-5 - 5√3 i = -5 (1 + √3 i )
We have modulus
|-5 (1 + √3 i )| = 5 √(1² + (√3)²) = 5√4 = 10
and argument
arg(-5 - 5√3 i ) = π - arctan(√3) = 2π/3
(we subtract from π because the given complex number lies in the third quadrant of the complex plane, whereas the arctan function only returns angles between -π/2 and π/2)
so that the polar form of the number is
-5 - 5√3 i = 10 exp(2π/3 i )
By DeMoivre's theorem, we have
(-5 - 5√3 i )³ = 10³ exp(3 × 2π/3 i ) = 1000 exp(2πi ) = 1000
A photography store develops 320 pictures on Monday, 564 on Tuesday, 281 on Wednesday, and 473
on Thursday. If the store typically averages at least 420 pictures daily, how many pictures would need to
be developed on Friday?
Answer:
462 pictures
Step-by-step explanation:
Average (mean) is calculated by adding up all the values and dividing by how many values there are, therefore to have an average 420 pictures daily, the sum of the 5 days must be: 5x420 = 2100
The current sum is: 320 + 564 + 281 + 473 = 1638
Therefore the number for Friday is 2100 - 1638 = 462 pictures.
Hope this helped!
Help pls and thank you
You and your friends have tickets to attend a music concert. While standing in line, the promoter states he will give a gift card for a free album download to each person that is a multiple of 2. He will also give a backstage pass to each fourth person and floor seats to each fifth person. Which person will receive the free album download, backstage pass, and floor seats? Explain the process you used to determine your answer.
9514 1404 393
Answer:
20th
Step-by-step explanation:
The person will receive all gifts if the are all of a multiple of 2, a multiple of 4, and a multiple of 5. Since 4 is already a multiple of 2, the person who will receive all is the one who is a multiple of 4 and 5.
20 is 4×5, so is a multiple of both numbers. There is no smaller number that is a multiple of both 4 and 5.
The 20th person will receive all gifts.
_____
The value we have determined here is called the "least common multiple" (LCM). It is the product of the unique prime factors of the numbers of interest, raised to the highest power that appears in any of the numbers.
2 = 2¹
4 = 2²
5 = 5¹
LCM(2, 4 5) = 2² × 5¹ = 20
A segment bisector is a line, ray or segment that divides a line segment into two equal parts. in the triangle formed by points A(-1,7), B(1,2), C(7,6) what is the slope of the line that goes through point A and bisects BC?
In decimal form, this is equivalent to -0.6
=================================================
Explanation:
This segment bisector is cutting side BC in half. So we have a point D such that it is between B and C. Also, we can say BD = DC. Refer to the diagram below.
To find the location of D, we'll apply the midpoint formula to points B and C.
B(1,2) and C(7,6) have x coordinates of 1 and 7 respectively. Average those x values to get (1+7)/2 = 8/2 = 4. This is the x coordinate of point D.
Repeat this idea for the y coordinates. We'll get (2+6)/2 = 8/2 = 4 which is the y coordinate of D.
Point D is located at (4,4)
---------------------
The takeaway from that last section, if we were to summarize it in one sentence, is that D is located at (4,4).
Now focus on the points A(-1,7) and D(4,4)
We'll apply the slope formula
m = (y2-y1)/(x2-x1)
m = (4-7)/(4-(-1))
m = (4-7)/(4+1)
m = -3/5 is the slope
Notice that to go from A to D, we can drop down by 3 units and move to the right 5 units. We can say rise = -3 and run = 5; therefore, slope = rise/run = -3/5
Find x so that the points (x,x+1), (x+2,x+3) and (x+3,2x+4) form a right-angled triangle.
Let a, b, and c be vectors each starting at the origin and terminating at the points (x, x + 1), (x + 2, x + 3), and (x + 3, 2x + 4), respectively.
Then the vectors a - b, a - c, and b - c are vectors that point in directions parallel to each of the legs formed by the triangle with these points as its vertices.
If this triangle is to contain a right angle, then exactly one of these pairs of vectors must be orthogonal. In other words, one of the following must be true:
(a - b) • (a - c) = 0
or
(a - b) • (b - c) = 0
or
(a - c) • (b - c) = 0
We have
a - b = (x, x + 1) - (x + 2, x + 3) = (-2, -2)
a - c = (x, x + 1) - (x + 3, 2x + 4) = (-3, -x - 3)
b - c = (x + 2, x + 3) - (x + 3, 2x + 4) = (-1, -x - 1)
Case 1: If (a - b) • (a - c) = 0, then
(-2, -2) • (-3, -x - 3) = (-2)×(-3) + (-2)×(-x - 3) = 2x + 12 = 0 ==> x = -6
which would make a - c = (-3, 3) and b - c = (-1, 5), and their dot product is not zero. Then the triangles vertices are at the points (-6, -5), (-4, -3), and (-3, -8).
