A system equation is-
[tex]\bf\begin{cases} & \bf x^4y^5+x^5y^4=810 \\ & \bf x^6y^3+x^3y^6=945 \end{cases}[/tex]
Solve for real x and y .
How to solve it? Please explain. The question is correct.
![A System Equation Is-[tex]\bf\begin{cases} & \bf X^4y^5+x^5y^4=810 \\ & \bf X^6y^3+x^3y^6=945](https://brainimage.s3.us-east-005.backblazeb2.com/contents/attachments/GFq0rvErL8cKD4pvNU6mODAKMM7eadYF.jpeg)
Answers
Answer:
Solution:Given that,
x⁴y⁵ + x⁵y⁴ = 810
➝ x⁴y⁴(x+y) = 810 ---(1)
[tex] \: [/tex]
Further given that,
x⁶y³ + x³y⁶ = 945
x³y³(x³y³) = 945
[tex] \: [/tex]
We know,
[tex] { \boxed{{x}^{3} + {y}^{3} = (x + y)( {x}^{2} - xy + {y}^{2}) }}[/tex]
So, using this identity, we get,
➝ x³y³( x + y )( x² - xy + y²) = 945
---(2)
[tex] \: [/tex]
On dividing equation (1) and (2), we get,
[tex] \longrightarrow\frac{ {x}^{2} - xy + {y}^{2} }{xy} = \frac{945}{810} [/tex]
[tex] \longrightarrow \: \frac{ {x}^{2} + {y}^{2} }{xy} - 1 = \frac{7}{6} [/tex]
[tex] \longrightarrow \: \frac{ {x}^{2} + {y}^{2} }{xy} = \frac{7}{6} + 1[/tex]
[tex] \longrightarrow \: \frac{ {x}^{2} + {y}^{2} }{xy} = \frac{7 + 6}{6} [/tex]
[tex] \longrightarrow \: \frac{ {x}^{2} + {y}^{2} }{xy} = \frac{13}{6} [/tex]
[tex] \: [/tex]
➝ 6x² + 6y² = 13xy
➝ 6x² - 13xy + 6y² = 0
➝ 6x² - 4xy - 9xy + 6y² = 0
➝ 2x( 3x - 2y ) - 3y( 3x - 2y ) = 0
➝ ( 3x - 2y ) ( 2x - 3y ) = 0
[tex] \longrightarrow \:{ \bold{ x = \frac{3y}{2} \: \: \: or \: \: x = \frac{2y}{3} }}[/tex]
[tex] \: [/tex]
[tex] \: [/tex]
[tex]{ \underline {\underline {\red{Case:- 1 }}}}[/tex]
[tex]{ \bold{When \: x = \frac{3y}{2}}} [/tex]
In Substating the value of x in equation (1) we get,
[tex] \frac{81 {y}^{4} }{16} \times {y}^{4} \times ( \frac{3y}{2} + y) = 810[/tex]
[tex] \frac{ {y}^{8} }{16} \times ( \frac{5y}{2} ) = 10[/tex]
[tex] {y}^{9} = 64[/tex]
[tex] {y}^{9} = {2}^{6} [/tex]
[tex] \: [/tex]
[tex] \longrightarrow \: { \bold{y = {(2)}^{ \frac{2}{3} } }}[/tex]
[tex] \longrightarrow \: { \bold{x = \frac{3}{2} {(2)}^{ \frac{2}{3} } }}[/tex]
[tex] \: [/tex]
[tex] \: [/tex]
[tex]{ \underline {\underline {\red{Case:- 2}}}}[/tex]
[tex]{ \bold{When \: x \: = \frac{2y}{3} \rightarrow \: \: y = \frac{3x}{2} }}[/tex]
On Substituting the value of y in equation (2), we get,
[tex] \frac{81 {x}^{4} }{16} \times {x}^{4} \times ( \frac{3x}{2} + x) = 810[/tex]
[tex] \frac{ {x}^{8} }{16} \times ( \frac{5x}{2} ) = 10[/tex]
[tex] {x}^{9} = 64[/tex]
[tex] {x}^{9} = {2}^{6} [/tex]
[tex] \: [/tex]
[tex] \longrightarrow \: { \bold{x \: = {(2)}^{ \frac{2}{3} } }}[/tex]
[tex] \longrightarrow \: { \bold{y = \frac{3}{2} {(2)}^{ \frac{2}{3} } }}[/tex]
Related Questions
An auto repair shop charged a customer $356 to repair a car. The bill listed $56 for parts and the remainder for labor. If the cost of labor is $50 per hour, how many hours of labor did it take to repair the car?
