Answer with explanation:
[tex]z=2^{\frac{1}{3}}\\\\z^3=2\\\\z^3=2 \times (1 + 0 i)\\\\z^3=2 \times [\cos 0^{\circ} + i \sin 0^{\circ}]\\\\z^3=2 \times [\cos (2 k\pi+ 0^{\circ}) + i \sin(2 k\pi+0^{\circ})],where,k=0,1,2,\\\\z=[2\times[ (\cos (2 k\pi+ 0^{\circ}) + i \sin(2 k\pi+0^{\circ})]]^{\frac{1}{3}}\\\\z=2^{\frac{1}{3}}\times[\cos \frac{2 k\pi+ 0^{\circ}}{3} + i \sin\frac{(2 k\pi+0^{\circ})}{3}]\\\\Z_{0}=2^{\frac{1}{3}},for, k=0\\\\z_{1}=2^{\frac{1}{3}}\times[\cos \frac{(2\pi)}{3} + i \sin\frac{(2\pi)}{3}][/tex]
[tex]z_{1}=2^{\frac{1}{3}}\times[\cos(120^{\circ})+i\sin(120^{\circ})],\text{Used Demoiver's theorem}[\cos A + i\sin A]^k=\cos Ak + i\sin Ak[/tex]
Option A: →Cube root of 2 [cos (120 degrees) + i sin (120 degrees)]
A store is having a 10% off sale. It gives an additional 20% off for an item that is above $100 after the first 10% discount.A jacket costs $124.99
if you buy the jacket, how much will you save in total?
*SHOW WORK* ...?
To calculate the total amount saved when buying a jacket at a store with a 10% discount and an additional 20% discount, follow these steps: find the savings from the first discount, calculate the price after the first discount, check if the price is above $100, calculate the additional discount, and add both savings together. In this case, the total amount saved is $34.9972.
Explanation:To calculate the total amount saved, we need to use the following steps:
Find the total savings from the first 10% discount: $124.99 * 0.10 = $12.499Find the price of the jacket after the first discount: $124.99 - $12.499 = $112.491Check if the price is above $100. If it is, calculate the additional 20% discount: $112.491 * 0.20 = $22.4982Add the savings from the additional discount to the previous savings: $12.499 + $22.4982 = $34.9972So, the total amount saved is $34.9972.
Final answer:
To find the total amount saved, apply the discounts and add the amounts together. The total amount saved is $35.00.
Explanation:
To find the total amount saved, you need to calculate the discount for each discount percentage. First, apply the 10% discount to the original price of the jacket:
10% of $124.99 = $12.499.
Next, apply the 20% discount to the price after the first discount:
20% of ($124.99 - $12.499) = 20% of $112.491 = $22.4982.
Finally, add the two discounts together to find the total amount saved:
$12.499 + $22.4982 = $34.9972.
Rounding to the nearest cent, the total amount saved is $35.00.
What is the solution to the system of equations?
y = 1.5x – 4
y = –x
a. (–1.6, 1.6)
b. (–1.5, 1.5)
c. (1.5, –1.5)
d. (1.6, –1.6)
Explain what the m and b variables represent in the y=mx b equation
What number should be added to the expression x^2 + 2x to change it into a perfect square trinomial?
Solve for x and show work. 2xln(1/x)-x=0
Assume the function has an inverse. Without solving for the inverse find the indicated function values: f(x)=x^3+4x-1, (a) f^-1 (-1) (b) f^-1 (4) ...?
To find the indicated function values of the inverse of a function, substitute the given values into the original function and solve for x.
Explanation:To find the indicated function values of the inverse of the function f(x)=x^3+4x-1, without solving for the inverse function, we substitute the given values into the original function and solve for x.
(a) To find f^-1(-1), we substitute -1 into the function: f(-1)=(-1)^3+4(-1)-1 = -1+(-4)-1 = -6.
(b) To find f^-1(4), we substitute 4 into the function: f(4)=(4)^3+4(4)-1 = 64+16-1 = 79.