Case 2: If (a - b) • (b - c) = 0, then
(-2, -2) • (-1, -x - 1) = (-2)×(-1) + (-2)×(-x - 1) = 2x + 4 = 0 ==> x = -2
which would make a - c = (-3, -1) and b = (-1, 1), and their dot product is also not zero. The vertices are the points (-2, -1), (0, 1), and (1, 0).
Case 3: If (a - c) • (b - c) = 0, then
(-3, -x - 3) • (-1, -x - 1) = (-3)×(-1) + (-x - 3)×(-x - 1) = x ² + 4x + 6 = 0
but the solutions to x here are non-real, so we throw out this case.
So there are two possible values of x that make a right triangle, x = -6 and x = -2.
lee is planning an event for 28 people, he wants to make a fruit drink and he thinks that each person will drink 3 glasses each. If he is correct , how many glasses of fruit should he make?
Answer:
84
Step-by-step explanation:
Since there will be 28 people, and each of them will drink 3 glasses, you just multiply the number of people times the number of glasses they will drink each, so 28*3. The result is 84.
I hope this helped! :D
Lee should need to make 84 glasses of fruit if is planning an event for 28 people.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
Let Lee needs to make x number of glasses of fruit.
From the question we can frame a linear equation in one variable:
x/3 = 28
As we know, the arithmetic operation can be defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.
After cross multiplication:
x = 28×3
x = 84 glasses
Thus, Lee should need to make 84 glasses of fruit if is planning an event for 28 people.
Learn more about the linear equation here:
brainly.com/question/11897796
#SPJ2
PLEASE HELP!!
find the value of r
The two sides and two top angles are identical so the two bottom halves are the same
18 -2r = 4R
Add 2r to both sides
18 = 6r
Divide both sides by 6
R = 3
The answer is A. 3
Hurry quick i have more questions answer then all for a total of about 100 points
Answer:
1/5
Step-by-step explanation:
.7555555(repeating )
writing as a fraction
x = .755555555
10 x = 7.555555
Subtract the two
10x = 7.555555
-x = .75555555
--------------------------
9x =6.8
Divide each side by 9
x = 6.8/9
x = 68/90
Divide by 2
x = 34/45
We do the same for .555555 repeating
y = .5555 repeating
10 y = 5.5 repeating
10y = 5.5
-y = .555
-------------------
9y = 5
y = 5/9
Subtract x - y
34/45 - 5/9
Get a common denominator
34/45 - 25/45
9/45
1/5
find the area of the triangle
9514 1404 393
Answer:
108 cm²
Step-by-step explanation:
The area of a triangle is given by the formula ...
A = 1/2bh
where b represents the base length, and h represents the height--the perpendicular distance from the base to the opposite vertex. The area of this triangle is ...
A = 1/2(12 cm)(18 cm) = 108 cm²
A cell phone company charges a monthly fee of $18 plus five cents for each call. A
customer's total cell phone bill this month is $50.50. Use n to represent the number of
calls.
Answer:
650 calls
Step-by-step explanation:
so since you have 18$ per month plus 5 cents per call you would do
18+0.5n(n represent the number of calls)= the total fee of $50.50 cents.
thus,now you need to figure out how much the phone calls were without the monthly fee so you would do:
50.50-18=32.50
so 32.50 is the price of all the phone calls
then you divide 32.50 by 0.05 which equals to 650
meaning that n=650
hope I helped!
Given f(x) = 4x - 3 and g(x) = 9x + 2, solve for (f + g)(x).
[tex]\\ \sf\longmapsto (f+g)(x)[/tex]
[tex]\\ \sf\longmapsto f(x)+g(x)[/tex]
[tex]\\ \sf\longmapsto 4x-3+9x+2[/tex]
[tex]\\ \sf\longmapsto 4x+9x-3+2[/tex]
[tex]\\ \sf\longmapsto 13x-1[/tex]
Answer:
13x - 1
Step-by-step explanation:
f(x) + g(x) = 4x - 3 + 9x + 2
f(x) + g(x) = 4x+9x + 2 - 3
f(x) + g(x) = 13x - 1
Two tablespoons of peanut butter contain 190 calories. Two tablespoons of grape jelly contain 122 calories. Which contains more calories, two tablespoons of peanut butter or two tablespoons of grape jelly?
Christopher has $1947 in his savings account. This weekend he will deposit another $99 in the account. How much money will be in Christopher savings account after this weekend
Answer:
$2046
Step-by-step explanation:
Add 1947 and 99 because he is depositing, as in adding, 99 dollars
A fifth grade teacher calculates that 27% of her students are late for class. If the teacher is right, what is the probability that the proportion of late students in a sample of 724 students would differ from the population proportion by less than 4%? Round your answer to four decimal places.