Answers
Answer:
6 hours
Step-by-step explanation:
356-56
=300
300/50
=6
bobby's cat runs x mph. bobby's dog runs twice as fast as his cat. if the cat and the dog start running away from each other, how far away from each other will they be after 30 minutes
Answers
Answer:
They will be 0.5x miles away from each other.
Calculation of the distance:
Since Bobby's cat runs x mph. Bobby's dog runs twice as fast as his cat.
So here the speed of the dog should be 2x
Now we know that
Here distance of cat should be x of 30 minutes or half hour = 0.5x miles
And, Distance of dog should be 2x of 0.5 = x miles
So, the difference should be
= x - 0.5
= 0.5x miles
hence, They will be 0.5x miles away from each other.
Step-by-step explanation:
Answer:
1.5x miles, because you already know that the cat's speed is 0.5x miles, and the dog is x miles, so when you add it together, you get 1.5x miles
HELP ASAP THIS IS ABOUT “Multistep Pythagorean Theorem” HELP
Answers
Answer:
8.1
Step-by-step explanation:
The length of the missing side is 8.1 inches. You apply the pythagorean theorem to 5,b,10 and get 5sqrt3. Next, you apply the pythagorean theorem to 3, b, 5sqrt3 to get the square root of 66, which is 8.1, rounded to the nearest tenth.
Answer:
[tex]\displaystyle 8,1[/tex]
Step-by-step explanation:
Use the Pythagorean Theorem twise [first time for the reflexive edge and the second time for the longer leg of the other triangle]:
[tex]\displaystyle a^2 + b^2 = c^2 \\ \\ a^2 + 5^2 = 10^2 \hookrightarrow 100 = 25 + a^2 \hookrightarrow \sqrt{75} = \sqrt{x^2}; 5\sqrt{3}\:[or\:8,6602540378...] = a \\ \\ \\ \\ a^2 + b^2 = c^2 \\ \\ x^2 + 3^2 = 5\sqrt{3}^2 \hookrightarrow 75 = 9 + x^2 \hookrightarrow \sqrt{66} = \sqrt{x^2}; \sqrt{66}\:[or\:8,1240384046...] = x \\ \\ \boxed{\boxed{8,1 \approx x}}[/tex]
I am joyous to assist you at any time.
A DVD is regularly $19.99 but is on sale today for $15.99. What percent would you save if you bought the DVD on sale?
Answers
Answer:
the sale price will be 130% off
Step-by-step explanation:
Are they functions or not ?
Answers
Answer:
10.) b. not a function
11.) a. function
Step-by-step explanation:
hope it helps. good luck :)
Which statement below best applies to the following expression?
Answers
Answer:
A.
Step-by-step explanation:
Radical expressions can only be simplified if their radicands are identical.
a=-13y solve for y
This is all the question says so idk
Answers
Given h(x)=x2-2, what is the value of h(-3)?
Answers
h(x) = x^2 - 2
h(-3) = (-3)^2 - 2
= 9-2
= 7
Find the product of (4c-5)(7x^2m- 3x + 3)
Answers
Answer:
28cx2m−12cx+12c−35x2m+15x−15
Step-by-step explanation:
Find the range of the data. 133,117,152,127,168,000,000
Answers
Answer:
168
Step-by-step explanation:
168 would be the range because the range is the highest number - the lowest number so 168=highest and 000=lowest
so 168-000 or just0=168
here's some extra answers.
The mean=100 rounded up to nearest 100
Mean= the average of the data set.
Median=127
The median is the middle number when the numbers in the data set are sorted least to greatest.
Mode=000 or just 0
The mode is the number that appear the most in the data set and 000 or just 0 appears twice rather than,all the other numbers only appear once.
Minimum=000 or just
The minimum is the lowest number in the data set and as for this one is is 0.
Maximum=168
The maximum is the highest number and the data set and 168 is the highest in this one.
Hope it helps have a great day:)
Solve the system of equations by graphing. Check the solution. y=-2x-3. y=2x+5. Graph each equation on the same coordinate plane. At what point do the graphs of the lines appear to intersect?
Answers
Answer:
[tex]\left \{ {{x=-2} \atop {y=1}} \right.[/tex]
Step-by-step explanation:
[tex]\left \{ {{y=-2x-3} \atop {y=2x+5}} \right.[/tex]
Substitute into one of the equations
[tex]-2x-3=2x+5[/tex]
Rearrange variables to the left side of the equation
[tex]-2x-2x=5+3[/tex]
Combine like terms
[tex]-4x=5+3[/tex]
Calculate the sum or difference
[tex]-4x=8[/tex]
Divide both sides of the equation by the coefficient of variable
[tex]x=-\frac{8}{4}[/tex]
Cross out the common factor
[tex]x=-2[/tex]
Substitute into one of the equations
[tex]y=-2\times\left(-2\right)-3[/tex]
Calculate
[tex]y=1[/tex]
The solution of the system is
[tex]\left \{ {{x=-2} \atop {y=1}} \right.[/tex]
I hope this helps you! Don't forget to check the picture I uploaded as well
:)
Answer:
[tex]\displaystyle [-2, 1][/tex]
Step-by-step explanation:
Use the Elimination method sinse both coefficients in the system are OPPOCITES:
[tex]\displaystyle \left \{{{y = -2x - 3} \atop {y = 2x + 5}} \right.[/tex]
2y = 2; 1 = y [Plug this y-coordinate back into the system to get the x-coordinate of −2 (−2 = x).]
