Consider the complex number z = 27i. What are the characteristics of the cube roots of z?
Use the drop down menus to complete each sentence.
The cube roots are located on a circle with center at the origin and radius of
.
The cube roots have arguments which differ by
Pi over 3.
Answer:
3 and 2
Step-by-step explanation:
The cube roots are located on a circle with a center at the origin and a radius of 3. The cube roots have arguments that differ by 2 Pi over 3.
What is the complex number?A complex number is one that has both a real and an imaginary component, both of which are preceded by the letter I which stands for the square root of -1.
The given complex number as;
z = 27i
The radius of the cube root is found as;
r=∛x
r=∛27
r=3
The cube roots are located on a circle with a center at the origin and a radius of 3 units.
The argument of a complex number,z=a+ib is;
Θ = tan⁻¹(b/a)
The argument of a complex number z=0+27i
Θ = tan⁻¹(27/0)
Θ = π/2
The cube roots have arguments that differ by 2 Pi over 3.
Hence, the correct answer for the drop-down menu will be 3 and 2.
To learn more about the complex number, refer to the link;
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Can someone help me with 13,14,15 and 16 please
Answer: -3/5, 18/32, -10/11, and horizontal.
Step-by-step explanation: Remember the equation for slope? Δy (the change in y), over Δx (the change in x). In other words, rise over run. To solve for Δ, you'd have to subtract the second output (y²) from the first (y¹). There are really no rules as to which has to be minuend and the subtrahend, so I chose to subtract (-1,6) from (4,3) for the first problem.
y¹-y² Δy 3-6 -3
------ or ---- so ------- = ----- The slope is represented by -3/5x
x¹-x² Δx 4-(-1) 5
__________________________________________________________
For the second, substitute the values again (make sure you keep the xs and ys together and in the right order, otherwise your answer will be incorrect). Remember that subtracting a negative number is basically just adding a positive number. That's why the slope is 18/32 and not 4/26.
11-(-7) 18
--------- = -------
29-(-3) 32
___________________________________________________________
For number three, they give you a point, then tell you the y-intercept. With that in mind, also know the second point is (0,17), because the x value at the y-intercept is always 0.
7-17 -10
------ = ------- The slope is -10/11x
11-0 11
___________________________________________________________
4-4 0
------ = --------
6-(-9) 15
Because there is no Δy, but there is Δx, we know that the line for y will be straight and shows no change- it will always be at 4. That said, the line will be horizontal.
I hope this helps. I know this is very confusing at first, but with practice, you'll eventually get the hang of it. I've tried to explain the rules to the best of my ability- let me know if there's anything you don't understand or need more help with.
Sincerely,
Lacia :))
the table shows the number of calories jane burns while exercising. How many calories would she burn for 29 minutes. Explain. Please help me! if u don't know this then don't answer!
Answer:
319
Step-by-step explanation:i just did it
pleaseeeeeeeee helpppp...
Answer:
x = 67
Step-by-step explanation:
∠ CRQ = ∠ BQR = 113° ( Alternate angles )
∠ CRQ and ∠ CRS are adjacent angles and supplementary, that is
x + 113 = 180 ( subtract 113 from both sides )
x = 67
An amount of $2,535.00 is deposited in a bank paying annual interest rate of 5.3% compounded quarterly find the balance after 3 years
Answer:
2968.78
Step-by-step explanation:
took the test
On a journey of 120 km, a motorist averages
less than 60 km/h. Will the journey take
more or less than 2 hours?
Answer:
More
Step-by-step explanation:
Because the journey is 120km long, and the mortoristgoes less than 60km per hour. So in 2 hours, the motorist will go less than 120 km. So he needs more than 2 hours to go 120 km
15,000,015,969+5,000,003
An insurance company charges Ted $1400 per year for insurance on his home. The company has predicted that there is a 10% chance that Ted will make a claim on the policy of $5000. Create a probability distribution and determine what the insurance company can expect to make on this policy, on average?
Answer:
The insurance company can expect to make $900 on the policy
Step-by-step explanation:
The given parameters are;
The amount Ted pays per year for insurance on his home = $1,400
The value of the insurance policy = $5000
The chance that Ted will make a claim on the policy = 10%
The expected value is given as follows
Incidence [tex]{}[/tex] Probability Value v × p
A claim is made [tex]{}[/tex] 0.1 $5,000 - $1,400 = -$3,600 -$360
No claim [tex]{}[/tex] 0.9 [tex]{}[/tex] $1,400 $1260
Expected value is $1,260 - $360 = $900
The value the insurance company can be expected to make on average on the policy is $900
PLEASE HELP
The slope of the line that represents the data Nicholas collected is -63, and the y-intercept is 825. Explain what these represent in the context of the situation. Remember that x is the number of days, and y is the number of canned goods. explain the answer
Answer:
sorry i coldent find the anser
Step-by-step explanation:
ello
+v+
Answer:
The slope indicates that the soup kitchen uses 63 cans per day. The y-intercept shows that there were initially 825 cans at the soup kitchen.
