Answers
Answer:
BRO, u dont need to be a god :D, This is simple math and you just need to use your brains
Step-by-step explanation:
Given is a polynomial, and the values of the variables in it are given by showing what set are they an element of, right? It just gets easier from here
They tell us that 'z' is an element of set C, which stands for Complex Numbers.
And they also tell us that 'a' is an element of set Z, which stands for Integers, which are just numbers with a sign :).
They have also given us a root (solution) to the polynomial, which is also a complex number.
The two statements given are just there for us to verify that we are on the right track to the solution.
We can see that (z = 3 + i) which of course is a complex number, due to the presence of 'i', and 'a' is an integer for when we find its value.
Put it all together and we will get the answer.
Like this,
take the given value of 'z' and place it into the polynomial given, now keep your eyes open here. They said the value of z is as such when the polynomial is an equation which equals 0, so hence we get this:
P(z) = a(3+i)³ - 37(3+i)² + 66(3+i) - 10 = 0,
now just go on simplifying,
=> a(3³+i³+3×3²i+3×3i²) - 37(3²+2×3×i+i²) + 66×3 + 66×i - 10 = 0
=> a(27-i+27i-9i) - 37(9+6i-1) + 198 + 66i - 10 = 0
=> a(27+17i) - 37(8+6i) + 188 + 66i = 0
=> a(27+17i) = 296 + 222i - 188 - 66i
=> a(27+17i) = 108 + 156i
=> a = (108+156i) / (27+17i)
=> a = (108+156i)(27-17i) / (27)² - (17i)²
=> a = (5568 + 2376i) / (699 + 289)
=> a = 5568 + 2376i / 1488
DONNEEE....yayyyy....lol
Related Questions
4. What is the solution to the system of equations?
Hint: Solve each equation for y first, then graph.
5. What is the solution to the system of equations?
Answers
Answer:
4. The solution to the system of equations is: (2,-1)
5. The solution to the system of equations is: (3,5)
Step-by-step explanation:
4. What is the solution to the system of equations?
[tex]2x+3y=1\\-3x+4y=-10[/tex]
Let:
[tex]2x+3y=1--eq(1)\\-3x+4y=-10--eq(2)[/tex]
Multiply eq(1) by 3 and eq(2) by 2 and add both equations
[tex]6x+9y=3\\-6x+8y=-20\\---------\\0x+17y=-17\\y=\frac{-17}{17}\\y=-1[/tex]
So, value of y=-1
Now finding the value of x bu putting value of y in eq(1)
[tex]2x+3y=1\\2x+3(-1)=1\\2x=1+3\\2x=4\\x=\frac{4}{2}\\x=2[/tex]
So, value of x=2
The solution to the system of equations is: (2,-1)
5. What is the solution to the system of equations?
[tex]y=2x-1\\6x-y=13[/tex]
Let:
[tex]-2x+y=-1--eq(1)\\6x-y=13--eq(2)\\------\\4x=12\\x=\frac{12}{4}\\x=3[/tex]
So, value of x=3
Putting value of x in equation 1 to find value of y
[tex]y=2x-1\\y=2(3)-1\\y=6-1\\y=5[/tex]
So, value of y=5
The solution to the system of equations is: (3,5)
Please help!!! Will mark brainliest!
Write a system of equation for each of the descriptions below, and then solve the systems. Hint: you can graph the equations to find the solutions.
13. A number is 7 more than another number. The sum of the numbers is 15. Find the numbers.
14. One number is two times the other, and their sum is 27. What are the numbers?
15. Thirteen is the sum of two numbers and their difference is equal to five. Find the numbers
16. Three times one number is equal to two times the larger one and their difference is 1. What are the numbers?
17. Joseph has 30 coins and they are all either dimes or nickels. The total $2.15. How many dimes does he have?
18. A golfer completed 18 holes with a total of 79 strokes. On each hole he met par, which was either four or five each time. How many holes were played in four strokes?
19. There are two numbers. The difference between them equals six, and one of the numbers is three times the other number. There are two pairs of numbers that satisfy these descriptions, What are they?
