lie even though the individual is actually telling the truth. Thus;
Probability of (type I error) = P(rejecting true null) = 0.045
B) For probability of type II error, it is defined as the error where we accept a null hypothesis that is false. We can say that it produces a false negative and the formula is;
P(Type II) error = 1 - reliability
Reliability in the question is 0.90
Thus;
P(Type II) error = 1 - 0.9
P(Type II) error = 0.1
Kala drove 819 miles in 13 hours.
At the same rate, how long would it take her to drive 441 miles?
Answer:
[tex]{ \tt{ \frac{819}{13} = \frac{441}{h} }} \\ { \tt{h = \frac{(441 \times 13)}{819} }} \\ h = 7 \: hours[/tex]
A sprinkler releases water st a rate of 150 liters per hour. If the sprinkler operated for 80 minutes how many liters of water will be released
The amount of water released from the sprinkler for 80 minutes is 200 L
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the amount of water from the sprinkler for 80 minutes be = A
Now , the value of A is given by the equation
A sprinkler releases water st a rate of 150 liters per hour
So , 60 minutes = 150 Liters of water
80 minutes = 1/60 hours
80 minutes = 1.333 hours
The amount of water released for 1.333 hours A = 150 x 1.333
On simplifying the equation , we get
The amount of water released for 1.333 hours A = 200 L
Therefore , the value of A is 200 L
To learn more about equations click :
https://brainly.com/question/19297665
#SPJ2
3/8-1/4=?
Answer ……..
Step 1: Find the LCD (Least Common Denominator)
The LCD between 4 and 8 is 8. Therefore, if I change all of the fractions to have a denominator of 8, the problem is as such:
3/8 - 2/8 = ?
Step 2: Subtract
3/8 - 2/8 = 1/8
Hope this helps!
Answer:
[tex]\frac{1}{8}[/tex] (1/8)
Step-by-step explanation:
1. The LCD & basics8·1=8
4·2=8
LCD=8
If the denominator is multiplied, the numerator also has to be multipled by the same value.
2. Solving[tex]\frac{3}{8} -\frac{2}{8} =\frac{1}{8}[/tex][tex]\frac{1}{8}[/tex]
Hope this helped! Please mark brainliest :)
(a) Find the average rate of change of the area of a circle with respect to its radius r as r changes from 2 to each of the following.
(i) 2 to 3
(ii) 2 to 2.5
(iii) 2 to 2.1
(b) Find the instantaneous rate of change when r =2.
Answer:
ai) 5pi
aii) 4.5pi
aiii) 4.1pi
b) 4pi
Step-by-step explanation:
a) Area of a circle is given by pi×r^2.
The average rate of change of the area of a circle from r=b to r=a is (pi×b^2-pi×a^2)/(b-a).
Let's simplify this.
Factor pi from the terms in the numerator:
pi(b^2-a^2)/(b-a)
Factor the difference of squares in the numerator:
pi(b-a)(b+a)/(b-a)
"Cancel" common factor (b-a):
pi(b+a).
So let's write a conclusive statement about what we just came up with:
The average rate of change of the area of a circle from r=b to r=a is pi(b+a).
i) from 2 to 3 the average rate of change is pi(2+3)=5pi.
ii) from 2 to 2.5 the average rate of change is pi(2+2.5)=4.5pi.
from 2 to 2.1 the average rate of change is pi(2+2.1)=4.1pi.
b) It looks like a good guess at the instantaneous rate of change is 4pi following what the average rate of change of the area approached in parts i) through iii) as we got closer to making the other number 2.
Let's confirm by differentiating and then plugging in 2 for r.
A=pi×r^2
A'=pi×2r
At r=2, we have A'=pi×2(2)=4pi. It has been confirmed.
Solve the literal equation: -24x-12=4y-12x
Answer:
y = 3(3x - 1)
Step-by-step explanation:
Given the equation :
24x-12=4y-12x
Collect like terms
24x + 12x = 4y + 12
36x = 4y + 12
4y = 36x - 12
Divide through by 4
4y / 4 = 36x / 4 - 12 / 4
y = 9x - 3
y = 3(3x - 1)
Hence, y = 3(3x - 1)
need help with algebra problem
Answer:
[tex]option \: d \: 4.2 \times {10}^{ - 3} [/tex]
Step-by-step explanation:
Multiplication,
[tex] = 8.4 \times {10}^{ 8 } \times 5 \times {10}^{ - 11} \\ = 8.4 \times 5 \times {10}^{8 + ( - 11)} \\ = 4.2 \times {10}^{8 - 11} \\ = 4.2 \times {10}^{ - 3} [/tex]
The largest angle in a triangle is six times the smallest angle. The middle angle is three times the smallest angle. Given that the sum of the angles in a triangle is , find the measure of each angle.
