Answer:
Step-by-step explanation:
The genral form of a complex number in rectangular plane is expressed as z = x+iy
In polar coordinate, z =rcos ∅+irsin∅ where;
r is the modulus = √x²+y²
∅ is teh argument = arctan y/x
Given thr complex number z = 6+6√(3)i
r = √6²+(6√3)²
r = √36+108
r = √144
r = 12
∅ = arctan 6√3/6
∅ = arctan √3
∅ = 60°
In polar form, z = 12(cos60°+isin60°)
z = 12(cosπ/3+isinπ/3)
To get the fourth root of the equation, we will use the de moivres theorem; zⁿ = rⁿ(cosn∅+isinn∅)
z^1/4 = 12^1/4(cosπ/12+isinπ/12)
When n = 1;
z1 = 12^1/4(cosπ/3+isinn/3)
z1 = 12^1/4cis(π/3)
when n = 2;
z2 = 12^1/4(cos2π/3+isin2π/3)
z2 = 12^1/4cis(2π/3)
when n = 3;
z2 = 12^1/4(cosπ+isinπ)
z2 = 12^1/4cis(π)
when n = 4;
z2 = 12^1/4(cos4π/3+isin4π/3)
z2 = 12^1/4cis(4π/3)
You buy a touch iPod for $200, but it loses value at a rate of 10% each year. How much is your phone worth after 3 years?
Answer:
145.8
Step-by-step explanation:
200 times .9 times .9 times .9
Because it is 3 years
Answer:
$266.20
Step-by-step explanation:
o=200
r=.1
t=3
w=200(1+.1)^3
w=200(1.331)=266.2
Each of the letters in the word MONASTIC are on separate cards face down on the table. If you pick a card at random, what is the probability that the letter on it will be "A"?
show work pls!
Answer:
1/8 = 12.5%
Step-by-step explanation:
There are 8 letters in the word MONASTIC. One of the letters is A.
So the probability is 1/8, or 12.5%.
A given line has the equation .
What is the equation, in slope-intercept form, of the line that is perpendicular to the given line and passes through the point (0, 9)?
Answer:
y=6x+9Step-by-step explanation:
The question is incomplete. find the complete question below;
A given line has the equation 2x + 12y = −1. What is the equation, in slope-intercept form, of the line that is perpendicular to the given line and passes through the point (0, 9)? y = ( )x + 9
The equation of a line is represented as y = mx+c where m is the slope and c is the intercept. our ficus is to get both the slope and the intercept and then substitute then into the equation of the line.
First let us get the slope of the known line:
Rewriting the equation 2x + 12y = −1 in its standard form, we have;
12y = -2x-1
y = -1/6 x - 1/12
the slope of the line is -1/6
Since this line is perpendicular to the unknown line, the slope of the unknown line say M = -1/(-1/6) = 6
For the intercept
we will substitute the point (0,9) and the slope M = 6 into the equation
y = Mx+c to get the value of the intercept.
9 = 6(0)+c
c = 9
Finally, we will find the equation of the line perpendicular to the given line using the equation y = mx+c
Substituting m = 6 and c = 9 into the equation, we have y = 6x+9 or y-6x = 9
The unknown equation in slope intercept form is y=6x+9
The new equation of the perpendicular line is y = 6x + 9.
The slope of the lineThe slope of the line is determined from the given equation of the line.
[tex]2x + 12 y = -1\\\\12y = -1 - 2x\\\\y = \frac{-1}{12} - \frac{2x}{12} \\\\y = \frac{-1}{12} - \frac{x}{6}\\\\M = \frac{-1}{6}[/tex]
The slope of the perpendicular line[tex]M_1 = \frac{-1}{M} = \frac{-1}{-1/6} = 6[/tex]
The new equation of the perpendicular line[tex]y = mx + c\\\\9 = 6(0) + c\\\\9 = c\\\\y = 6x + 9[/tex]
The complete question is below:
A given line has the equation 2x + 12y = −1. What is the equation, in slope-intercept form, of the line that is perpendicular to the given line and passes through the point (0, 9)? y = ( )x + 9
Learn more about equation of line here: https://brainly.com/question/13763238
The scatter plot shows the time spent studying compared to test scores for Mr. Stone’s eighth-grade class. Predict the score that a student would earn if she studied for 7 hours. Round your answer to the nearest whole number. Enter your answer in the box.
Answer:
80 (I think)
Step-by-step explanation:
I would just go to x=7 and look up until i reach the line of best fit. The intersection is at y=80
The score of student is 80 marks if she studied for 7 hours.
