Answer:
The product of
36√cis(π/8) and 25√cis(7π/6)
is
(225√2)√[√(2 + √2) + i√(2 - √2)][√(3(-1 + i))]
Step-by-step explanation:
First note that
cis(π/8) = cos(π/8) + isin(π/8)
cis(7π/6) = cos(7π/6) + isin(7π/6)
cos(π/8) = (1/2)√(2 + √2)
sin(π/8) = (1/2)√(2 - √2)
36√cis(π/8) = (36/√2)√[√(2 + √2) + i√(2 - √2)]
cos(7π/6) = -(1/2)√3
sin(7π/6) = (1/2)√3
25√cis(7π/6) = (25/2)√3(-1 + i)
The product,
36√cis(π/8) × 25√cis(7π/6)
= (36/√2)√[√(2 + √2) + i√(2 - √2)] × (25/2)√3(-1 + i)
= (225√2)√[√(2 + √2) + i√(2 - √2)][√(3(-1 + i))]
Answer:
32.86 cis ( 4.06 )
Step-by-step explanation:
TTT
Based on the side lengths alone, could the triangles be similar? Triangle R S T. Side R S is 3 centimeters, side S T is 6 centimeters, and side R T is 6.4 centimeters. Triangle W X U. Side W X is 16 centimeters, side X U is 7.5 centimeters, and side W U is 15 centimeters. No, the sides are not proportional. Yes, the sides are in the ratio 2:5. Yes, the sides are in the ratio 4:5. Yes, the sides are in the ratio 1:5.
Answer:
Yes, the sides are in the ratio 2:5.
Step-by-step explanation:
All sides divided by each congruent side are = to .4 and 2/5 is = to 4/10
The sides of triangles are not proportional, thus the triangle is not similar triangle.
What is triangle?Triangle is "a polygon that has three sides and three angles. The sum of the angle of the triangle is 180 degrees".
What is similar triangles?
If the ratio of the "sides of the triangles ΔABC and ΔDEF are equal then the triangles are similar triangles".
According to the question,
In ΔRST and ΔWXU are similar triangle if ∠R = ∠W; ∠S = ∠W; ∠T=∠U
then [tex]\frac{RS}{WX} = \frac{ST}{XU}[/tex] .
In ΔRST, side RS is 3 centimeters, side ST is 6 centimeters, and side RT is 6.4 centimeters. In ΔWXU, Side WX is 16 centimeters, side XU is 7.5 centimeters, and side WU is 15 centimeters.
[tex]\frac{3}{16} = \frac{6}{7.5} = \frac{6.4}{15}[/tex]
Hence, the sides are not proportional then the triangle is not similar triangle.
Learn more about similar triangles here
https://brainly.com/question/27609371
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Estimate how many minutes Jessica must practice basketball free throws if she has to shoot a total of 50 successful free throws, and he
average is 3 successful free throws a minute.
A.3
B.17
C.47
D.53
E.150
Answer:
17
Step-by-step explanation:
average per minute is 3, and you need 50, so 3x?=50
to know "?" we change how the question is, so it ends 50/3=?
50/3= 16.6666666667 and the closest is 17
Leeza’s aquarium holds 55 gallons of water. She is filling the tank and has already put in 22 gallons. Write and solve an inequality to find out how many more gallons she might put in the tank.
Step-by-step explanation:
the answer is 55 is less than or equal to 22
Devaughn's age is three times Sydney's age. The sum of their ages is 76. What is Sydney's age?
Answer:
22
Step-by-step explanation:
Basically you can think of Devaughn as 3x and Sydney as 1x, which gives you 4x=88. 88/4= 22, so Sydney is 22
HELP HELP. Look at the factors of 50 and 75.
Factors of 50: 1, 2, 5, 10, 25, 50
Factors of 75: 1, 3, 5, 15, 25, 75
The GCF of 50 and 75 is ______
Answer:
25
Step-by-step explanation:
25 bc it is the largest number than can go both into 50 and 75
Answer:
GCF =25
Step-by-step explanation:
The prime factorization of 50 is: 2 x 5 x 5.
The prime factorization of 75 is: 3 x 5 x 5.