20. There is a number that is three-fifths the total of the other number. When four is added to one of the numbers their sum will be equal to the other number. There are two pairs of numbers that satisfy these descriptions. What are they?
Answers
Answer:
4, 11
Step-by-step explanation:
Q# 13 :
Let the first number be 'x'
the 2nd number would be ' x + 7'
x + x + 7 = 15
2x= 15-7
x= 8/2
x= 4
2nd number: x + 7
= 4+7
= 11
In a regular polygon the interior angle is thrice the exterior angle. The number of sides of the polygon is.
Answers
Answer:
8
Step-by-step explanation:
Measure of one interior angle of a regular polygon of n sides:
(n - 2)180/n
Measure of one exterior angle of a regular polygon if n sides:
360/n
"the interior angle is thrice the exterior angle"
(n - 2)180/n = 3 * 360/n
(n - 2)180 = 3 * 360
n - 2 = 3 * 2
n = 8
The number of sides is 8.
7/2x + 1/2x = 9 + 9/2x
the value of x is
Answers
Answer:
Step-by-step explanation:
X is -18
Which inequalities have no solution? Check all of the boxes that apply. 1. x > x 2. –3x –3x 3. –4 + x > –2 + x 4. x – 2 < x + 3
Answers
Answer:
1, 3
Step-by-step explanation:
1. x > x
Technically, one number cannot be more than itself. It can only equal to itself.
3. –4 + x > –2 + x
If you minus x from both sides of the equation, it becomes:
-4 > -2
This is not true no matter what x is, thus it has no solution.
4. x – 2 < x + 3
If you add 2 on both sides, it becomes:
x < x + 5
This inequality is possible and has infinitely many solutions.
Note: I will update this answer and address Question 2 once the inequality sign is given :)
Find the missing side length of JK .
Answers
Answer:
I'm pretty sure it's 16
Step-by-step explanation:
it measures up with the other triangles side
Write the slope-intercept form of the line that passes through the point (1, 0) and is parallel to x - y = 7. Type your answer in the box provided or use the upload option to submit your solution.
Answers
Answer:
y = x - 1
Step-by-step explanation:
If it's parallel to x - y = 7, that means the slope of that equation is the slope for the equation you're looking for.
To get the slope, you need to put the given equation into slope intercept form, so move x to the other side. You should get: -y = 7 - x
Then, to get the y positive, divide by -1: y = -7 + x
Slope intercept form is as follows: y = mx + b, so whatever the number is in front of x is your slope. In this instance, your slope is 1.
You now have your slope, and a point in which your new line passed through. Using slope intercept form, y = mx + b, if you substitute in what you know, you can find your answer. Right now you know y, m, and x, and you're looking for b.
x=1; y=0; m=1.
So, substituting, you'd get 0 = (1)(1) + b
0=1+b Solve
You should get b= -1, leaving your final answer as y = x - 1
y=x+1 is the slope-intercept form of the line that passes through the point (1, 0) and is parallel to x - y = 7.
What is Slope of Line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=y₂-y₁/x₂-x₁
We need to find slope-intercept form of the line that passes through the point (1, 0) and is parallel to x - y = 7.
The slope will be same as it is parallel.
x - y = 7.
-y=7-x
y=x-7
Slope is 1.
Now equation of line passing through (1,0)
0=1(1)+c
c=-1
y=x-(-1)
y=x+1
Hence y=x+1 is the slope-intercept form of the line that passes through the point (1, 0) and is parallel to x - y = 7.
To learn more on slope of line click:
https://brainly.com/question/14511992
#SPJ2
A. Paul notices that the shape of the pond is shaped somewhat like a triangle. He claims that he can approximate the perimeter of the pond without doing any measurement of the actual pond or on the diagram. What assumption would Paul need to make in order to justify his claim? B. Based on the assumption in part A, determine the approximate length of side c of the pond. Explain your reasoning in at least two sentences. C. Determine the approximate perimeter of the pond. Explain your reasoning
Answers
9514 1404 393
Answer:
A) the curves are ellipses
B) 161 yards
C) 366 yards
Step-by-step explanation:
A) The general shape of the side marked c has the appearance of two quarter-ellipses. The major axis is approximately 125 yards, and the minor axis is approximately 80 yards. Paul could assume that the curves are quarter-ellipses.
