If you raise a cube root of -2 to the third power, the resulting number will have a congruent argument. We have
-2 = 2(cos 180º + i sin 180º)
Pick a number from the 4 given options, and raise it to the third power using DeMoivre's theorem. For example,
[tex]\left(\sqrt[3]{2}\left(\cos90^\circ+i\sin90^\circ\right)\right)^3=2\left(\cos(3\cdot90^\circ)+i\sin(3\cdot90^\circ)\right)=2(\cos270^\circ+i\sin270^\circ)=-2i[/tex]
so the first option is not a cube root of -2 because the argument 270º is not congruent to 180º. Similarly, the second and fourth options are also not cube roots of -2.
On the other hand,
[tex]\left(\sqrt[3]{2}(\cos60^\circ+i\sin60^\circ)\right)^3=2(\cos180^\circ+i\sin180^\circ)[/tex]
so the third option is a cube root of -2.
A class goes to a science museum. There is an exhibit which has a giant sphere that shows different weather patterns. The surface area of the sphere is 24,316.16 ft. What is the radius of the sphere? Use 3.14 for pi.
Answer: sjsjsjdjffj
Step-by-step explanation:
what is the difference between - 21 and -8 on a number line?
Answer:
They are 13 units apart. -8 is closer to zero while -21 is farther ways from zero.
simplify x^2 + (y - 4)^2
10) A spinner has an equal chance of landing
on each of its four numbered regions. You
spin twice. The first spin lands in region
one and the second spin lands in region
one.
Are the events independent or dependent?
What is the probability?
Answer:
independent and 1/16
Step-by-step explanation:
independent because you are not getting it you are just spinning.
1/4 times 1/4
i may be wrong on this
At the school track meet, Dita ran 100 meters at a rate of How long did it take Dita to finish the race?
6.25 meters per second.
16 seconds
093.75 seconds
106.25 seconds
*help asap*
Answer:
the answer is (16 seconds)
Step-by-step explanation:
The time spent by Dita to finish the race is 16 seconds.
What is a word problem?Word problems in mathematics are applications of arithmetic operations, variables, and the use of basic algebra in solving challenges in real life cases.
From the information given;
Dita ran a distance of = 100 meterSpeed used to cover the distance = 6.25 m/sUsing the relation;
[tex]\mathbf{Speed = \dfrac{distance}{time}}[/tex]
[tex]\mathbf{6.25 m/s = \dfrac{100 \ m }{time}}[/tex]
[tex]\mathbf{time = \dfrac{100\ m }{6.25 \ m/s}}[/tex]
time = 16 seconds
The time spent by Dita to finish the race is 16 seconds.
Learn more about word problem here:
https://brainly.com/question/25693822
( Quick Response) Which expressions are equivalent?
Answer:
A, 3x-7y=-7y+3x
Step-by-step explanation:
Find the area of the un-shaded region. The perimeter of the square is 16 feet. ( with explanation)
Answer:
12.56
The answer is 12.56 since the radius if the circle is 2². Multiply 2 by 2 since it is squared. Then multiply that product (4) by pi. 4 x π = 12.56
Makayla has 90 minutes to answer 36 questions on a school survey. How many minutes per
question does she have?
Answer:
Makayla has 2 and a half minutes to answer each question.
Step-by-step explanation:
To get two and half you will have to divide 90 from 36 then you get 2 and a half minutes. hope this helps =D
By using division as mathematical operation,
Makayla need 2 and half minutes to answer each question
What is division?"The division is one of the four basic mathematical operations, the other three being addition, subtraction, and multiplication. In simple words, division can be defined as the splitting of a large group into smaller groups such that every group will have an equal number of items. It is an operation used for equal grouping and equal sharing in mathematics."
We have
Number of minutes to answer 36 questions = 90
We have to divide 90 by 36
= [tex]\frac{90}{36}[/tex]
= 2.5 minutes
Hence, By using division as mathematical operation, Makayla need
2 and half minutes to answer each question.
Learn more about division here
https://brainly.in/question/5910014
#SPJ2
What is the solution to this system of equations?
Negative 3 x + 5 y = negative 2. 3 x + 7 y = 26.
(4, 2)
(2, 3 and one-third)
no solution
infinitely many solutions
Answer:
4,2
Step-by-step explanation:
did the test
The solution of the system of equation is (4, 2) which is correct option(A).
What is equation?Equation is the defined as mathematical statements that have a minimum of two terms containing variables or numbers is equal.