Answer:
answer: 0.9479
hope I helped
A square has a side length of 520
meters. What is the perimeter of
the square in kilometers?
Answer: 2.08 km
Step-by-step explanation:
Side of Square = 520 m
Perimeter of Square = Side × 4
= 520 × 4
= 2080 m
1000 m = 1km
2080 m = 2080 ÷ 1000
= 2.08 km
What is the difference between the centroid and the center of mass?A: When (), ,, ,x y zc x y zthen the center of mass is the centroid.
The centroid and center of mass need not be the same point. They are the same only when a body's mass is uniformly distributed.
find the surface area of the prism HURRY
Answer:
does the answer help you?
You pick a marble from a bag containing 1 green marble, 4 red marbles, 2 yellow marbles, and 3 black marbles. You replace the first marble and then select a second ones find p(blue, then black).
If you do not replace the first marble in the previous question before you select the 2nd one, find p(red, then red)
Show your work!!
Answer:
First question:0
Second question:2/15
Step-by-step explanation:
First:
Total of marbles=10
since there is no blue the probability is 0, since black is 3. then prob= number of black/total number of marbles. =3/10
therefore 0*3/10 =0
second:
probability of red is 4/10
since the first marble wasn't returned,the total number of marbles=9
therefore probability if the second red marble is =3/9 =1/3
probability of first marble *probability of second marble
(4/10)*(1/3) =(4/30)= 2/15
If the Miller's spend $1200 on housing each month, then what is their total monthly budget?
Answer:
2400$
Step-by-step explanation:
Miller's Family spends 50% of their budget on housing and we know that they spent 1200$ this month, so 1200$*2 = 2400$.
Have a nice day! :-)
Find the common factor of 75,00 and 60
The common factors of 60 and 75 are
1, 3, 5 and 15
And GCF is 15
Must click thanks and mark brainliest
Give two Examples of workers targeted for by minimum waged
Answer:
Minimum wage refers the smallest wage an employee can make per hour for all hours he or she works on the job. ... For example, New York has a higher minimum wage than Maine, as the cost of living is higher in New York.
if my answer helps you than mark me as brainliest.
Please help with step by step.
Show that Reſiz) = -Im(z)
Step-by-step explanation:
[tex]re(i(x + yi) = - im(x + yi) \\ re(xi - y) = - im(x + yi) \\ - y = - (y) \\ - y = - y \\ proved \: is \: correct[/tex]
How much would you have to
deposit today to have an
accumulated amount of
$20,000 in 20 years if yearly
interest is 4.75% compounded
continuously?
Because the account is compounded continuously, Euler number is required
e = 2.7182818
in alska the colderst temprauter ever recorded is -80 that is much colder than in hawil where the coldest temperature is 15
Answer: What are we supposed to do ???
Determine the coordinates of the ordered pairs on the coordinate grid.
Answer:
A = (5,7)
B = (0, -1)
C = (-8, -3)
D = (5, -8)
Step-by-step explanation:
Answer:
A = (5, 7)
B = (0, -1)
C = (-8, -3)
D = (5, -8)
To do these problems, trace along in a straight line from the coordinate to the x- axis line and then to the y-axis line. Whatever number you reach will be part of the coordinate.
Hope this helped.
find the length of leg x
x=
side a is 15
side b is 12
side x=
Answer:
x=9
Step-by-step explanation:
a=hyp=15
b=base=12
x=perp=?
using pathagorus theorem:
[tex] {hyp}^{2} = {base}^{2} + {perp}^{ 2} \\ {15}^{2} = {12}^{2} + {x}^{2} \\ 225 = 144 + x \\ 225 - 144 = {x}^{2} \\ 81 = {x}^{2} \\ x = 9[/tex]
438 Friday night, 820 Saturday night and 636 Sunday afternoon. How many more people attended the play on Sunday than on Friday?
Answer:
198 more people attended the play on Sunday than on Friday
Step bye step explanation:
638 - 438 = 198.
(438 Friday night
(438 Friday night 636 Sunday night)
Help me please and thx
Answer:
or,x*10=5*6
or, 10x=30
or,x=30/10
or,x=3
X/6 = 5/10 // - 5/10
X/6-(5/10) = 0
X/6-1/2 = 0
1/6*X-1/2 = 0 // + 1/2
1/6*X = 1/2 // : 1/6
X = 1/2/1/6
X = 3
X = 3
Here's a link to help with future problems and it helped me with this question
https://www.geteasysolution.com/
What is the value of |-6|-|6| -(-6)
Answer:
6
Step-by-step explanation:
Solve the absolutes: |-6| becomes 6
and |6| doesn't change and still is 6
Substitute: 6-6-(-6)
- * - = +
6-6+6 = 6