Dayla earns $108.75 for working 15 hours of holiday open rap at this rate how much money will see you earn if she works 18 hours the next week explain
What is the ratio of julios 22 to jonah 8 points?
what is 2/3x5/6x14 can you help me on this problem
If h(x) = -3x - 10, find h(-3).
Answer
-1
2.3
-19
1
...?
Linda Frankell pays $50.00 a month for group health insurance. There is a $300 deductible. Her medical bills for the last year were $2,600.00. Linda's insurance company provided payment of 80% of the bills less the deductible.
What was the insurance company's payment? $
What was Linda's total cost (including the monthly premium)? $
graph the equation. y = 4x - 3
Simplify: log base 3 (1/3) ...?
Read the numbers and decide what the next number should be 8,4,2,6,3,2,4.
The given sequence involves a two-part pattern. One part is halving the previous number and the other part alternates between 4 and 6. Considering the pattern, the next number should be 0.5.
Explanation:The sequence 8,4,2,6,3,2,4 appears to have a pattern. It seems to be a two-part pattern that alternates. The first part, observed in the numbers 8, 2, and 2, is halving (8 divided by 2 is 4, and 2 divided by 2 is 1, and 1 by 2 is 0.5). Then, the second part, observed in 4,6,4, seems to alternate between 4 and 6. So, if the pattern continues, the next number after 4 should be 0.5 from the first part of the pattern.
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The sequence could actually be representing two series - one series is halving the number (8 to 4 to 2) and the other is multiplying each number by 2 (3 to 2 to 4 to 8). Thus, the next number could either be 1 (if we continue the halving series) or 12 (if we continue the multiplying by 2 series).
Explanation:The number sequence provided seems to be made of two different series interwoven. One series is halving each number (8 to 4 to 2), and the other series is multiplying each number by 2 (2 to 4 to 6 to 12).
Therefore, the next number after 8, 4, 2, 6, 3, 2, 4 should be 1 (half of 2) whereas the next number in the second series after 6, 3, 2, 4 should be 12 (four times 3). So, depending on which pattern the sequence is following, the next number could be either 1 or 12.
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What is the square root of 59,005?
A sneaker store salesman had $4,125 in total monthly sales last month. He made $165 in commission from those sales. What is the salesman's commission as a percent of his total monthly sales? Enter your answer in the box. %
Answer:
Salesman's commission 4% of total monthly sales.
Step-by-step explanation:
A sneaker store salesman had $4,125 in total monthly sales last month.
He made $165 in commission from those sales.
Suppose, it is x% of the total sale.
So, x% of $4125 will be,
[tex]=4125\times \dfrac{x}{100}[/tex]
According to the question it is equal to $165, so
[tex]\Rightarrow 4125\times \dfrac{x}{100}=165[/tex]
[tex]\Rightarrow x=\dfrac{165\times 100}{4125}[/tex]
[tex]\Rightarrow x=\dfrac{16500}{4125}[/tex]
[tex]\Rightarrow x=4\%[/tex]
Therefore, salesman's commission 4% of total monthly sales.
Answer: 4%
Step-by-step explanation:
Due to the fact that the salesman had $4,125 in total monthly sales the previous month, the answer would be 4%
y times 6 for y = 2/3
Which equation shows the substitution method being used to solve the system of linear equations?
x – y = 7
x = y + 3
A.
(y + 3) – y = 7
B.
x = (7 – x) + 3
C.
x – (y + 3) = 7
D.
x – y = y + 3
what is the 10th term of this geometric sequence?
1,2,4 ,8...
A)128
B)256
C)512
D)1024
How many millimeters are in 50 centimeters?
A conical tank has height 3 m and radius 2 m at the top. Water flows in at a rate of 0.7m^3/min. How fast is the water level rising when it is 0.8 m?
What is the solution of the equation?
4p/6+27=39
A. 22
B. 99
C. 4
D. 18
what are the translation rules in geometry?