Given,
The scatter plot shows the time spent studying compared to test scores for Mr. Stone’s eighth-grade class. From the plot it is clear that time is shown on x axis and test scores is shown on Y axis.
We have to predict the score that a student would earn if he studied for 7 hours.
Here look at the Scatter plot we find that 7 hours is on x axis and the respective line of best fit of test score is passing through score 80.
Hence if a student is studied for 7 hours he would earn 80 marks.
For more details on scatter plot follow the link below:
https://brainly.com/question/2659237
Choose the correct simpilfication of (7x^3-8x-5)+(3x^3+7x+1)
Answer:
Step-by-step explanation:
(7x³-8x-5)+(3x³+7x+1) =7x³ - 8x - 5 + 3x³ + 7x + 1
Combine the like terms
= 7x³ + 3x³ - 8x + 7x - 5 + 1
Now, add/ subtract the like terms
= 10x³ - x - 4
Answer:
[tex]10x^{3} -x-4[/tex]
Step-by-step explanation:
[tex](7x^3-8x-5)+(3x^3+7x+1)[/tex]
[tex]7x^3+-8x+-5+3x^3+7x+1[/tex]
[tex](7x^{3} +3x^{3} )+(-8x+7x)+(-5+1)[/tex]
[tex]10x^{3} -x+-4[/tex]
2x + 4y = 12 y = A system of equations. 2 x plus 4 y equals 12. y equals StartFraction one-fourth EndFraction x minus 3.x – 3 What is the solution to the system of equations? (–1, 8) (8, –1) (5, StartFraction one-half EndFraction) (StartFraction one-half EndFraction, 5)
Answer:
This guy is a fooooool the real answer is
Step-by-step explanation:
x=8 and y=−1
so : (8,-1)
From the system of equation 2x + 4y = 12 and y equals StartFraction one-fourth EndFraction x minus 3. The solution to the system of equations in terms of (x, y) is equal to ( (8, -1)
The system of equations is given as:
2x + 4y = 12 ------- (1)
[tex]\mathbf{y = \dfrac{1}{4}x - 3} \ \ \ ----(2)[/tex]
So, from equation (1), we will replace the value of y which is [tex]\mathbf{ \dfrac{1}{4}x - 3} }[/tex] in order to be able to solve for x.
i.e.
[tex]\mathbf{2x + 4\Big ( \dfrac{1}{4}x -3 \Big) = 12 }[/tex]
Open brackets
2x + x -12 = 12
3x - 12 = 12
3x = 12 + 12
3x = 24
x = 24/3
x = 8
Now, we will replace the value of x into equation (2) to be able to solve for y.
[tex]\mathbf{y = \dfrac{1}{4}(8) - 3} }[/tex]
y = 2 -3
y = -1
Therefore, the solution to the system of equations in terms of (x, y) is equal to ( (8, -1)
Learn more about the system of equations here:
https://brainly.com/question/12895249?referrer=searchResults
BRAINLIEST!!! Divide. (See image.)
Answer:
Step-by-step explanation:
x-6)3x²-24x+35 (3x-6
3x²-18x
- +
__________
-6x+35
-6x +36
+ -
________
- 1
_________
quotient=3x-6
remainder=-1
can someone help me solve this please?
Answer:
h = 9
Step-by-step explanation:
You can use the Pythagorean theorem to solve this. Consider each half of the main triangle their own triangles.
h = a
a^2 + b^2 = c^2
or
a^2 = c^2 - b^2
a^2 = 10^2 - 5^2
a^2 = 100 - 25
a^2 = 75
a = √75
a = 8.66, or 9
h = 9 (when rounded)
Please help will give brainist
Answer:
80 & 105
Step-by-step explanation:
Howard needs new gutters for the front and both sides of his home. The front of the house is 50 ft 8 in., and each side is 22 ft 9 in. Wide. What length of gutter must he buy?
Answer:
95 ft 10 in
Step-by-step explanation:
We need to add the lengths of the front of the house and both sides of the house:
50 ft 8 in + 2(22ft + 9in)
= 50ft + 8 in + 44ft + 18in
= 94ft + 22in
12 inches = 1 foot
22 inches = 1 ft 10 in
Therefore, the length of the gutter he must buy must be:
94 ft + 1 ft + 10 in
= 95 ft 10 in
Calculate area of triangle
Answer:
60cm^2
Step-by-step explanation:
15 times 8 = 120
divided by 2 = 60
Answer:
60
Step-by-step explanation:
8x15=120
120/2=60
William’s salary is £24 000
His salary increases by 4%.
