Which expression is a cube root of -2?
A. Cubed root of 2 (cos(90°) + isin(90°))
B. Cubed root of 2 (cos(120°) + isin(120°))
C.cubed root of 2 (cos(60°) + isin(60°)).
D. Cubed root of 2 (cos(260°) + isin(260°))
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.
Please help what is the solution to the equation AX = B?
Answer:
The first one
Step-by-step explanation:
In this question, we are trying to find X, so can solve this by back-solving. multiply the choices by the A until they equal B. If you do it for the first one then you should gett B.
Answer:
Option D.
Step-by-step explanation:
edge test
Any help someone....
(solve triangles using the law of sines)
Answer:
[tex]B=51[/tex]°
Step-by-step explanation:
Use the Law of Sines as follows:
[tex]\frac{sinC}{c} =\frac{sinB}{b}[/tex]
Insert the appropriate values:
[tex]\frac{sin100}{14} =\frac{sinB}{11}[/tex]
Isolate B. Multiply both sides by 11:
[tex]11*(\frac{sin100}{14} )=11*(\frac{sinB}{11})\\\\\frac{11*sin100}{14} =sinB\\\\sinB=\frac{11*sin100}{14}[/tex]
Use the inverse:
[tex]B=sin^{-1}(\frac{11*sin100}{14})[/tex]
Insert the equation into a calculator and round to the nearest degree:
[tex]B=50.7\\\\B=51[/tex]
Angle B is 51°.
:Done
A pair of jeans is on sale for 25% off the original price of $75. What is the
new price?
Answer:
$56.25 is the new price
Step-by-step explanation:
75 - 18.75 = 56.25 dollars
Answer:
56.25
Step-by-step explanation:
75*.25=18.75
75-18.75=56.25
Mark bought 29 gummy worms at the candy store. His friend Camille also bought some gummy worms. When they counted all of them together, Mark and Camille had 78 gummy worms. Which equation, when solved, will show how many gummy worms Camille bought?
Answer:
camillie bought 49 gummy worms
Step-by-step explanation:
78-29= 49
Answer:
49
Step-by-step explanation:
If all together they have 78. Subtract 29 from 78 to get the answer 49.
The amount of tomato sauce in an 8 oz. can of tomato sauce has a normal distribution with a mean of
8.15 oz. and a standard deviation of 0.07 oz. Which of the following is the 2-score for 7.90 oz.?
Answer:
The z-score for 7.90 oz. is -3.57
Step-by-step explanation:
Data
mean: 8.15 oz.standard deviation, sd: 0.07 oz.value of interest, x = 7.90 oz.From definition of z-score:
Z = (x - mean)/sd
Replacing with data:
Z = (7.9 - 8.15)/0.07
Z = -3.57
Help asap pleaseee!
A climber is on a hike. After 2 hours, he is at an altitude of 400 feet. After 6 hours, he is at an altitude of 700 feet. What is the average rate of change?
200 ft per hour
105 ft per hour
300 ft per hour
75 ft per hour
Answer:
75
Step-by-step explanation:
700-400=300
6-2=4
300/4=75
Answer:
75 ft per hour.
Step-by-step explanation:
because
PLEASE HELP ME!!!!!!!! I CANT GET IT! PLEASE HELP QUICKLY!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
The length of a rectangle is four times its width. The width of this rectangle is 9 inches less than its length. Find the length and the width of the rectangle.
You answer would be 27, if I did my maths correct.
You get 27 by doing:
9*4=36
36-9=27
Correct me if I am wrong thank you!
Answer:
At first I got 39 but then I redid it and got 27!
What is 2(12) 3/2 in its simplest form?
Answer:
1 1/2
Step-by-step explanation: it is 1 1/2 because 3/2 is improper there is one left over and a half therefore 1 1/2 is the answer not 11/2 just to be clear
The value of the mixed expression 2 x (12) x 3/2 will be 36.
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
Given expression is 2 x (12) x 3/2. the value of the expression will be calculated as below:-
E = 2 x (12) x 3/2.
E = 12 x 3
E = 36
Therefore, the value of the mixed expression 2 x (12) x 3/2 will be 36.