I am joyous to assist you at any time.
Find the missing side lengths. Leave your answers as radicals in simpler form. Please explain it
Answers
Answer:
Step-by-step explanation:
CAN SOMEONE HELP ME OUT PLEASE AND THANK YOU
Answers
Answer:
10x+2
Step-by-step explanation:
2×(2x+1+3x)
4x+2+6x
10x+2
Answer:
10x + 2
Step-by-step explanation:
The perimeter is the sum of the 4 sides of the rectangle, where opposite sides are equal in measure, thus
perimeter = 3x + 3x + 2x + 1 + 2x + 1 = 10x + 2
Make
x
the subject of the formula
3
a
x
+
2
c
=
b
2
Answers
Answer:
x= (2b-2c)/3a
Step-by-step explanation:
3ax+2c=2b
or, 3ax= 2b-2c
Therefore, x= (2b-2c)/3a
If you claim a dependent and have to pay for child
care while you're at work, you can claim a tax credit of
$780. If you owed $5,638 in federal income taxes, how
much do you owe after claiming that credit?
Answers
Answer:
4858
Step-by-step explanation:
5,638-780=4,858
In a high school of 1000 students, 355 are playing sports and 233 are in a school band. If there are 175 students playing sports and are in a school band, how many are in neither activity?
Answers
Answer:
237
Step-by-step explanation:
1000 minus 355= 645
645 minus 233= 412
412 minus 175= 237
Answer:
237 students
Step-by-step explanation:
355 are playing sports
233 are in a school band.
175 in both
355 + 233 + 175 = 763
763 students are in sports, band or both
1000 - 763 = 237
237 students aren't participating in neither.
hope this helps :)
Please answer :) much appreciated
Answers
m=12
He received $12
what is the constant of posprtainality in the equation y=0.41
Answers
Answer:
The constant of proportionality in the equation y=0.41 is 0.41
Step-by-step explanation:
Need help with geometric series'!
Please include a step by step explanation.
Answers
Answer:
[tex] - 13107[/tex]
Step-by-step explanation:
We would like to evaluate the following Geometric Series ,
[tex]\displaystyle\longrightarrow \sum _{n=1}^8 (-4)^{n-1 }[/tex]
In a geometric series, a common number is multiplied to the previous term in order to find the next term . And that common number is called common ratio (r) .
As we know that ,
[tex]\displaystyle\longrightarrow \sum_{x = 1}^n f(x) = f(1) + f(2) + \dots + f(n) [/tex]
So , we can write the series as ,
[tex]\displaystyle\longrightarrow (-4)^{1-1}+(-4)^{2-1}+\dots +(-4)^{8-1} [/tex]
Simplify,
[tex]\displaystyle\longrightarrow (-4)^0 + (-4)^1+(-4)^2+\dots +(-4)^7 [/tex]
We can find the common ratio by dividing and successive term by its preceding term , as ;
[tex]\displaystyle\longrightarrow r =\dfrac{-4}{1}=-4 [/tex]
Again , here ;
First term = a = [tex](-4)^0=1[/tex]Common ratio = [tex]-4[/tex]number of terms (n) = 8And we can find the sum of geometric series using the formula , ( this is used when the value of r is less than 1 , here it is -4 ) .
[tex]\displaystyle\longrightarrow \Bigg[ Sum = \dfrac{a(1-r^n)}{1-r}\Bigg] [/tex]
where the symbols have their usual meaning.On substituting the respective values, we have;
[tex]\displaystyle \longrightarrow\rm{ Sum }=\dfrac{ 1\{1-(-4)^8\}}{1-(-4)}\\ [/tex]
Simplify ,
[tex]\displaystyle\longrightarrow \rm{Sum} = \dfrac{1-65536}{1+4}\\[/tex]
[tex]\displaystyle\longrightarrow \rm{Sum} = \dfrac{-65535}{5} [/tex]
Simplify by dividing ,
[tex]\displaystyle\longrightarrow \underline{\underline{ \rm{Sum} = -13107}} [/tex]
And we are done !