Given the two systems of equations,
-3x + 5y = -2
3x + 7y = 26
Adding the both equations
-3x + 5y + 3x + 7y = -2+26
12y = 24
y = 2
Substitute the value of y in any one of the equations,
3x + 7 y = 26
3x + 7(2) = 26
3x = 26-14
3x = 12
x = 4
Hence, the solution of the system of equation is (4, 2).
Learn more about equation here:
brainly.com/question/10413253
#SPJ2
Please help!!
Simplify the expression.
csc^2x-1/ 1 +sinx
Answer:
Step-by-step explanation:
Determine the intercepts of the line.
y = 5x - 13
Answer:
x intercept(s): (13/5,0)
y intercept(s): (0,-13)
Step-by-step explanation:
I don’t understand how to do this. “Finding the absolute value of an expression”
Answer:
To find the absolute value of an expression think of every number as a positve one. So if you see a number in parenthesis that is negative, make it a positive and then solve! If a number is already positive, it is already in its absolute value form.
For example:
(-4) + (2)= ?
We know that every number has to be positive to be absolute value so we would make -4 a 4 and 2 is already in absolute value so we will keep it as it is and solve.
4-2=?
Now we will solve the expression as normally which would be 2. Hope this helps!
Step-by-step explanation:
Answer:
So from what I see on the screen you have to find more than one way to solve for each problem but first you need to know what you are trying to solve for so lets go to the second problem
15+6
so 15 + 6 = 21 and now you can put 21 at the right end and in the middle you would make 2 different problems to put in the middle like 10+11 and 3 x 7
so it would look like this for the second one
[15+6] = 10+11 = 3 x 7 = 21
I hope this helps you and good luck. :D
What is the value of the variable?
A. 55
B. 74
C. 70
D. 110
Answer:
74
Step-by-step explanation:
The number of hours worked by the employees of Bob's Car Wash in one week are listed.
20, 40, 30, 36, 36, 40, 39, 36, 38
The mean is 35 hours per week and the median is 36 hours per week.
Which statement best explains why the mean is less than the median?
O
A. There are only 9 employees.
O
B. Nobody works more than 40 hours.
O
c. The smallest number is half the largest.
O
d. One worker works much fewer hours than everyone else.
PLEASE HURRY
Answer:
Option D
One worker works for much fewer hours than everyone else
Step-by-step explanation:
First of all, we will need to clarify the concepts.
The median of a distribution is the middle number in that distribution, after the values have been arranged in either an ascending or descending order.
The mean is a weighted average of a distribution.
The mean has the characteristic of usually being affected by extremely low or extremely high values.
In our case, we have a relatively low value in terms of hours worked. This means that in the distribution, the worker that worked only 20 hours, will affect the mean hours worked by all the workers, making it lower than the median value.
Means give better results, when used to analyse distributions with smaller ranges.
16. Use the net to find the surface area of the prism.
(1 point)
16.6 m
16.6 m
10 m
1
16.6 m
14 m
Not drawn to scale.
9 m
10 m
O276 m²
O 22 m²
O 522 m²
0968 m²
17. Find the volume of the rectangular prism. (1 point)
can you show me a picture then maybe i can help you
1. Use substitution to create a one-variable linear equation: -3= 4x - 5.
2. Solve to determine the value of the unknown variable.
3. Write the solution to the system of equations as an ordered pair.
The solution to the system is (
-3).
Intro
3 of 15
Answer:
x = 1/2
Step-by-step explanation:
-3= 4x - 5 becomes 5 - 3 = 4x when 5 is added to both sides. Then:
2 = 4x, and x = 2/4, or x = 1/2.
The solution of the linear equation -3= 4x - 5 is x = 1/2.
What is linear equation?Equations whose variables have a power of one are called linear equations. One example with one variable is where ax+b = 0, where a and b are real values and x is the variable.
Given:
An equation: -3 = 4x - 5.
Simplifying,
by using substitution,
4x - 2 = 0
This is a one variable linear equation. Where x is a variable.
In order to solve the equation:
Simplifying,
4x = 2
x = 1/2
Therefore, the solution of the equation is 1/2.
To learn more about the linear equation;
https://brainly.com/question/29739212
#SPJ6
Use the inverse of this function to select the correct graph.
Answer:
D
Step-by-step explanation: (i know this part. its the graph im a tiny bit unsure about)
x __ y
2 __2
3 __ 2.387
7__ 3
Find the range of the data in the box plot below.
pencils
PLZ ASAP PLZ ASAP
Answer:
12
Step-by-step explanation:
the range is = maximum value given - the minimum value given
the data is spread from 0 -12. that means that someone either had 0 pencils or any other number of pencils to 12.
the range would then be 12 - 0.
Can someone please help me out
Determine the center and radius of the following circle equation:
x² + y² - 10x + 20y + 89 = 0
Answer:
The center is ( -5, -10) and the radius = 6.