Work out William’s new salary.
£ ............................
write an expression that shows the cost of brochures each brochure cost 40 cents i need 4100 brochures and have a total budget of 1900 dollars
Answer:
1900 ≥50 + .40 * b
1900 ≥50 + .40 *4100
Step-by-step explanation:
Cost = rush fee + cost per brochure * number of brochures
cost= 50 + .40 * b where b is the number of brochures
This must be less than or equal to 1900 dollars
1900 ≥50 + .40 * b
We are getting 4100 brochures
1900 ≥50 + .40 *4100
1900≥50 + 1640
1900 ≥1690
We can get the brochures
Select all the points that are on the graph of the line below. Y=5-1/2x A: (0,5) B (0,10) C(1,2) D(1,4) E(5,0) F(10,0). Please help.
Answer:
A: (0,5)
F(10,0)
Step-by-step explanation:
Y=5-1/2x
Substitute the point into the equation and see if it is true
A: (0,5)
5 = 5 - 1/2(0)
5=5 true on the line
B (0,10)
10 = 5 - 1/2(0)
10=5 false not on the line
C(1,2)
2 = 5 - 1/2(1)
2=4 1/2 false not on the line
D(1,4)
4 = 5 - 1/2(1)
4=4 1/2 false not on the line
E(5,0)
0 = 5 - 1/2(5)
0=2 1/2 false not on the line
F(10,0)
0 = 5 - 1/2(10)
0=5-5 true on the line
Calvin was told he should drink 2 liters of water
everyday. If he did this, how much water would
he drink in 1 week (7 days)?
｡☆✼★ ━━━━━━━━━━━━━━ ☾
Multiply the values
2 x 7 = 14
He would drink 14 litres of water in a week
Have A Nice Day ❤
Stay Brainly! ヅ
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Simplify the equation
Answer:
option c is the correct.
Step-by-step explanation:
[tex]\frac{2x^4*6x^2}{3x^2}[/tex]
by using the laws of exponent
a^m×a^n=a^m+n
12x^4+2/3x²
[tex]\frac{12x^4}{3x^3}[/tex]
4x^4-3
4x³
Answer:
4x^3
Step-by-step explanation:
In the numerator, (top part) we have 2x^4 times 6x^2
2 times 6 is 12, and x^4 times x^2 is x^6.
Thus, in the top part, we have 12 times x^6.
In the bottom part we have 3 times x^3.
This is exactly the answer for d, but this is not a simplified answer.
Dividing 12 by 3 we have 4, and x^6/x^3 gives us x^(6-3) which is x^3.
Therefore, we have the correct answer: 4x^3
Please answer correctly!!!!!!! Will mark brainliest !!!!!!!!!!!!!
Answer:
60
Step-by-step explanation:
At the time of launch, x will be 0 because the object hasn't been thrown yet. Therefore, its height will be 60.
Answer:
The answer for it is 60.
Step-by-step explanation:
5*0+20*0+60
And due to the simplification by keeping the value 0 in place of x. So if any term is multiplied with 0 the value of that term will be 0. So by adding 0+0+60 . Therefore , the height will be 60 .
More explanation:
At the time of launch, x will be 0 because the object have not been thrown yet.So its height will be 60.
the value of 1.666.. in the form p/q is ?
Answer:
15/9
Step-by-step explanation:
let the recurring decimal be (n)
we need to find a number that will subtract the number to remove the decimal
the nearest number is 16.666...
because the decimal has moved one step ahead, we will call the new number (10n)
16.666 - 1.666 = 15.
10n - n = 9n.
=15/9
Paula wants to know the favorite type of music for students at her school. She surveys the first 60 people who enter the school doors in the morning. (circle the correct choice below) FAIR or BIASED
Answer:
Fair
Step-by-step explanation:
Based on the description provided in the question it is safe to say that the survey that Paula conducted is completely Fair. This is mainly due to the fact that her pool of participants are completely random. Paula does not control who will walk through the schools doors first. Therefore she cannot be biased since she is surveying whoever walks through the doors first regardless of her personal opinions or feelings.
if a=3/6 and b=-3/-5 find -3a+4b
Answer:
Step-by-step explanation:
-3(3/6) + 4(3/5)
-3(1/2) + 4(3/5)
-3/2 + 12/5
-15/10 + 24/10
9/10
i need help good explanation and answer for more points
Let's start with sectioning off the little squares on the left that are jutting out of the top and bottom. Both of the squares are C*E, so multiply C*E twice to get the area of those little squares. That comes out to 12 feet.