__
B) For an ellipse with this eccentricity, its perimeter is within 2% of that of a circle with a diameter equal to the average of these dimensions.*
So, the approximate length of side c is ...
c ≈ π(80 +125)/4 ≈ 161 . . . . yards; length of side c
__
C) The perimeter of the pond is the sum of the side lengths, so will be ...
80 yds + 125 yds + 161 yds = 366 yds . . . pond perimeter
_____
* Indian mathematician Ramanujan developed an approximate formula for the circumference of an ellipse, which would otherwise need to be computed using an elliptic integral. it is ...
C = π(a+b)(1 + 3λ²/(10 +√(4 -3λ²))
where λ = (a -b)/(a +b) and a, b are the semi-axis lengths.
For this ellipse, λ = 9/41, so the last factor is about 1.01208313. Using this factor, the circumference is expected to be good to about 7 significant digits. Continuing the calculation, we find ...
C ≈ 325.904 . . . . circumference of an ellipse 125 yd long by 80 yd wide
This is twice the length we imagine for c, so c ≈ 163 yards. As we said, the approximation used above is within 2% of this value.
The attachment shows the shape if the curve is actually an ellipse.
Find the product of (x + 3)^2
Answers
Answer:
(x+3)² = (x+3)(x+3)
When we distribute polynomials, we have to make sure each term mutliplies to all of the terms in the other polynomial.
x(x+3) + 3(x+3)
x² + 3x + 3x + 9
x² + 6x + 9
Methods such as FOIL (first, outside, inside, last) and creating a table can help you with this.
Step-by-step explanation:
Answer:
x^(2)+6x+9 also x=-3
Step-by-step explanation:
3/5 of Camden's toys are orange. What percentage of Camden's toys are not orange?
Answers
Answer:
2/5
Step-by-step explanation:
Answer:2/5
Step-by-step explanation:
Please help Express both quantities in each comparison
using the same units. Write the comparison
as a ratio in fraction form. Then write an
equivalent ratio using whole numbers.
a) 85¢ to $1.20 b) 24 kg to 80 g
Answers
Answer:
1a) .85/1.20 = 85/120 = 17/24. 2a) 17:24
1b) 24000/80 = 2400/8 = 300/1. 2b) 300:1
_______________________________
I believe this is what the problem is asking.
A triangle has sides which are consecutive odd integers and an
angle of 120°. What is the perimeter of the triangle?
Answers
Answer:
Perimeter = 15
Step-by-step explanation:
We are told that the length of each of the 3 sides of the triangle are consecutive odd integers.
Thus means that we can write the 3 terms as;
(x - 2), x, (x + 2)
Thus, perimeter is;
P = (x - 2) + x + (x + 2)
P = 3x
If an angle is 120°, it means that the corresponding side that is directly opposite the angle is the largest side of the triangle.
Thus, this side is (x + 2)
Using cosine rule, we have;
(x + 2)² = x² + (x - 2)² - 2(x(x - 2))cos 120
Expanding, we have;
x² + 4x + 4 = x² + x² - 4x + 4 - (2x² + 4x)(-½)
This reduces to;
4x = x² - 4x + x² - 2x
2x² = 10x
2x = 10
x = 10/2
x = 5
Thus, other sides are;
(x - 2) = 5 - 2 = 3
And (x + 2) = 5 + 2 = 7
So,perimeter is;
P = 3x = 3 × 5 = 15
Mr. Schneider paid $2276.35 to have a landscaper build a patio with the dimension below. How much did the landscaper charge for each square metre of patio? 3.2m 5.4m 1.8m 1.2m
Answers
Answer:
Step-by-step explanation:
Since we are not given the dimension. Let us say the shape of the patio is a rectangle with length 30m and width 18m.