Step-by-step explanation:
What is 100 times 100
Answer:
hii
Step-by-step explanation:
10,000
Answer:
the anwser would be 10000
Step-by-step explanation:
lol
15. Write the slope-intercept form of the line described in the following:
Parallel to 3x + y = 5 and passing through (2,3)
Answer:
2x
Step-by-step explanation:
3x + y = 5
= 5 - 3x
= 2x
Bob and Carl each rented the same kind of moving truck from EZ Move. There was a flat rental fee plus a charge per mile that the truck was driven. Bob's cost for his truck was $112.96 for 138 miles. Carl's cost for his truck was $142.78 for 209 miles. Which equation can be used to represent the cost of the rental truck? Round to the nearest hundredth if necessary.
Answer:
Total cost= 55 + 0.42*x
x= miles driven
Step-by-step explanation:
Giving the following information:
Bob's cost for his truck was $112.96 for 138 miles.
Carl's cost for his truck was $142.78 for 209 miles.
To calculate the fixed cost and variable cost per mile, we need to use the high-low method:
Variable cost per unit= (Highest activity cost - Lowest activity cost)/ (Highest activity units - Lowest activity units)
Variable cost per unit= (142.78 - 112.96) / (209 - 138)
Variable cost per unit= $0.42 per mile
Fixed costs= Highest activity cost - (Variable cost per unit * HAU)
Fixed costs= 142.78 - (0.42*209)
Fixed costs= $55
Fixed costs= LAC - (Variable cost per unit* LAU)
Fixed costs= 112.96 - (0.42*138)
Fixed costs= $55
Finally, the cost equation:
Total cost= 55 + 0.42*x
x= miles driven
Answer:
The answer is D
Step-by-step explanation:
In the figure below, points J, K, and L are the midpoints of the sides of AXYZ.
Suppose JK=38, X2=96, and YX=56.
Find the following lengths.
Answer:
28 ; 76 ; 38
Step-by-step explanation:
KL = [tex]\frac{XY}{2}[/tex] = [tex]\frac{56}{2}[/tex] = 28 units
YZ = 2 × JK = 38 × 2 = 76 units
LZ = 76/2 = 38 units
The lengths are: KL = 28 units, YZ = 76 units and LZ= 38 units.
What is Mid point theorem?The line segment in a triangle connecting the midpoint of two sides of the triangle is said to be parallel to its third side and is also half the length of the third side, according to the midpoint theorem.
Given:
J, K, and L are the midpoints of the sides of ΔXYZ.
JK=38, X2=96, and YX=56.
Now, using Mid point theorem
JK= 1/2 YZ
38 = 1/2 YZ
YZ= 2 x 38
YZ = 76 units.
and, KL= 1/2 YX
KL = 1/2(56)
KL= 28
LZ = 1/2 (YZ)
LZ = 1/2(76)
LZ = 38 units
Learn more about Mid point theorem here:
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Which of these is an example of a literal equation?
A. 6+ 30 = 62
B. 3x - 4y
C. 12 = 9 + 3x
D. ax - by=k
Please help
What is the average rate of change of the function f(x) = 2x2 + x + 5 over the interval −2 ≤ x ≤ 2?
A. −4 B. −1 C. 1 D. 4
Answer:
d
Step-by-step explanation:
The average rate of change the function f(x) = 2x² + x + 5 is 1.
So, Option C is correct.
The average rate of change
The average rate of change in a function is the rate at which one value changes with respect to another value.
Given function: [tex]f(x)=2x^2+x+5[/tex] on interval [tex][-2,2][/tex]
Therefore,
Average rate of change = [tex]\frac{f(2)-f(-2)}{2-(-2)}[/tex]
[tex]f(2)=2(2)^2+2+5\\f(2)=15\\f(-2)=2(-2)^2-2+5\\f(2)=11[/tex]
Substitute the values,
Average rate [tex]=\frac{15-11}{2+2}[/tex]
Average rate [tex]=\frac{4}{4}[/tex]
Average rate [tex]=1[/tex]
So, the average rate of change is [tex]1[/tex]
Option C is correct.
Find out more information about the average rate of change here:
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Write 2x+y=17 in slope-intercept form
Answer:
y=-2x+17
Step-by-step explanation:
Find the solution set of 3x + 11 < 50 using inverse operations and properties of inequality.
Answer:
the answer is 13
Step-by-step explanation:
x < 13 that's what the answer is
Answer: (-♾️ 13)
Step-by-step explanation:
3x+11<50
3x<50-11
3x<39
X<13
The solution will be (-♾️ 13)
HELPPPPP PLZ AND THANK U
Answer:
0.6
Step-by-step explanation:
multiply all of the numbers
A survey asked students whether they would like a drama club, a step team, both clubs, or neither club. The results are below:
1. 34 students like a drama club
2. 27 students like step team
3. 14 students like both
4. 13 students like neither
Hi, you've asked an incomplete question. Here are the remaining questions:
a) Describe what each region in the Venn diagram represents.
Region I: In drama club, not in step team.
Region II: In both clubs.
Region III: In step team not in drama.
Region IV: Not in either club.
b) How many students were in only one of the two clubs?
c) How many students were in the drama club or in the step team?
d) How many students were surveyed?