The prime factors in multiplicities 50 and 75 have in common are 5 x 5.
5 x 5 is the GCF of 50 and 75.
I hope this helps!! :]
Solve for the volume of the cylinder.
(Use picture below)
solve for a 7a - 2b =5a + b
Answer:
a = 3/2 b
Step-by-step explanation:
7a - 2b =5a + b
Subtract 5a from each side
7a-5a - 2b =5a-5a + b
2a -2b = b
Add 2b to each side
2a-2b+2b = b+2b
2a = 3b
Divide each side by 2
2a/2 = 3b/2
a = 3/2 b
Which ratio is equivalent to the ratio 30:48?
Answer: 5:8
Step-by-step explanation:
By reducing both sides equally, the ending answer is 5:8
(There can be many answers to your question but the one i told you is the most reduced one)
Answer:
10 : 13
Step-by-step explanation:you can find equivalent ratios by dividing or multiplying both the ratios by the same number.
eg 30 : 48 can be divided by 3 which gives 10:16
Hope it is clear,Thank you
Which equation shows the correct use of the Distributive Property? −4(3/2x−1/2)=−15
A. 6x + 4 = –15
B. 2x – 12 = –15
C. –6x – 2 = –15
D. –6x + 2 = –15
Answer:
D
Step-by-step explanation:
1 1/3 x 6/7 (the 1 in the front is a whole)
Look at the attached picture
Hope it will be helpful to you
Answer:
well it would be 9 over 14 hope this helps
Step-by-step explanation:
Solve the system. -3x + 4y = -22 2x + 7y = 5 A) (6, -1) B) (-1, 6) C) (-6, 1) D) (-1, -6)
Answer:
A
Step-by-step explanation:
We have the system of equations:
-3x + 4y = -22
2x + 7y = 5
Let's solve this using elimination, so multiply the first equation by 2 and the second equation by 3:
2 * (-3x + 4y = -22) ⇒ -6x + 8y = -44
3 * (2x + 7y = 5) ⇒ 6x + 21y = 15
Our equations are now:
-6x + 8y = -44
6x + 21y = 15
Add these two together to eliminate the x term:
-6x + 8y = -44
+ 6x + 21y = 15
______________
0x + 29y = -29
y = -29/29 = -1
Plug this back into one of the equations to find x:
-3x + 4y = -22
-3x + 4 * (-1) = -22
-3x - 4 = -22
-3x = -18
x = -18/(-3) = 6
The answer is (6, -1) or A.
Answer:
A. (6,-1)
Step-by-step explanation:
-3x + 4y = -22
2x + 7y = 5
x = (5 - 7y)/2
-3[(5 - 7y)/2] + 4y = -22
-15/2 + 21y/2 + 4y = -22
29y/2 = -29/2
y = -1
x = (5 - 7(-1))/2
x = 12/2
x = 6
Solve the system of equations :
2x -5y=-22
X+7y=27
Answer:
x=−1 y=4
Step-by-step explanation:
Let's solve your system by substitution.
2x−5y=−22; x+7y=27
Rewrite equations:
x+7y=27;2x−5y=−22
Step: Solve x+7y=27for x:
x+7y=27
x+7y+−7y=27+−7y(Add -7y to both sides)
x=−7y+27
Step: Substitute−7y+27 for x in 2x−5y=−22:
2x−5y=−22
2(−7y+27)−5y=−22
−19y+54=−22(Simplify both sides of the equation)
−19y+54+−54=−22+−54(Add -54 to both sides)
−19y=−76
−19y
−19
=
−76
−19
(Divide both sides by -19)
y=4
Step: Substitute 4 for y in x=−7y+27:
x=−7y+27
x=(−7)(4)+27
x=−1(Simplify both sides of the equation)
Find the value of x
MATH HELP PLEASE !50 POINTS!
Answer: 108
Step-by-step explanation: You take the x and the 2/3x and combine them to get 1 2/3x, so 1 2/3x=180. 180 divided by 5 is 36, and 36 times three is 108
Answer:
108
Step-by-step explanation:
Angles on a line add up to 180 degrees.
x + 2/3x = 180
5/3x = 180
x = 180 × 3/5
x = 108
Jana predicts that the population, y, will grow according to y = 12 log(x + 1) + 10, where x is the time in minutes. How much greater does Kirk’s model predict the population will be after 60 minutes than Jana’s model?
Answer:
Greater by about 50 bacteria
Step-by-step explanation:
Greater by about 50 bacteria
Answer:
Greater by about 50 bacteria
Step-by-step explanation:
After decoding the clues on the map, they found out that they needed to go to the
Island of Mysteries which was 120 miles away. To get there, they could either
take a plane for $600 or a boat for $254. How much money can they save if they
took a boat to the island?
Answer:
$346.00
Step-by-step explanation:
We know that the price to take a plane to the Island of Mysteries is $600 and the price to take a boat is $254.
To find how much money they will save if they were to take a boat, you would subtract the cost of the boat ride from the plane ride to find the difference.
$600 - $254 = $346.00
Jorge is comparing two data sets. He uses the mean and mean absolute deviation to compare the center and variability of the data sets. If the measures of center and variability accurately describe the sets, which best describes both data sets?
a. not symmetrical without outliers
b. not symmetrical or containing outliers
c. symmetrical and containing outliers
d. symmetrical without outliers
Answer:
C. Symmetrical without outliers
Step-by-step explanation:
It's talking about BOTH and how they compare. :)
Answer:
C
Step-by-step explanation:
Sorry i'm late
Anyway i wish you have a good day!
:)
What is the value of x
Answer:
x= ?
Step-by-step explanation:
Answer:
depends on the equation u didnt give us
Step-by-step explanation:
Joan receives a 9% commission on appliances she sells. Last month she sold $18,500 worth of appliances. How much did Joan earn in commissions last month?
Answer:
She earned $1,665.
Step-by-step explanation:
x / 18500 = 9/100
What did you do to transform 18500 into 100? Divide by 185
Since you divided the denominator 185, you must do the same to the numerator.
x / 185 = 9 OR 9 * 185 = x
x = 1665
PLEASE ANSWER MY QUESTION IT IS URGENT I AM BEING TIMED
Write each fraction as a percentage. Include a fraction in the hundredths place if needed.
Example: 12 3/4%
First question: 1/2
second question: 1/4
Answer: The 1st one is 0.5%
The 2nd one is 0.25%
Step-by-step explanation:
Pip and Sara win some money and share it in the ratio 7:3. Pip gets £36 more than Sara. How much did they get altogether?
Answer:
I think its 90 but im not sure.
Step-by-step explanation:
Final answer:
To find the total amount won by Pip and Sara, a ratio problem was solved by establishing an equation from the given ratio 7:3 and the fact that Pip gets £36 more than Sara, resulting in a total amount of £90.
Explanation:
The question involves solving a problem based on a ratio and determining the total amount of money shared by Pip and Sara. The ratio in which Pip and Sara share the money is 7:3, and since Pip gets £36 more than Sara, we can set up equations to find the individual and total amounts.
Let's denote Sara's share as S, hence Pip's share will be S + £36.
According to the ratio given, Pip's share to Sara's share is 7 to 3, so we can write the equation:
7S = 3(S + 36)
7S = 3S + 108
4S = 108
S = 27
So Pip's share is £27 + £36 = £63.
Adding both shares, the total amount is £63 + £27 = £90.
Therefore, Pip and Sara got £90 altogether.
The names of nine boys and six girls from your class are put into a hat. What is the probability that the first two names chosen will both be girls?
Final answer:
The probability that the first two names chosen will both be girls from a hat that contains the names of nine boys and six girls is 1/7.
Explanation:
The question involves determining the probability of selecting two girls' names from a hat that contains the names of nine boys and six girls. We are dealing with a situation of probability without replacement, which means that once a name is drawn, it is not put back into the hat.
To calculate the probability of the first name drawn being a girl, we have 6 girls out of the total 15 students, which gives us a probability of 6/15. If a girl's name is drawn first, there will then be 5 girls' names left and 14 names total. So, the probability of the second name drawn being a girl as well is then 5/14.