Area of the rectangle = Length * Width
Area of the rectangle = 30 * 18
Area of the rectangle = 540m²
This means that 540m² of the patio costs $2276.35. To get the cost of each square metre of patio, we will say;
540m² = $2276.35
1m² = x
cross multiply;
540x = $2276.35
x = $2276.35/540
x = $4.22
Hence each square meter of patio will cost $4.22
Note that the dimension of patio was assumed. Same explanation can be employed for any dimension.
When multiplying 1,729 times 308, Clayton got a product of 52,253. Does his answer seem reasonable
Answers
Answer:
No, it does not
Step-by-step explanation:
Well first we round off the factors 1790 and 308 to 2000 and 300These are numbers which we are kind of close to our original numbers, but easier to multiply without a calculator or anything of the kindThen we easily multiply and estimate if the answer is rightSo [tex]2000*300=600,000[/tex] Now how close is 600,000 to 52,253? They are way too far apart!So that means the product is not reasonable, it's not even close to our estimation.Peter hired a cleaning company to clean his house. The cleaning company charges a fixed fee of $15 plus $17 per hour to clean a house. A second cleaning company charges $20 per hour to clean a house. The second company does not charge a fixed fee in addition to their hourly rate. For what number of hours is the total amount charged for cleaning a house the same for both companies? Show or explain how you got your answer.
Answers
Answer:
5 hours
Equations:
first company: 17x+15
second company: 20x
Proof:
17(5)+15 => 85+15 => 100
20(5) => 100
Answer:
5 hours
Step-by-step explanation:
What is opportunity cost?
1. the limited availability of goods or services
2. a benefit lost when choosing between two options
3. the resources used to produce finished goods or services
4. a system of directly exchanging goods or services for other goods or services
Answers
I just did this on edge
Answer:
the answer is 2
Step-by-step explanation:
Bcz u choseine option and lose the next bet benefit
What is the lowest term of 110/33
Answers
Answer:
10/3
Step-by-step explanation:
110/33
lowest term of 110/33 is 10/3
110/11=10
33/11=3
10/3 is your answer
Whats the ANSWER GIVING BRAINLIEST TO RIGHT ONE:)
Answers
Answer:
C
Step-by-step explanation:
I believe this is the correct one.
Answer:
C
Step-by-step explanation:
C has the point (-2, -3.5) and the point (0.5, -4)
Given two sides of a triangle, find a range of possible side lengths for the third side.
9 and 32
Answers
Answer: Two sides of a triangle have lengths 2 and 7. Find all possible lengths of the third side. Show Answer. difference $$< x <$$ sum $$7 -2 < x < 7+2$$ Answer: $$5 < x < 9$$ Problem 7. Two sides of a triangle have lengths 12 and 5. Find all possible lengths of the third side
Step-by-step explanation: i hope i helped
A clown sells large balloon animals for $25 each. Small balloon animals sell for $10 each. Jordan is buying 2 large balloon animals and x small balloon animals. Let y represent the total cost Jordan must pay in dollars. Part 1: Write an equation in slope-intercept form to model this description. Part 2: What is Jordan’s total cost if she purchases 4 small balloon animals? Show your work.
Answers
Answer: Part 1: y =10x+50
Part 2: Jordan’s total cost = $90
Step-by-step explanation:
Given: Price of each large balloon = $25
Price of each small balloon = $10
Price of 2 large balloons = 2 (Price of each large balloon)
= $2 (25)
= $50
Part 1: Total cost = (Number of small balloons)(Price of each small balloon) + (Number of large balloons)(Price of each large balloon)
Let x = Number if small balloons , y= total cost Jordan must pay in dollars.
Then, y= (x)(10)+(2)(25)
⇒ y =10x+50
Part 2: If she purchases 4 small balloon animals, put x=4
Then, y= 10(4)+50=40+50= 90
i.e. Jordan’s total cost = $90
AB=3x-4 and BC=5x-10
Answers
Answer:
Step-by-step explanation:
an isosceles triangle two adjacent sides are equal
so AB = BC
3x-4 = 5x-10
2x = 6
x= 3
so ,
3 ( 3 ) -4 = 5
5 ( 3 ) -10 = 5
A system of equations is shown below: 2x = 5y + 4 3x − 2y = −16 What is the solution to this system of equations? (5 points) (−8, −4) (8, 4) (−4, −8) (4, 8)
Answers
Answer:
(-8,-4)
Step-by-step explanation:
Answer:
EASY (-8,-4)
Step-by-step explanation:
x^2- 11 = 70 I need help on how to solve this
Answers
Answer: Add 11 to the other side of the equation, giving you 81. Then, since x is square you are going to need to square root both sides ([tex]\sqrt{x}[/tex] this symbol). When you do that, you should get what x is! Let me know if you still need help!