Attached is the Venn diagram depicting the regions.
Explanation:
b) By adding the number of students that like drama club and those that like step club we can derive the answer: 34 + 27 = 61.
c) By adding 34 + 27 + those that like both (14) = 75.
d) The total number of students surveyed is gotten by summing any number in attached the diagram: 34 + 27 + 14 + 13 = 88.
I am having trouble understanding this: Sam bought 86 pounds of flour for his bakery. Every day he used the same amount of flour to make bakery items. After 10 days, Sam was left with 25.2 pounds of flour. On average, how many pounds of flour did Sam use each day?
A. 3.01 Pounds
B. 5.65 Pounds
C. 6.08 Pounds
D. 11.12 Pounds
Please also include an explanation. Thanks!
Answer:
the average amount of flour used each day=6.08 pounds
Step-by-step explanation:
Sam bought 86 pounds of flour for his bakery.
Every day he used the same amount of flour to make bakery items.
After 10 days, Sam was left with 25.2 pounds of flour.
Now we are asked to find the average pounds of flour that Sam used each day.
Total amount of flour used=86-25.2=60.8 pounds.
As he used the flour equal amount each day for 10 days.
So, the average flour used each day=
amount of flour used/ number of days=60.8/10=6.08.
the average amount of flour used each day=6.08 pounds
Answer:
C
Step-by-step explanation:
So since Sam have 25.2 leftover pounds of flour, we can subtract that from 86, knowing that will be left over in the end. Next, we divide the number left. 86 - 25.2 = 60.8
Finally, divide that by 10, since there are 10 days.
We end up with 6.08 pounds.
Ms. Reynold's sprinkler system has 3 stations that water all parts of her front and back lawn. Each station runs for an equal amount of time. If it takes 14 minutes for the first 2 stations to water, how long does it take to water all parts of her lawn?
Answer:
21 minutes
Step-by-step explanation:
Given that :
Sprinkler has 3 stations
Each waters for an equal amount of time ;
First 2 stations water for 14 minutes
Time taken per station :
14 / 2 = 7 minutes
Time taken to water all part of her lawn :
Time taken per station * number of stations
7 minutes * 3 = 21 minutes
Independent activity 4
Ano po sagot
9514 1404 393
Answer:
A, B, C, E, D
F, G, H, I, J
Step-by-step explanation:
You can go at this a couple of ways.
Consider the squares of number 1 through 9.
[tex]\begin{array}{cccccccccc}n&1&2&3&4&5&6&7&8&9\\n^2&1&4&9&16&25&36&49&64&81\end{array}[/tex]
Then when the number under the radical is close to n², the root on the number line will be close to n.
The other way you can do this is to find the square root using your calculator.
√10 ≈ 3.2 ⇒ A√35 ≈ 5.9 ⇒ B√48 ≈ 6.9 ⇒ C√71 ≈ 8.4 ⇒ E√54 ≈ 7.3 ⇒ D√19 ≈ 4.4 ⇒ F√89 ≈ 9.4 ⇒ G√6 ≈ 2.4 ⇒ H-√20 ≈ -4.5 ⇒ I-√2 ≈ -1.4 ⇒ JThe cost of tickets is $36 for three students an $72 for six students. What’s the rate and change?
Answer:The cost of a ticket is $12 per student
Step-by-step explanation:
36/3=$12 per students
$72/6=$12 per student
If (x+k) 2 (x+2) = x² +14x²+60x+72
Find the value of k.
I will give brainliest
Determine if the relation represents a function. (2,1) (4,-7) (6,0) (4,-1) (2,9)
Answer:
It isn't a function
Step-by-step explanation:
2 and 4 both have 2 x values, and on a graph, a function cannot have more than 1 x value.
Help me Please!!!!! I will give brainliest to the person who does it first
Answer:
5x + 3y - 4
This expression has three terms (5x, 3y, and -4), 2 different variables (x and y), and a constant (-4)
Step-by-step explanation:
#teamtrees #WAP (Water And Plant)
Given the points (2, k) and (0, -6), for which values of k would the distance between the points be square root of 5?
Answer:
k = -5
k = -7
Step-by-step explanation:
*look at the picture*
Maya purchased a prepaid phone card for$25. Long distance calls cost 9cent a minute using this card. Maya used her card only once to make a long distance call. If the remaining credit on her card is 24.01, how many minutes did her call last?
Answer:
Her call lasted for 1 minutes.
Step-by-step explanation:
She bought a prepaid card ($25)
0.9 times 11 = 0.99
25 - 0.99 = 24.01
Express this number in scientific notation. 0.000000591 A. 5.91 × 10–7 B. 5.91 × 10–6 C. 5.91 × 106 D. 5.91 × 107
Answer:
A
Step-by-step explanation:
five hundred fifty five divided in five
Answer:
Well I'm not sure if its a joke but here is the answer anyways LOL Its 111
Step-by-step explanation:
Answer:
111
Step-by-step explanation:
If you think about it, 5 ÷ 5 = 1
So all the digits are 1
111
(Plus I just used a calculator)
Hope I helped :)