Final answer:
The translation rules in geometry involve moving every point in a figure the same distance and direction. For a horizontal translation, add or subtract the same value from the x-coordinate of each point. For a vertical translation, add or subtract the same value from the y-coordinate of each point.
Explanation:
In geometry, translation is a transformation that moves every point in a figure the same distance and direction. The translation rules involve determining the new coordinates of the translated figure.
The translation rules in geometry can be summarized as:
For a horizontal translation, add or subtract the same value from the x-coordinate of each point.For a vertical translation, add or subtract the same value from the y-coordinate of each point.For example, if you have a point with coordinates (2, 3) and you want to translate it 3 units to the right and 2 units up, you would add 3 to the x-coordinate and 2 to the y-coordinate to get the new coordinates of the translated point: (5, 5).
13 tenths plus 8 tenths plus 32 hundredths <,> =,to 2.42
If f(x) is an odd function and the graph of f(x) includes points in Quadrant IV, which statement about the graph of f(x) must be true?
It includes points in Quadrant I.
It includes points in Quadrant II.
It does not include points in Quadrant I.
It does not include points in Quadrant II.
Answer:
It includes points in Quadrant II.
It does not include points in Quadrant I.
Step-by-step explanation:
Given : If f(x) is an odd function and the graph of f(x) includes points in Quadrant IV.
To find : which statement about the graph of f(x) must be true.
Solution : We have given that f(x) is an odd function is lies in Quadrant IV.
Definition of an odd function: the y-value of the function at negative x is always opposite sign as the y-value of function at opposite x.
Like (x ,-y) or (x , -y)
In odd function x and y values are in opposite sign that mean odd function always lies in Quadrant II and Quadrant IV.
It does not include points in Quadrant I
Therefore, It includes points in Quadrant II.
It does not include points in Quadrant I.
Answer:
includes quad 2
Step-by-step explanation:
Give 9.7814 correct to the nearest whole number
Final answer:
9.7814 rounded to the nearest whole number is 10, as the first digit after the decimal point is 7, which requires rounding up.
Explanation:
To find the nearest whole number to 9.7814, we need to look at the first digit after the decimal point. Since this digit is 7 (which is equal to or greater than 5), we round up the number. Rounding up changes 9.7814 to the next whole number, which is 10.
The general rule for rounding to the nearest whole number is:
If the first decimal place is 5 or greater, round up.If the first decimal place is less than 5, round down.Therefore, 9.7814 rounded to the nearest whole number is 10.
A bag cost 10.50 but you get 20 percent off how much is the bag now?
Which of the following is the statement of the triangle inequality theorem?
A. The sum of the measures of any two angles of a triangle is greater than the measure of the third angle.
B. The sum of the lengths of any two sides of a triangle is greater than the length of the third side.
C. The longest side of a triangle is opposite the largest angle.
D. The largest angle of a triangle is between the two longest sides.
we know that
The triangle inequality theorem states that the sum of the lengths of any two sides of a triangle is greater than the length of the third side
so
Let
a,b,c------> the length sides of a triangle
The theorem states that three conditions must be met
case 1)
[tex] a+b > c [/tex]
case 2)
[tex] a+c > b [/tex]
case3)
[tex] c+b > a [/tex]
therefore
the answer is the option
B. The sum of the lengths of any two sides of a triangle is greater than the length of the third side.
The hand on a clock shows 6:00pm what is the measure of the angle
what is an estimation of 492.6 divided by 48
Answer:
10.
Step-by-step explanation:
We are asked to find the estimation of 492.6 divided by 48.
First of all, we will round 492.6 to nearest hundreds and 48 to nearest tens.
Since tens digit of 492.6 is greater than 5, so we will round up to nearest hundred as: [tex]492.6\approx 500[/tex]
Since ones digit of 48 is greater than 5, so we will round up to nearest tens as: [tex]48\approx 50[/tex].
Now, we will find the quotient as:
[tex]\frac{500}{50}=10[/tex]
Therefore, an estimation of 492.6 divided by 48 would be 10.