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Look at the pic in the corner it’s math
Answer:
The third one
Step-by-step explanation:
Its because we need to find the number that it has grown.
so we add the number that it grew to the size it was before.
Answer: 1.85 + x = 5.30
Step-by-step explanation: If we know that Ethan planted a tree that was 1.85 meters tall from the start and several years later it's 5.30 meters tall, we know that something must have been added to the 1.85 in order to get 5.30 meters tall. Since we don't know what that value is, we can use x.
X is an example of a variable. A variable is just a letter that represents any number so in this case, it represents how much the tree has grown over a time period of several years.
So we can write this as 1.85 + x = 1.30.
PLEASE HELP! The density of atmosphere (measured in kilograms/meter) on a certain planet is found to decrease as altitude increases (as measured from
the planet's surface). What type of relationship exists between the altitude and the atmospheric density, and what would the atmospheric
density be at an altitude of 1.291 kilometers?
Answer:
The relationship that exist between the altitude and the atmospheric density is an inverse relationship.
[tex]D = \frac{k}{1291} kg/m^3[/tex]
Step-by-step explanation:
since the density of the atmosphere decreases as the altitude increases, the relationship that exist between the altitude and the atmospheric density is an inverse relationship. This can be represented by:
[tex]D = \frac{k}{H}[/tex], where k is the constant, H is the altitude in meters and D is the atmospheric density in kg/m.³
When the altitude is 1.291 km, i.e H = 1.291 km = 1291 m,the atmospheric density D is:
[tex]D = \frac{k}{1291} kg/m^3[/tex]
line q goes through points (-3,3) and (-5,-3). At what point does line q cross the y-axis
Answer:
(0,12)
Step-by-step explanation:
Answer:
-3
Step-by-step explanation:
The width of a rectangular room is 60% of its length. The length of the room is 10 feet. What is the area of the room?
The area of the room is blank square feet.
Answer:
60ft^2
Step-by-step explanation:
60% of 10 is 6 and LxW is 10x6 so the area is 60 feet
Enter your answer in the box.
Answer: 69
Step-by-step explanation:
360
Answer:
528
Step-by-step explanation:
To the nearest cubic inch, what is the volume of the
right triangular prism?
Answer:
The Volume of right triangular prism is 240 cubic inches
Step-by-step explanation:
Volume of right triangular prism =[tex]\text{Area of base} \times height[/tex]
In triangle ABC
AC = Hypotenuse = 13 in.
AB = Height
BC = Base = 12 in.
Using Pythagoras theorem
[tex]Hypotenuse^2=Perpendicular^2+base^2\\13^2=Perpendicular^2+12^2\\\sqrt{13^2-12^2}=Perpendicular[/tex]
5=Perpendicular
Area of base = [tex]\frac{1}{2} \times Base \times Height = \frac{1}{2} \times 12 \times 5 = 30 in^2[/tex]
Height of prism = 8 in
Volume of right triangular prism =[tex]\text{Area of base} \times height[/tex]
Volume of right triangular prism =[tex]30 \times 8 = 240 in^3[/tex]
Hence The Volume of right triangular prism is 240 cubic inches
Write a problem that could be modeled with y = 200(0.9)^x
Answer:
Step-by-step explanation:
A new TV sells for $200. Every year, the TV loses 10% of the initial value.
1. Which money market account will earn the most interest?
(33 puntos)
$500 principal at 0.5% monthly for 10 years.
$200 principal at 1% monthly for 20 years.
$1,000 principal at 3% monthly for 2 years.
$100 principal at 8% monthly for 1 years.
What are m<1 and m<2?
Answer:
m<2 is 66 and m<1 is 114
Step-by-step explanation:
add the given angles together, that is the outaide angle. then subtract that from 180 and you get angle 2
I have no access at 6 pm
Answer:
A and E
Step-by-step explanation:
I would plug in N as any number just to see if they are equal. I did 5.
A. 28(5)-35= -105
B. 28(5-35)= -840
C. 28(5-7)= -56
D. 7(4*5-35)= -105
E. 7(4*5-5)= 105
Find the quotient.
1. 48÷3=
.
2. In the expression, 96 divided by 8 = a , the quotient a =
.
3. Divide 12 lizards into 6 equal groups. How many lizards are in each group?
There are
lizards in each group.