Next is the main quadrilateral, the big one. You have to cut it off at the point the triangle starts to slope, so the end fo B.
But you also have to get the left part, so you have to add the length of C to the length of B to get the length of the quadrilateral. A encompasses the entire height, but not the part we want, because we already isolated those little squares. To get the height, just subtract the two E parts. The height is 6. The length is 8 feet. Multiply and get 48.
Add that to the previous 12 feet calculated to get 60.
Next, the triangle. The height is A, but only with one E. So subract the other E to get a height of 9. The length is D, but you have to subract B because that is part of the earlier quadrilateral. That makes it 9.
The formula for a triangle is height * length / 2. So, plug in the numbers-- 9 * 9 / 2
81/2
40.5.
Add to the previous 60 we got and that makes 100.5 square feet.
Hope this helped!
how many diagonals are there in a polygon of 6o sides
Answer:
9 diagonals
Step-by-step explanation:
Number of Diagonals = n(n-3)/2
For example, in a hexagon, the total sides are 6. So, the total diagonals will be 6(6-3)/2 = 9.
Answer:
9 diagonals
Bit by bit clarification:
Number of Diagonals = n(n-3)/2
For instance, in a hexagon, the complete sides are 6.
Along these lines, the complete diagonals will be 6(6-3)/2 = 9.
A news report says that 28%
of high school students pack their lunch.
Your high school has 600
600
students.
How many students in your high school would you expect to pack their lunch?
Answer:
168
Step-by-step explanation:
28% = 28/100
28/100 * 600 = 168
8. ¿Cuál es la media de las calificaciones de los alumnos de quin-
to grado?
9, 9, 6, 8, 7, 9, 7, 6, 8,9, 8, 6, 7
a) 6.98
b) 7.75
c) 7.61
d) 9.03
Hey can someone help please Whatb is the value of the 8 in 873 119
Calculate the volume of this cylinder, giving your answer to 1 decimal place.
Answer:Sorry but I know only this much...
Step-by-step explanation:I don't say u must have to mark my ans as brainliest but if it has really helped u plz don't forget to thank me....
Answer:
192π^3
Step-by-step explanation:
the formula for calculating volume of a cylinder is πr^2h (r : radius, h : height)
π×4^2×12 = 192π^3
which of the following functions is graphed below?
PLEASE HELP WITH MATH
Answer:
Volume: 105 cubic centimeters
Mass of doorstop: 924 grams
Step-by-step explanation:
First, you need to find the area of the triangular base of the prism. The area of the triangle is bh/2=10*6/2=30 square centimeters. Multiplying this by the height of the doorstop of 3.5, you get a total volume of 105 cubic centimeters. Since each cubic centimeter weighs 8.8 grams, the whole thing weighs 105*8.8=924 grams. Hope this helps!
Answer:
volume 105 cm³
mass 924 g
Step-by-step explanation:
This is triangular prism so (Volume) V = (Area of base) B * (Height) H
In this case is triangle is the base shape with base b =10cm and height h= 6cm so
B =1/2 bh = 1/2 *10*6 =30 cm²
(Height) H = 3.5 cm
so V = 30*3.5 = 105 cm³
1 cm³ has a mass ≈ 8.8g
so the mass of the doorstop is volume * mass per cm³
105 * 8.8 = 924 g
FOR 14 points! A group of friends are going to see the newest action movie. The price of a ticket is $6.25. As a group, they spent $12 on refreshments. If they spent a total of $30.75 on tickets and refreshments, how many people went to the movies? Which equation represents the scenario? How many people went to the movies?
x = number of people went to movies
equation
6.25x + 12 = 30.75
6.25x = 30.75 - 12
6.25x = 18.75
x = 18.75 / 6.25
x = 3
answer
3 people
Answer:
6.25x + 12 = 30.75
3 people
Step-by-step explanation:
I NEED HELP. THIS IS ABOUT SCATTER PLOTS PLEASE PROVIDE AN EXPLANATION!! HELPPPPPPPP
Answer:
A y = -3/4x + 6
Step-by-step explanation:
We know that the plot decreases from left to right so the slope is negative
That eliminates choices B and D
We also know that the y intercept is between 5 and 8
That eliminates choice C