Solve for x and y :
x + y = 1 → y = 1 - x
x ² + y ² = -1
x ² + (1 - x)² = -1
x ² + (1 - 2x + x ²) = -1
2x ² - 2x + 1 = -1
2x ² - 2x + 2 = 0
x ² - x + 1 = 0
x ² - x + 1/4 = -3/4
(x - 1/2)² = -3/4
x - 1/2 = ±√(-3/4)
x - 1/2 = ±√3/2 i
x = 1/2 ± √3/2 i → x = exp(± iπ/3)
y = 1 - (1/2 ± √3/2 i ) → y = -1/2 ± √3/2 i → y = exp(± 2iπ/3)
Then
x ⁷ + y ¹³ = exp(± 7iπ/3) + exp(± 26iπ/3)
… = exp(± iπ/3) + exp(± 2iπ/3)
since 7π/3 is equivalent to π/3, and 26π/3 is equivalent to 2π/3 (both modulo 2π).
In either case, we get
x ⁷ + y ¹³ = x + y = 1
so the answer is (2) 1.
Roxie is picking out some movies to rent, and she is primarily interested in horror films and foreign films. She has narrowed down her selections to 20 horror films and 8 foreign films. How many different combinations of 3 movies can she rent if she wants at least two horror films?
Answer:
She has 2,660 combinations
Step-by-step explanation:
Here, we want to calculate the number of different combinations of 3 movies that can be rented
The condition is at least two horror movies
What this means is that she can select 2 or 3 horror movies
if two horror movies, then 1 foreign film
The combination is as follows;
20 C 2 * 8 C 1
= 190 * 8 = 1,520
If she is selecting 3 horror movies, then no foreign film will be selected
Number of ways this can be done is;
20 C 3 = 1,140
So the
number of different combinations would be;
1,140 + 1,520 = 2.660
The equation of line t is y = -2x + 9. Perpendicular to line t is line u, which passes through
the point (-10, 4). What is the equation of line u?
Write the equation in slope-intercept form. Write the numbers in the equation as proper
fractions, improper fractions, or integers.
Answer:
Equation of line u in slope-intercept form is: [tex]\mathbf{y=\frac{1}{2}x+9 }[/tex]
Step-by-step explanation:
Equation of line t : y = -2x + 9.
We need to find equation of line u, which is perpendicular to line t and passes through point (-10,4)
The equation must be in slope-intercept form.
The general equation of slope-intercept form is: [tex]y=mx+b[/tex] where m is slope and b is y-intercept
Finding Slope:
If two lines are perpendicular, their slopes are opposite i.e [tex]m=-\frac{1}{m}[/tex]
Slope of line t: y=-2x+9 we get m =-2 (Comparing with general form y=mx+b, we get m =-2)
Slope of line u: [tex]\frac{1}{2}[/tex]
So, we get Slope of line u: m= [tex]\frac{1}{2}[/tex]
Finding y-intercept:
Using slope m= [tex]\frac{1}{2}[/tex] and point(-10,4) we can find y-intercept
[tex]y=mx+b\\4=\frac{1}{2}(-10)+b\\4=-5+b\\b=4+5\\b=9[/tex]
Equation of line u:
So, equation of line u, having slope m= [tex]\frac{1}{2}[/tex] and y-intercept b=9, we get:
[tex]y=mx+b\\y=\frac{1}{2}x+9[/tex]
So, Equation of line u in slope-intercept form is: [tex]\mathbf{y=\frac{1}{2}x+9 }[/tex]
Keiko's Coffee Shop makes a blend that is a mixture of two types of coffee. Type A coffee cost Keiko $4.15 per pound, and type B coffee costs $5.25 per pound. This month's blend used four times as many pounds of type B coffee as type A, for a total cost of $980.85. How many pounds of type A coffee were used?
Answer:
39 pounds of type A coffee were used.
Step-by-step explanation:
Given: Cost of type A coffee is $4.15 per pound and cost of type B coffee is $5.25 per pound. Also, blend used four times as many pounds of type B coffee as type A.
To find: How many pounds of type A coffee were used.
Let [tex]x[/tex] be the number of pounds of type A coffee and [tex]y[/tex] be the number of pounds of type B coffee.
Then, according to question,
[tex]4.15x+5.25y=980.85[/tex] and [tex]y=4x[/tex]
Substituting [tex]y=4x[/tex] in [tex]4.15x+5.25y=980.85[/tex], we get
[tex]4.15x+5.25(4x)=980.85[/tex]
⇒[tex]4.15x+21x=980.85[/tex]
⇒[tex]25.15x=980.85[/tex]
⇒[tex]x=\frac{980.85}{25.15}[/tex]
⇒[tex]x=39[/tex]
Therefore, 39 pounds of type A coffee were used.
15 points! Please help
Answer:
I'm pretty sure it's reflection
Step-by-step explanation:
The triangle to the right is basically a reflection of the first triangle
Classify the following as either a discrete random variable or a continuous random variable.
The amount of time six randomly selected volleyball players play during a game.
Is it: Discrete or Continuous
Answer: continuous random variable.
Step-by-step explanation:
A discrete random variable is defined as a random variable which consists of countable number. Examples include numbers of shoes, number of sales etc.
A continuous random variable is a random variable whereby the data can take several values. It is a random variable that takes time into consideration.
Therefore, the amount of time six randomly selected volleyball players play during a game will be a continuous random variable since time so involved.
After selecting 180 of its employees to from a new division, a company discovers that engineers outnumber analysts by a 3:1 ratio in the division. Oly analysts and engineers work in the new division. How many more analysts must the company add to the division if it wants to have a 1:1 ratio of engineers to analysts at the new division?
Answer:
I think its 90
Step-by-step explanation:
3x plus 1x is 4x divide 180 but 4 and get 45 so that meab there are 135 and 45
you need 90 more analysts to have a 1 to 1 ratio
Which of the following is a solution to the system of two equations 4x + y = 51 and 2x – 6y = 6?
Answer:
The solution to the system of equations given is:
y = 3x = 12Step-by-step explanation:
First, we must see our two equations given:
4x + y = 512x – 6y = 6We can use the reduction method, with this, we must eliminate a variable, in this case, de x variable, this can do multiply the equation 2 by (-2) and add the two equations:
(2x – 6y = 6)*(-2) = (-4x+12y = -12)3. -4x+12y = -12
Now, we operate the equations 1 and 3:
(4x + y = 51) + (-4x+12y = -12) = (13y = 39) "The variable x dissapears because 4x - 4x = 0"4. 13y = 39
We solve the equation 4 and obtain the value for "y":
13y = 39y = 39/13y = 3With the value of "y," we can replace this value in equation 1 or 2 to obtain the value of "x," in this case, we're gonna use the equation 1:
4x + y = 514x + 3 = 514x = 51 - 34x = 48x = 48/4x = 12In this form, we know the solution to the system of two equations is: x = 12 and y = 3.
Damian’s father purchases 8 notebooks for school. The total amount for the notebooks is $31.68.
How much does each notebook cost individually
Answer:
Each notebook costs $3.96 each.
3168 divided by 8 = 396
move the decimal two places left.
Step-by-step explanation:
May I have brainiest I'm trying to level up!
</3 PureBeauty
Answer:
Each notebook costs $3.96
Step-by-step explanation:
We assume each notebook costs the same amount, the total cost is $31.68, and that is for 8 notebooks. So, we divide 31.68 by 8 and get our answer of $3.96 per notebook.
I hope this helps:)
Find the equation of the line with slope of 4 and y-intercept of -3.
A. y = 1/4x - 3
B. y = -1/4x – 3. C. y = 1/4x + 3
D. y = 4x - 3
Answer:
y = 4x -3
Step-by-step explanation:
The slope intercept form of an equation is
y = mx+b where m is the slope and b is the y ntercept
y = 4x -3
Find the simple interest paid on a deposit of $225 at a rate of 1.5% over 2 years.
Answer:
$6.75
Step-by-step explanation:
Interest = [tex]\frac{1.5}{100}[/tex] × 2 × $225
= $6.75
Finding the slope of a line.
The moon is about 382,500km away from Earth. This distance actually varies by about 22,500km. What are the maximum and minimum distances to the moon?
Answer:
The minimum distance to the moon is of 360,000 km and the maximum distance is of 405,000 km
Step-by-step explanation:
The maximum distance is found adding the variation.
The minimum distance is found subtracting the variation.
We have that:
Distance: 382,500 km
Variation: 22,500 km
So
Maximum distance: 382500 + 22500 = 405,000 km
Minimum distance: 382500 - 22500 = 360,000 km
The minimum distance to the moon is of 360,000 km and the maximum distance is of 405,000 km
6 min to 1 hour
as a fraction in simplest form
Step-by-step explanation:
[tex]1 \: hour \: = 60 \: min \\ \\ \frac{6}{60} = \frac{1}{10} \\ [/tex]
Answer:1/10
Step-by-step explanation:
Can anyone solve this? And I’d appreciate if you explain how to do it.
2 divided into 3 multiply 1
Answer:
either 2/3
or 3/2
but its probably 2/3
thanks for the easy points!
Step-by-step explanation:
Mr. Lopez, a Language Arts teacher, has his students read a certain number of pages out loud in class to start a book, and then a set number of pages for homework each night to complete the book. The graph displays the total number of pages read each day.
A graph has days on the x-axis and pages read on the y-axis. Points are at (0, 35), (1, 57), (2, 79), (3, 101), (4, 123).
What does the point (0, 35) represent?
The students will read 35 pages a day to complete the book.
The book begins on page 35.
None of the students read 35 pages.
The students read 35 pages in class to start the book..
Answer:
The students read 35 pages in the class to start the book.
Step-by-step explanation:
Given: A Language Arts teacher, Mr. Lopez has his students read a certain number of pages out loud in class to start a book, and then a set number of pages for homework each night to complete the book.
The graph displays the total number of pages read each day.
The point (0,35) represents the y-intercept of the function.
Since y axis representing the number of pages read each day.
It implies (0,35) represents the students read 35 pages in the class to start the book.
Answer:
The students read 35 pages in the class to start the book.
Step-by-step explanation:
on edge
The model of a 1955 Ford Thunderbird has a scale factor of 1/24. if the model of the car is 7 inches long how long is the actual car in feet?
Answer:
14
Step-by-step explanation:
Help I don’t understand
Step-by-step explanation:
Answer:
1 pounds
Step-by-step explanation:
It basically means theres 1000 things that all weigh the same, so they add up to 0.1 pounds (0.1/1000= 0.00001 ) All you need to do is multiply by 10 so it would be 1 pound :)
What is the x and y value in -3x + y = 4 and -9x + 5y =-1
Answer:
y=291
Step-by-step explanation:
I did the math got 291.
Answer:
-9x + 5y =-1
x-intercept: ( 1 9 , 0 )
y-intercept: ( 0 , − 1 5 )
-3x + y = 4
x-intercept: ( − 4 3 , 0 )
y-intercept: ( 0 , 4 )
2 3/5 ÷ 2/3
3 9/10
2 9/10
1 11/15
1 4/5
Answer:
Solving the expression: [tex]2\frac{3}{5}\div \frac{2}{3}[/tex] we get [tex]\mathbf{3\frac{9}{10}}[/tex]
Option A is correct.
Step-by-step explanation:
We need to solve the expression: [tex]2\frac{3}{5}\div \frac{2}{3}[/tex]
We need to divide both the terms.
Solving:
[tex]2\frac{3}{5}\div \frac{2}{3}[/tex]
First we will convert the mixed fraction into improper one
[tex]\frac{13}{5}\div \frac{2}{3}[/tex]
Now, we will convert division sign into multiplication, the term 2/3 is reciprocated
[tex]\frac{13}{5}\times \frac{3}{2}[/tex]
Now, multiply numerator with numerator and denominator with denominator
[tex]\frac{39}{10}[/tex]
Now, we will convert into mixed fraction
[tex]3\frac{9}{10}[/tex]
So, Solving the expression: [tex]2\frac{3}{5}\div \frac{2}{3}[/tex] we get [tex]\mathbf{3\frac{9}{10}}[/tex]
Option A is correct.
Which explains why the graph is not a function?
5
4
3-
2+
O It is not a function because the points are not
connected to each other.
O It is not a function because the points are not related
by a single equation
It is not a function because there are two different x-
values for a single y-value.
O It is not a function because there are two different y-
values for a single x-value.
1 +
-5 -4 -3 -2 -11
1
2 3 4 5
X
-2
+
.
-3
-4
-5
Answer:
We conclude that it is not a function because there are two different y-values for a single x-value.
Hence, option D is true.
Step-by-step explanation:
We know that a function is a relation where each input or x-value of the X set has a unique y-value or output of the Y set.
In other words, we can not have duplicated inputs as there should be only 1 output for each input.
From the graph, we can determine the table such as:
x y
-2 -5
-1 3
1 -2
3 0
4 4
4 -2
It is clear that the values of x = 4, is repeated twice.
In other words, the input value x = 4 is duplicated.
We know that we can not have duplicated inputs as there should be only 1 output for each input.
Therefore, we conclude that it is not a function because there are two different y-values for a single x-value.
Hence, option D is true.
help me out please. what is 5 ÷ 9/10 ?
EMERGENCY HELP PLEASE
Answer:
11x+21
Step-by-step explanation:
blue square= x squared
green square=3x
pink square=7x
orange square=21
=
11x+21
In a study, the sample is chosen by writing everyone's name on a playing card, shuffling the deck, then choosing the top 20 cards. What is the sampling method?
A. Simple Random.
B. Systematic.
C. Stratified.
D. Convenience.
Answer: A. Simple Random Sampling
Step-by-step explanation:
A simple random sampling technique could be explained as being the most basic and approach to choosing an unbiased Number of samples from a given population. This technique simply involves choosing a specified Number of samples at random (each member of the larger sample or population has equal Chance of being selected) from a larger sample or population. It does not require any sort of partitioning during selection. As in the scenario above, the deck of cards represents the large lr population from which 20 cards are to be selected, since the card has been shuffled then each card has equal Chance of being selected.
Guys i actually need help
Answer:
Rotation
Step-by-step explanation:
Answer:
That is just rotation.
Step-by-step explanation:
It is rotation because if you were to spin it to the right on a 57 degree it will be that angle.
It also not the others because if you were to put reflection that would it would the opposite.
helpppppppppppppppppppppp
Answer:
(A) Mean
(B) Mean
(C) Mode
Hope this helps!
And hit Brainlest if ya want! ;))
Evaluate the following logarithm 3/4log16
14 POINTS! PLEASE HELP!!!!
Answer:
Do (8, -9) times 5 for both numbers
Step-by-step explanation:
What is 3x-6+7y-4y plsssssssssss helpppppppp meeere
Answer:
3
+
3
−
6
Step-by-step explanation:
Two boats traveling the same direction leave a harbor at noon. After 3 hr they are 60 miles apart, if one boat travels twice as fast as the other find the average rate of each boat
Answer: The boat 1 moves with a speed of 40mi/h, and boat 2 moves with a speed of 20mi/h.
Step-by-step explanation:
First, we know the relation:
Distance = Speed*Time.
We can define the average rate of the boats as the average speed of the boats.
Now, we know that two boats travel in the same direction, let's define:
S₁ = speed of boat 1.
S₂ = speed of boat 2.
We know that one travels twice as fast as the other, then we can write:
S₁ = 2*S₂
We also know that after 3 hours of travel, they are 60mi apart, then if the slower one travelled a distance D in 3 hours, then:
S₂*3h = D
And the faster one will travel D + 60mi
S₁*3h = (D + 60mi)
Then we have the equations:
S₂*3h = D
S₁*3h = (D + 60mi)
We can replace S₁ by 2*S₂ to get:
S₂*3h = D
(2*S₂)*3h = (D + 60mi)
Now we have isolated D in the above equation, we can just replace it in the second equation to get:
(2*S₂)*3h = (S₂*3h + 60mi)
Now we can solve this for S₂
S₂*6h = S₂*3h + 60mi
S₂*6h - S₂*3h = 60mi
S₂*3h = 60mi
S₂ = 60mi/3h = 20mi/h
The speed of boat 2 is 20mi/h
And we knew that:
S₁ = 2*S₂
then:
S₁ = 2*(20mi/h) = 40mi/h