Answer:
48÷3=16
Step-by-step explanation:
In the expression, 96 divided by 8 = a , the quotient a =12
. Divide 12 lizards into 6 equal groups. How many lizards are in each group?
There are2
lizards in each group.
Answer:
1. 16
2. 6
3. 2
Step-by-step explanation:
If 50% of an item is 22.00 what is the original price ?
Answer:
$44
Step-by-step explanation:
Answer:
44
Step-by-step explanation:
I need help with this please, I’m not sure if I should use the a^2+b^2=c^2
Answer:
yes, use the Pythagorean theorem
Step-by-step explanation:
it would be 6^2+15^2=c^2
Jackson at the collectibles fair. He has exactly $8 and will purchase a collectible from a vendor for $5. What percent of his money will Jackson spend on the purchase?
Answer:
62.5%
Step-by-step explanation:
Total money with Jackson = $8
Money spent for buying collectible = $5
__________________________________________________
Percentage of any number A with respect to another number B is calculated by multiplying fraction A/B with 100
Numerically A as percentage of b will be expressed as (A/B)100 %
It means that if there are 100 items instead of B item then what will be the value of A.
______________________________________________________
Percentage of money spent = (Money spent for buying collectible /Total money with Jackson)
Substituting the total money and money spent for buying collectible
we have
Percentage of money spent = 5/8 * 100 = 0.625*100 = 62.5%
Thus, 62.5% percent of his money will Jackson spend on the purchase of collectible.
Select the correct answer.
Which statement describes the situation shown in the graph?
Answer:
there is no photo??where are the graphs??
What is the volume of this rectangular prism?
4 cm
[tex] \frac{5}{2} cm[/tex]
[tex] \frac{1}{2} cm[/tex]
need answer asap
Answer:
D on Edg
Step-by-step explanation:
Answer: V = 5cm³
Step-by-step explanation: We have to follow the formula to get the volume of this rectangular prism, Volume = Length * Height * Width.
First, let's turn the fractions into deciamls:
4 cm
2.5 cm
0.5 cm
The length is 4 cm, the width is 0.5 cm, and the height is 2.5 cm.
4 x 2.5 x 0.5 = 5
5cm³
I hope this helps!
Part A: The area of a square is (4a2 − 20a + 25) square units. Determine the length of each side of the square by factoring the area expression completely. Show your work. (5 points) Part B: The area of a rectangle is (9a2 − 16b2) square units. Determine the dimensions of the rectangle by factoring the area expression completely. Show your work. (5 points)
Answer:
(2a -5)²(3a -4b)(3a +4b)Step-by-step explanation:
There are a couple of factored forms that are used here:
(a +b)² = a² +2ab +b² . . . . the sign of "2ab" will match the sign of b
a² -b² = (a -b)(a +b)
__
Part A:
Since this trinomial is known to be a perfect square, you can find the binomial(s) by looking at the roots of the first and last terms.
√(4a²) = 2a
√25 = 5
The factoring is ...
4a² -20a +25 = (2a -5)²
__
Part B:
This is the difference of perfect squares, so the terms of the factors can be found as in the previous part.
√(9a²) = 3a
√(16b²) = 4b
Using the above factored form, we have ...
9a² -16b² = (3a -4b)(3a +4b)
Change these times to the 12-hour clock.
07:10
17:30
Answer:
7:10 am
5:30 pm
Given the equation, (x - h)2 + (y - k)2 =r2, what are the coordinates of the center?
The coordinates of the center are ( , )
Answer:
(h, k).
Step-by-step explanation:
This is the standard form of the equation of a circle
The coordinates of the center are (h, k)
The radius is r.
The coordinates of the center are (h, k).
What is Circle?The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.
Given that;
The equation is,
⇒ (x - h)² + (y - k)² = r²
Now, We know that;
The standard form of the equation of circle is,
⇒ (x - h)² + (y - k)² = r²
Where, (h, k) is coordinates of the center and r is the radius of the circle.
Hence, By comparing, we get;
The coordinates of the center are (h, k).
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SDRTYUK243567Iaqwertyh.
Answer
B, i think
Step-by-step explanation:
Rewrite using only positive exponents.