To find the overall probability of both events happening, we multiply the two probabilities together: (6/15)
x (5/14) = 30/210 = 1/7. Therefore, the probability that the first two names chosen will both be girls is 1/7.
1) During skating practice, Sasha landed 7 out of 12 jumps. What is the experimental
probability that she will land her next jump?
Answer:
14 maybe
Step-by-step explanation:
Caren has 6 oranges to share. If she
gives one third of an orange to each
person, how many people can share
Caren's oranges?
Answer:
6/ 1/3
6 x 3/1
6 x 3 = 18
Hope this helps Your answer is 18
Step-by-step explanation:
Answer:
she can share with 18 people
whats the radius of a sphere if its volume is 1928pi
Answer:
Cube root of 1446
Step-by-step explanation:
The formula for the volume of a sphere is [tex]\frac{4}{3} \pi r^3[/tex]. Therefore, if we divide 1928pi by 4/3pi and then take the cube root, you will find the radius. In this case, 1928pi/(4pi/3)=1446, meaning that the radius is the cube root of 1446. Hope this helps!
The formula for the volume of a sphere is 4/3 the product of π and the cube of the radius of the sphere.
Therefore, if we're working backwards, we can start by multiplying 1928 by 4/3.
1928 x (4/3) = 2570.66666667
From there, we can find the cube root to find our radius.
(cube root) of 2570.6666667 = 13.698781
Therefore, the radius of the circle is 13.698781, or about 13.7.
Hope this helps! :)
Which statements about this system of equations are true? Check all that apply
.
2x - 7y=-13
- 2x + 11y = 1
The x-variable will be eliminated when adding the system of equations.
The y-variable will be eliminated when adding the system of equations.
The sum of the system of equations is 4y = -12.
Ox=17
y=-3
There are infinitely many solutions to the system of equations.
Answer:
the x-variable will be eliminated when the adding the system of equations. The sum of the system of equations is 4y = -12.
x= - 17
y= - 3
Step-by-step explanation:
B. Mercury, Venus, and Earth are the three planets closest to the sun. Would their combined distance from
the sun be greater or less than the distance from the sun to Neptune? Show your work and justify your
answer.
Answer:
Mercury Venus and earth together would be greater than the distance from Neptune to the sun neptune is 2.759 billion miles away from the sun and the three others combined are 196.18 million miles away from the sun.
find the exact length of the third side
Answer:
≈7.48, exact would be 7.48331477355
Step-by-step explanation:
Pythagorean Theorem
c is the hypotenuse (longest side)
a and b are interchangeable
a^2 + b^2 = c^2
3^2 + 7^2 = c^2
(9 + 47 = 56)
56= c^2
[tex]\sqrt{56}[/tex] = c
7.48 ≈ c
hope this helps :)
8x-72=2x-36
I need the answer
Answer: [tex]x=6[/tex]
Subtract 2x from both sides
[tex]8x-72-2x=2x-36-2x\\6x-72=-36[/tex]
Add 72 to both sides
[tex]6x-72+72=-36+72\\6x=36[/tex]
Divide both sides by 6
[tex]6x/6=36/6\\x=6[/tex]
Answer:
x=6
Step-by-step explanation:
first thing first you always need to get x alone and since you have an X on both side we need to move one of them to the same side as the other one.
8x-72=2x-36
add 72 on both sides ( the opposite of subtracting is adding)
8x=2x-36+72
8x=2x+36
then we subtract 2x on both sides to get X alone
8x-2x=36
6x=36
then we divide 36 by 6 to get our answer for x
X= 6
and that's your answer, hope this helped
PLEASE HELP!!!!!!! PLEASE!!
Find the indicated limit, if it exists. (2 points)
limit of f of x as x approaches negative 10 where f of x equals negative 4 minus x when x is less than negative 10, 6 when x equals negative 10, and x plus 16 when x is greater than negative 10
6
0
16
The limit does not exist.
Answer:
limit does not exist
Step-by-step explanation:
From the left: f(x) = x + 10 (for x < 8), as x --> 8, f(x) --> 18
From the right: f(x) = 10 - x (for x >= 8), as x --> 8, f(x) --> 2
Since the limits on either side do not converge to the same point, the limit does not exist