Answer:
Smallest: 18° Middle: 54° Largest: 108°
Step-by-step explanation:
We can start by writing out what we know in a series of equations:
s= smallest angle, m= medium angle, L= largest angle.
Since the largest is 6 times the smallest we have:
L=6s
Since the middle is 3 times the smallest we have:
m=3s
Since the 3 interior angle measures of a triangle always must equal 180°, we have:
s+m+L=180
Then we plug in our L and m into the third equation:
s+3s+6s=180
Combining like terms and solving:
10s=180
s=18
Then we plug in 18 for s into the first 2 equations to get:
L= 6* 18
L= 108
and
m= 3* 18
m= 54
So s= 18, m= 54, and L=108.
To check the answer we can:
Add the three to make sure they equal 180. Make sure the smallest is the smallest, and the largest is the largest.Tan^2t /sin t = tan t sec t
Answer:
Step-by-step explanation:
[tex]\frac{tan^2t}{sint}=\frac{tan t\times tant}{sin t} =\frac{tan t}{sint} \times \frac{sin t}{cos t} =\frac{tan t}{cos t} =tan t ~sec t[/tex]
Please help ASAP. No links
Hello my dear friend of USA !!!
DB/AD = BE/EC
=> 6/4 = x+1/x
=> 6x = 4x + 4
=> 2x = 4
=> x = 2
So x = 2
I am from INDIA.
Lots of love ❤️!!!
Have a great day ahead!
Answer:
x = 2
Step-by-step explanation:
[tex]\frac{6}{4} = \frac{x+1}{x}[/tex]
6x = 4x + 4
2x = 4
x = 2
una fuerza constante F de magnitud igual a 3lb se aplica al bloque que se muestra en la figura. F tiene la misma dirección que el vector a= 3i + 4j. determine el trabajo realizado en la dirección de movimiento si el bloque se mueve de P1 (3, 1) a P2 (9, 3). Suponga que la distancia se mide en pies.
HELP!!!!!! I need an answer fasttttt
Answer:
see the attachment
Step-by-step explanation:
Hope it helps you
Write 2 1/4 as a decimal
Hey there!
2 1/4
= 2 * 4 + 1 / 4
= 8 + 1 / 4
= 9 / 4
= 9 ÷ 4
= 2.25
Therefore, your answer is: 2.25
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
Solve the following system of equations
Answer:
Given Two equations :-
[tex]3x {}^{2} - 2 {y}^{2} = 57 .\: .\: .\: . \:(i) \\ - 2 {x}^{2} + 3 {y}^{2} = -23.\: .\: .\: . \:(ii)[/tex]
multiplying eq.(i) by 2 eq.(ii) by 3.[tex](3x {}^{2} - 2 {y}^{2} = 57 ) \times 2 .\: .\: .\: . \:(i) \\ ( - 2 {x}^{2} + 3{y}^{2} = - 23) \times 3.\: .\: .\: . \:(ii)[/tex]
[tex]6x {}^{2} - 4 {y}^{2} =114 .\: .\: .\: . \:(i) \\ - 6 {x}^{2} + 9 {y}^{2} = - 69.\: .\: .\: . \:(ii)[/tex]
[tex]0 + 5 {y}^{2} = 45 \\ 5y {}^{2} = 45 [/tex]
diving both sides by 5[tex] {y}^{2} = 9[/tex]
taking Square root[tex]y = + - 3[/tex]
placing this value of y² in eq. (i)3x²- 2×9 = 57
3x² - 18 = 57
adding 18 to both sides3x² = 57 + 18
3x²= 75
diving both sides by 3x² = 25
x = ± 5
So, the values of x are +5 and -5 and the values of y are +3 and -3in the figure JKLM ~ EFGH. complete the following table.
Answer:
scale factor 5:2
x= 27.5
y=12
z=7.5
Step-by-step explanation: