Therefore , the solution of the given problem of function comes out to be 2.
Function DefinitionA function connects various inputs together or produces a single output from each input. Simply explained, a function is a collection of equations that are linked to a single, identifiable output. A statement, rule, or law which explains the connection between two variables is known as a function in mathematics (the dependent variable). When a rule of this type is applied, there is just one output. by photographer Alex Federspiel.
Here,
=> (1−α)(1−β)(1+α)(1+β)
=>(1−α−β+αβ) /(1+α+β=αβ)
=> (1−(α+β)+αβ ) / ( 1+(α+β)+αβ)
=>(1 + 2/3 + 1/3 )/ (1 -2/3 + 1/3)
=> 2 x 3 /2 =3
=> (1−α)(1+β)+(1−β)(1+α) / (1+α+β+αβ)
=> 3(2−2αβ)/2
=>3(1−αβ)
=>3(1− 1/3 )
=>2
Therefore , the solution of the given problem of function comes out to be 2.
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Help me please! Whoever answers correctly gets brainliest and 40 points!
Which number is equivalent to the fraction 15/7?
O 2
O 2 1/7
O 7/15
O 1 8/7
Tell whether each system of equations has no solution, one solution, or infinitely many solutions. Show how you arrived at your conclusion for each.
a. y = 5x + 11 and y = 5x
b. y = 6x + 3 and y = 3x
c. x + 4y = 8 and y = -1/4x + 2
System of equations y = 5x + 11 and y = 5x has no solution, y = 6x + 3 and y = 3x has one solution and x + 4y = 8 and y = -1/4x + 2 no solution.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
The given system of equations are
a. y = 5x + 11 and y = 5x
Substitute the y value in first equation
5x=5x+11
So the system of equations y = 5x + 11 and y = 5x has no solution.
b. y = 6x + 3 and y = 3x
Substitute the y value in first equation
3x=6x+3
-3x=3
x=-1
y=-3
The system of equations has one solution
c. x + 4y = 8 and y = -1/4x + 2
x+4(-1/4x + 2)=8
x-x+2=8
The system of equations has one solution has no solution
Hence, system of equations y = 5x + 11 and y = 5x has no solution, y = 6x + 3 and y = 3x has one solution and x + 4y = 8 and y = -1/4x + 2 no solution.
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Hexagon DEFGHI is translated on the coordinate plane below to create hexagon D′E′F′G′H′I′: Hexagon DEFGHI and Hexagon D prime E prime F prime G prime H prime I prime on the coordinate plane with ordered pairs at D 2, 5, at E 5, 5, at F 6, 3, at G 5, 1, at H 2, 1, at I 1, 3, at D prime negative 6, negative 2, at E prime negative 3, negative 2, at F prime negative 2, negative 4, at G prime negative 3, negative 6, at H prime negative 6, negative 6, at I prime negative 7, negative 4
Answer: To find the image of a figure under a translation, you need to apply the same translation to every point in the figure.
In this case, the image of hexagon DEFGHI is hexagon D′E′F′G′H′I′. To find the image of each point, you can apply the translation that maps point D to point D′.
For example, to find the image of point E under the translation, you can apply the same translation that maps point D to point D′:
Point D is located at (2, 5).
Point D′ is located at (-6, -2).
The translation that maps point D to point D′ is a translation 6 units to the left and 2 units down.
To find the image of point E under this translation, you can apply the same translation to point E:
Point E is located at (5, 5).
The image of point E is located at (5 - 6, 5 - 2) = (-1, 3).
You can follow the same process to find the images of the other points under the translation.
Alternatively, you can use the coordinates of point D and point D′ to find the translation vector that describes the translation. The translation vector is a displacement that describes the change in position of a point under the translation.
In this case, the translation vector is given by the displacement from point D to point D′:
Point D is located at (2, 5).
Point D′ is located at (-6, -2).
The translation vector is given by the displacement (-6 - 2, -2 - 5) = (-8, -7).
To find the image of any point under the translation, you can add the translation vector to the coordinates of the point. For example, to find the image of point E under the translation, you can add the translation vector to the coordinates of point E:
Point E is located at (5, 5).
The translation vector is (-8, -7).
The image of point E is located at (5 - 8, 5 - 7) = (-3, -2).
You can follow the same process to find the images of the other points under the translation.
Step-by-step explanation:
Claudia is making a gelatin dessert for a party. She plans on making 12 servings for every 5 people. If each pan Claudia uses to make the dessert holds 8 servings, what is the minimum number of these pans that she needs in order to make enough to feed 10 people?
Answer:
She would need a minimum of 15 pans for 10 people
Step-by-step explanation:
12(5) = 60 12(10) = 120
8(?) = 120
120/8 = 15
Use the given data to find the equation of the regression line. Round the final values to three significant digits, if necessary. Ten students in a graduate program were randomly selected. Their grade point averages (GPAs) when they entered the program were between 3.5 and 4.0. The following data were obtained regarding their GPAs on entering the program versus their current GPAs.Use the given data to find the equation of the regression line. Round the final values to three significant digits, if necessary.Ten students in a graduate program were randomly selected. Their grade point averages (GPAs) when they entered the program were between 3.5 and 4.0. The following data were obtained regarding their GPAs on entering the program versus their current GPAs.
Entering GPA Current GPA
3.5 3.6
3.8 3.7
3.6 3.9
3.6 3.6
3.5 3.9
3.9 3.8
4.0 3.7
3.9 3.9
3.5 3.8
3.7 4.0
Answer: y=3.67+0.313x
Step-by-step explanation:
I just took the test. Good luck, future hustlers.
2,082 divided 694
What is the value of the expression?
Answer:
3
Step-by-step explanation:
2,082/694 = 3
Answer:
3
Step-by-step explanation:
2,082/694 = 3
please help!!!!!!!!!!!
Answer:
50 weeks
Step-by-step explanation:
Which pair represents opposite numbers?
Answer:
Choice B 2 and -2
Step-by-step explanation:
2 would be opposite of -2
Mark brainliest
A bomber aircraft on take-off carries twelve dozen bombs, each weighing ten kilos; the aircraft takes off for Warsaw, the international center of Jews. It bombs the town. On take-off with all the bombs on board and a fuel tank containing 1000 kilos of fuel, the aircraft weighed about eight tons. When it returns from the crusade, there are still 230 kilos of fuel left. What is the weight of the aircraft when empty?
Answer:
The aircraft when empty weighs 4,817.48 kilograms.
Step-by-step explanation:
Since a bomber aircraft on take-off carries twelve dozen bombs, each weighing ten kilos; and the aircraft takes off for Warsaw, the international center of Jews bombing the town, and on take-off with all the bombs on board and a fuel tank containing 1000 kilos of fuel, the aircraft weighed about eight tons, while when it returns from the crusade, there are still 230 kilos of fuel left, to determine what is the weight of the aircraft when empty, the following calculation must be performed:
1 ton = 907.185 kg
8 x 907.185 = 7,257.48
7,257.48 - (12x12x10) - 1000 = X
7,257.48 - 1,440 - 1000 = X
7,257.48 - 2,440 = X
4,817.48 = X
Therefore, the aircraft when empty weighs 4,817.48 kilograms.
What is the Slope of x-y=6?
I WILL MARK BRAINLIEST
What is the shape of the cross section of the figure that is perpendicular to the rectangular base and passes through the top vertex of the figure?
A rectangular pyramid.
a parallelogram that is not a rectangle
a rectangle
a triangle that must have the same dimensions as one of the faces
a triangle that does not have the same dimensions as one of the faces
Answer:
it would be a rectangular pyramid
PLEASE HELP ME ILL MARK YOU AS A Brainiest
Answer:
Hey do you have a more clear picture
Step-by-step explanation:
I will be able to help if you have a better picture
Hot dogs and corndogs were sold at last night's football game. A total of 81 were sold which allowed the concession stand to bring in $201. How many of each were sold?
The total number of corn dogs sold is 28 corn dogs and number of hotdogs is 53
What is total cost?Total cost is the overall expense incurred for a particular product, service, or project. It includes both fixed and variable costs, such as materials, labor, and overhead. It is often used in business and economic analysis as a measure of the efficiency and profitability of a particular venture. The total cost of a product or service can also be used to set prices and make pricing decisions.
According to question:-
step1
h = number of hotdogs
c = number of corndogs.
cost of hotdog = $3
corn dog = $1.50
The equation:
3h + 1.50c = 201 (1)
h = 2c - 3 (2)
step2
substitute (2) into (1)
3(2c - 3) + 1.50c = 201
6c - 9 + 1.50c = 201
7.50c - 9 = 201
7.50c = 201 + 9
7.50c = 210
c = 210/7.50
c = 28
Therefore,
h = 2c - 3
= 2(28) - 3
= 56 - 3
= 53
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If you were to deposit 2000 in an account that earns simple interest of 3.5% per year, how much would the account be worth in 50 years
Answer:the interest would be $3,500
Step-by-step explanation: you have to multiply all of the numbers together but change the 3.5% to a decimal of 0.035
Of the first 14 people to enter a department store, 9 were carrying a purse. If there are now 56 people in the department store, how many do you expect to not be carrying a purse?
please help me !!!
Answer:
36 estimated amount of people
Hope this helps!!!! Love the pig pic btw ^-^
Ling wants to determine the average distance she travels each day in her car. She records the odometer reading, which measures the distance the car has traveled, each morning for a week. What is the mean distance Ling travels each day? Show your work.( Will Mark Brainliest if answer is correct)
Answer: [tex]10,724.28[/tex]
Step-by-step explanation:
Given
Distance traveled on each consecutive day is given as
[tex]10150,10211,10424,10769,10884,11155,11477[/tex]
Mean is given by the sum of the observations divided by the total no of observations.
There are 7 observations in total, so the mean is
[tex]\Rightarrow \mu =\dfrac{10150+10211+10424+10769+10884+11155+11477}{7}\\\\\Rightarrow \mu=\dfrac{75,070}{7}\\\\\Rightarrow \mu =10,724.28[/tex]
thus, the mean is [tex]10,724.28[/tex]
The mean distance Ling travels each day is [tex]10724.28 \: \rm miles[/tex] approximately.
How to find the mean value of a data set?The mean value of the data set is the ratio of sum of data set's values to number of values it has.
If the data set consists of values [tex]x_1, x_2, ..., x_n[/tex], then we get the mean value as:
[tex]\overline{x} = \dfrac{x_1 + x_2 + \cdots + x_n}{n}[/tex]
For this case, we have to find the average distance(in miles) from the distance Ling traveled for 7 days.
Thus, we get the average distance he traveled as:
[tex]\overline{d} = \dfrac{10150 + 10211 + 10424 + 10769 + 10884 + 11155 + 11477 }{7}\\\\\overline{d} = \dfrac{75070}{7} \approx 10724.28 \: \rm miles[/tex]
Thus, the mean distance Ling travels each day is [tex]10724.28 \: \rm miles[/tex] approximately.
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Find the area of the figure below. Round answer to nearest tenth.
Answer:
[tex] \approx \: 198.1 \: {cm}^{2} [/tex]
Step-by-step explanation:
Given figure consists of a parallelogram and two semicircles with diameters 14 cm and 8 cm
(Opposite sides of a parallelogram are equal in measure and they are the diameters of the semicircles)
Therefore,
Area of the figure = Area of the parallelogram with base 8 cm and height 12 cm + Area of semicircle with radius (14/2 = 7) 7 cm + Area of the semicircle with radius (8/2 =4) 4 cm
[tex] = b \times h + \frac{1}{2} \times \pi {(7)}^{2} + \frac{1}{2} \times \pi {(4)}^{2} \\ \\ = 8 \times 12 + \frac{1}{2} \pi(49 + 16) \\ \\ = 96 + \frac{1}{2} \times 3.14 \times 65 \\ \\ = 96 + 102.05 \\ \\ = 198.05 \\ \\ \approx \: 198.1 \: {cm}^{2} [/tex]
A cylindrical tank has a diameter of 30m and height 20m.
a) Find its volume in m³, correct to two decimal places.
b) What is the capacity of the tank in litres?
Step-by-step explanation:
d = 30m, so r = 15m
h = 20m
We know,
V = πr^2h= (22×15×15×20)/7 [Taking π = 22/7]
= 14142.86m^3
= 14142875.14 litres
Find the value of X. Round your answer to the nearest tenth.
Answer:
60°
Step-by-step explanation:
check the above attachment to verify the answer.
Which is the graph of the inequality p≤-6(5-1)?
Answer:
C) -24 and shaded circle
Step-by-step explanation:
You can simplify -6(5 - 1) by distributing -6, which would be -30 + 6. Then, you can add the numbers up to get -24. The inequality can be written as p ≤ −24.
Please explain if possible, thank you!
a recipe says 4 cups of flour makes up to 280 mini cupcakes. If you want to make 120 mini cupcakes how many cups of flower do you need?
If the polynomials p(x)=2x³ +bx² +3x-5 and q(x)= x³+x² -4x-b leave the same remainder, when divided by x-2, prove that b = -13/5.
Step-by-step explanation:
Lets first find the remainder when p(x) is divided by x-2
p(2)=2(2)³+b(2)²+3(2)-5
p(2)=16+4b+6-5
p(2)=4b+17
Now let's find the remainder when q(x) is divided by x-2
q(2)=(2)³+(2)²-4(2)-b
q(2)=8+4-8-b
q(2)=4-b
Now let's equate both of them
4b+17=4-b
4b+b=4-17
5b=-13
b=-13/5 as required
Fatheya and Fatema, along with 30 other people, sign up to audition for a talent show. Contestants are called at random to perform for the judges. What is the probability that Fatheya will be called to perform first and Fatema will be called second?
So there's 30 people or slots. The odds that Fatheya will be chosen to perform first is 1/30. But now there's one less slot.
Now with Fatema, there's 29 slots, so there's a 1/29 chance. Then combine these values by multiplying them:
1/30 * 1/29 = 1/870
All done!
Question 3
Use the quadratic formula to complete the table. To verify your solutions, graph the equations.
BIU X² X₂ 10pt
Help !!!
The linear equation in this case is . The [tex]$3 x^2+4 x+4=0$[/tex] answer is [tex]x=-\frac{2}{3}+i \frac{2 \sqrt{2}}{3}, x=-\frac{2}{3}-i \frac{2 \sqrt{2}}{3}[/tex] and [tex]$3 y^2+2 x+4=0: \quad$[/tex]: quadratic [tex](h, k)=(-2,0), p=-\frac {1} {6}[/tex] , is the solution.
What do you meant by quadratic equation ?[tex]$3 x^2+4 x+4=0 \quad: \quad x=-\frac{2}{3}+i \frac{2 \sqrt{2}}{3}, x=-\frac{2}{3}-i \frac{2 \sqrt{2}}{3}$[/tex]
[tex]$3 x^2+4 x+4=0$[/tex]
Apply the quadratic formula to the problem. [tex]$x_{1,2}=\frac{-4 \pm \sqrt{4^2-4 \cdot 3 \cdot 4}}{2 \cdot 3}$[/tex]
Simplify [tex]$\sqrt{4^2-4 \cdot 3 \cdot 4}: \quad 4 \sqrt{2} i$\\[/tex]
[tex]$x_{1,2}=\frac{-4 \pm 4 \sqrt{2} i}{2 \cdot 3}$[/tex]
Distinguish the answers
[tex]x_1=\frac{-4+4 \sqrt{2} i}{2 \cdot 3}, x_2=\frac{-4-4 \sqrt{2} i}{2 \cdot 3}\\x=\frac{-4+4 \sqrt{2} i}{2 \cdot 3}: \quad-\frac{2}{3}+i \frac{2 \sqrt{2}}{3}\\x=\frac{-4-4 \sqrt{2} i}{2 \cdot 3}: \quad-\frac{2}{3}-i \frac{2 \sqrt{2}}{3}[/tex]
The following are the quadratic equation's solutions:
[tex]x=-\frac{2}{3}+i \frac{2 \sqrt{2}}{3}, x=-\frac{2}{3}-i \frac{2 \sqrt{2}}{3}[/tex]
2) [tex]$3 y^2+2 x+4=0: \quad$[/tex] A parabola with a focal length of and a vertex at (h,k)=(-2, 0) [tex]$|p|=\frac{1}{6}$[/tex]
[tex]$3 y^2+2 x+4=0$[/tex]
[tex]$4 p(x-h)=(y-k)^2$[/tex] is the common formula for a right-to-left parabola with a vertex at (h, k) and a focal length of |p|.
Rewrite [tex]$3 y^2+2 x+4=0$[/tex] using the proper form: [tex]$4\left(-\frac{1}{6}\right)(x-(-2))=(y-0)^2$[/tex]
The following are characteristics of parabolas:
[tex](h, k)=(-2,0), p=-\frac {1} {6}[/tex]
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Which segment is parallel
Justify the answer with a converse theorem
Answer:
Ah and mc are parallel segments
The function y = f(x) is graphed below. What is the average rate of change of the function f(x) on the interval -5 < x < -4?
Under the < is a _ thing
Answer: “Rate of change” just means “slope”. All of calculus is just ways to find the slope for curves. Find y at -5 and at -4 and calculate the slope.
Step-by-step explanation:
Pls help I need this I’m begging you
Answer:
Option H
Step-by-step explanation:
y = 3x - 4
this is the correct answer.
Answer:
H- y=3x-4
The reason I answered this is because the equations are in slope-intercept format (y=mx+b), the slope(m), is 3. The y intercept(b) is -4. Hope this helped :)
m3 - 8m + 2 cuando m = -5
Answer:
-5*3 -8*-5 +2= -15 +40 +2= 27A rectangular prism has a length of 6 cm, a width of 3 cm, and a height of 4 cm. The prism is filled with cubes that have edge lengths of į cm. How many cubes are needed to fill the rectangular prism?
Answer:
I think 72 would be the answer