Step-by-step explanation:
Convert the equation to standard form by completing the square;
x^2 + y^2 - 10x + 20y + 89 = 0
x^2 + y^2 - 10x + 20y = -89
x^2 - 10x + y^2 + 20y = -89 Completing the square:
(x + 5)^2 - 25 + (y + 10)^2 - 100 = -89
(x + 5)^2 + (y + 10)^2 = -89 + 125
(x + 5)^2 + (y + 10)^2 = 36
Comparing this to the standard form:
( x - h)^2 + (y - k)^2 = r^2
- we see that the center is ( -5, -10) and the radius = 6.
How much is the ENDING Balance...
$53,300 at 6% for 9 years?
Answer:
The ending balance is $90049.2285
Step-by-step explanation:
Principal = 53300
Rate of interest =6%
Time = 9 years
We are supposed to find How much is the ENDING Balance
Formula : [tex]A=P(1+r)^t[/tex]
A = Amount
P = Principal
r = rate of interest in decimals
t =time
Substitute the values in the formula "
So,[tex]A=53300(1+0.06)^9[/tex]
A=90049.2285
Hence The ending balance is $90049.2285
Use the graph or table to write a linear function that relates to y to x.
Answer:
the answer to the question is D
Coordinates A (1, 2), B (3, 2) and C (3,5) are connected to form AABC. If ADFE is similar to AABC, what are the coordinates of F?
(5, 10)
(10,5)
(12,7)
Math question down below
Help! I don't know how to do this! I will mark Brainliest!
Answer:
- 3y² - 7y + 6
Step-by-step explanation:
Given
(- 3y + 2)(y + 3)
Each term in the second factor is multiplied by each term in the first factor, that is
- 3y (y + 3) + 2(y + 3) ← distribute both parenthesis
= - 3y² - 9y + 2y + 6 ← collect like terms
= - 3y² - 7y + 6
Answer:
is it A?
Step-by-step explanation:
i choose that because its the only one with -3y² which is correct
Which ordered pair is a solution of y = x + 12? (9, 21) (24, 12) (–12, –24) (0, –12)
Answer:
(9, 21)
Step-by-step explanation:
Which point represents the center of the circle shown below?
Answer:
Point A
Step-by-step explanation:
Point A
The center of the circle is in the middle of the circle. Points C, T, R, and P are on the circumference of the circle, and A is in the middle of the circle, so it is point A
Point A represents the center of the circle, the correct option is D.
What is a Circle?A circle is a round shaped figure, all the points of a circle lie on the same plane and all the points on the circle are at equal distance from a single point called as center.
The image shows a circle.
The point which is equidistant from R,P,G, and T is A.
A is the center of the circle.
To know more about Circle
https://brainly.com/question/11833983
#SPJ5
Aisha is playing a game in which she can gain or lose points on each turn. The table below
shows the points she scores on each of four turns in the game.
Aisha states that her highest score is on Turn 3, because 16 is greater than 3, 10, or 9. Use the
drop-down menus to explain Aisha's mistake.
Answer:compares the absolute value ,score of 16 represents greatest lost ,highest score farthest away from 0, on a number line that number is 10
Step-by-step explanation:ig/ 6k.mar
A score of -16 represents the lowest of points for these four turns.
The number for Aisha's highest score will be turn 2 on the number line.
That number is 10.
What is number?A number is a mathematical object used to count, measure, and label. The original examples are the natural numbers 1, 2, 3, 4, and so forth. Numbers can be represented in language with number words.
here, we have,
Since the options of the drop down menu are not included, you should choose any option similar to lowest.
Aisha's highest score was obtained in turn 2 and that is 10.
we have,
Aisha is comparing absolute terms, that is why she believes that -16 represents a good score, while in reality is the worst she got.
Hence, A score of -16 represents the lowest of points for these four turns.
The number for Aisha's highest score will be turn 2 on the number line.
That number is 10.
To learn more on number click:
brainly.com/question/17429689
#SPJ7
To find the mileage, or how many miles a car can travel per gallon of gasoline, you can use the expression m/g, where m is the distance in miles and g is the number of gallons of gas used. Find the mileage in miles per gallon for a car that travels 585 miles on 18 gallons of gas? (Your answer does not need miles per gallon at the end.)
Answer:32.5
Step-by-step explanation:
585/18
(4x + 30)
What’s the answer
Answer:
Fraction form -15/2
Decimal form -7.5
Step-by-step explanation:
4x+30=0
subtract 30 from both sides
4x=-30
divide both sides by 4
x=-30/4
simplify
-15/2 or -7.5