Picture a rectangular prism with a volume of 150 cubic units. What is the number of unit cubes that would fill the volume of this prism if they were packed without any gaps or overlaps?
Answers
Answer:
150 units woild fill the volume of the prism.
factorise the following fully:
6a⁴b⁶-8a³b⁵+12a²b³
Answers
Answer:
2a^2 b^3(3a^2 b^3 - 4ab^2 + 6)
Write an equation of a line through (15, 8) that is perpendicular to the line y =57 x −1.
Answers
Answer:
Equation of a line through (15, 8) that is perpendicular to the line y =57 x −1 is [tex]\mathbf{y=-\frac{1}{57}x+\frac{157}{19}}[/tex]
Step-by-step explanation:
We need to write an equation of a line through (15, 8) that is perpendicular to the line y =57 x −1.
The equation will be in slope-intercept form: [tex]\mathbf{y=mx+b}[/tex]
Where m is slope and b is y-intercept.
Finding Slope of new line
We are given equation [tex]y =57x-1[/tex] of line, which is perpendicular to the line whose equation we need to find.
If the lines are perpendicular there slopes are inverse of each other i.e [tex]m_1=-\frac{1}{m_2}[/tex]
Slope of given line is m= 57 ( compare the given equation with standard slope-intercept form the value of m is 57
Slope of new line is m= [tex]-\frac{1}{57}[/tex]
Finding y-intercept of new line
Now finding y-intercept (b) for new line. It can be found using point (15,8) and slope m = [tex]-\frac{1}{57}[/tex]
[tex]y=mx+b\\8=-\frac{1}{57}(15)+b\\8=-\frac{15}{57}+b\\b=8+\frac{15}{57}\\b=\frac{8*57+15}{57}\\b=\frac{471}{57}\\b=\frac{157}{19}[/tex]
So, y-intercept b of new line is: [tex]b=\frac{157}{19}[/tex]
Equation of required line
Equation of line having slope m= [tex]-\frac{1}{57}[/tex] and y-intercept [tex]b=\frac{157}{19}[/tex] is:
[tex]y=mx+b\\\mathbf{y=-\frac{1}{57}x+\frac{157}{19}}[/tex]
So, equation of a line through (15, 8) that is perpendicular to the line y =57 x −1 is [tex]\mathbf{y=-\frac{1}{57}x+\frac{157}{19}}[/tex]
write the slope intercept-form of the equation of the line through the given points.
Answers
Answer:
qs,wdnfm.ew fw v
Step-by-step explanation:
wdmc vw.mv / n,v
Unit Test Review Active 1 2 3 Which best describes a model of ? five wholes divided into 12 equal pieces twelve wholes divided into 5 equal pieces a whole divided into 5 equal pieces with 12 pieces shaded in O a whole divided into 5 equal pieces and another whole divided i
Answers
Answer:
15%
Step-by-step explanation:
Trust me, i took the K12 test and got it correct :)
What’s the angles relationship?
Answers
Answer:
The relationship between the angles would be parallel because they are the exact same degree now if they were different degrees their relationship would be perpendicular but with them being the same the answer is parallel
A city council consiste of 8 democrats and 6 republicans. If a committee of 4 people is selected,find the probability of selecting 2 democrats and 2 republicans
Answers
Answer:
Step-by-step explanation:
8C2 * 6C2
============
14C4
8C2 = 8*7/1 * 2 = 28
6C2 = 6*5 / 1*2 = 15
14C4 = 14*13 *12 * 11 / (1 * 2 * 3 * 4) = 1001
28 * 15 / 1001 = .4195