Convert 12/25 to percent
Answers
Answer:
48%
Step-by-step explanation: multiply 4 with the numerator and denominator
Use the grouping method to factor the polynomial below completely.
x3 + 2x2 + 5x + 10
O A. (x2 + 5)(x+5)
O B. (x2 + 5)(x+2)
O C. (x2 + 5)(x+5)
O D. (x2 + 5)(x+2)
Answers
Answer:
(x²+5)(x+2)
simple find the common factor between x³ and 2x² and the cf of 5x and 10
u will end up with these results then^
URGANT PLEASE HELP!!
Solve the triangle for x. (1 point)
A) 41.8°
B) 89.6°
C) 48.6°
D) 90.4°
Answers
Answer:
it looks like c
Step-by-step explanation:
its not quite 50 but its extreemly close so its got to be c
[tex]12 {}^{2} = 9 {}^{2} + 8 {}^{2} - 2(9)(8)(cosx)[/tex]
[tex]144 = 81 + 64 - 2(72)(cosx)[/tex]
[tex]144 = 145 - 144(cosx)[/tex]
[tex] - 144(cosx) = 144 - 145[/tex]
[tex](cosx) = \frac{ - 1}{ - 144} [/tex]
[tex]arccos( \frac{1}{144} ) = > a = 89.6[/tex]
Find the value of x.
(2x + 21)
54°
(5x + 6)
Answers
Answer:
x= 9.3 but im not to sure this is right
Step-by-step explanation:
(2x+21)+(5x+6)+90+54=360
7x + 171 = 360
7x = 360 - 171
7x = 189
Divide through by 7
x = 27
Note the other unnamed angle in the fig is 90 ° .The sign there is the conventional sign for angle 90 °
I will mark brainliest please help ASAP :)
the distance a car travels d, is a function of t the time it travels a certain car travels 425 miles at a speed of 50 miles per hour. What are the domain range of the function described?
The domain is all real values from 0 to 8.5 and the range is all real values from 0 to 50
The domain is all real values from 0 to 8.5 and the range is all real values from 0 to 425
The domain is all real values from 0 to 50 and the range is all real values from 0 to 425
The domain is all real values from 0 to 425 and the range is all real values from 0 to 8.5
Answers
The domain and range of the linear function described are given as follows:
The domain is all real values from 0 to 8.5 and the range is all real values from 0 to 425.
What is a linear function?A linear function is modeled by:
[tex]y = mx + b[/tex]
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0.In this problem, the car travels 425 miles at a speed of 50 miles per hour, hence for the amount of miles left for the car to travel after t hours is given by a linear function with m = -50 and b = 425, that is:
d(t) = 425 - 50t.
The domain is the set of all possible values of the input, which considering that the car travels while the distance is greater than 0, is given by:
d(t) > 0 -> 425 - 50t > 0 -> t < 8.5.
The range is the set of all possible values of the input, which is the distance remaining, assuming real values from 0 to 425.
Hence, the correct option is:
The domain is all real values from 0 to 8.5 and the range is all real values from 0 to 425.
More can be learned about linear functions at https://brainly.com/question/24808124
The volume of a cone is 1967 cubic feet. Its
radius is 7 feet. Find the height.
Answers
Answer:
38.33 feet.
Step-by-step explanation:
Answer: 38.33ft
Explanation: I looked it up :)
The diameter of a circle is 9 ft. Find the circumference and round it to the nearest tenth.
Answers
Answer:
9*3.14=28.26
Step-by-step explanation:
Hope this Helps!
Answer:
[tex]C\approx28.27ft[/tex]
Step-by-step explanation:
[tex]C=\pi d\\C=\pi(9)\\C=9\pi\\C\approx28.27[/tex]
Thus, your circumference is about 28.27 ft
What is the equation of the line that passes through the point (-1,-5) and has a
slope of -1?
Answers
explanation: put this in the form of y=mx+b form. m is the slope of the line so it’s -1. b is the y intercept so that means the answer must be -5 from the set of points you provided. hope that helps
Answer:
5 x - 6 y - 8 = 0
Step-by-step explanation:
Gm!!! everyone (who see's this)
Answers
Answer:
GOODMORNING!!!
Step-by-step explanation:
I pray you, have a wonderful day!!
Kilani and Adrian are starting a nutrition program. Kilani currently consumes 1200 calories a day and will increase that number by 100 calories each day. Adrian currently consumes 3230 calories a day and will decrease that number by 190 each day. They will continue this pattern until they are both consuming the same number of calories per day. In how many days will that be? Be sure to define your variables, write an equation, and answer the question in context.
Answers
Answer:
7 days
Step-by-step explanation:
Let us represent the number of days = a
Kilani currently consumes 1200 calories a day and will increase that number by 100 calories each day.
1200 calories + 100 calories × a
1200 + 100a
Adrian currently consumes 3230 calories a day and will decrease that number by 190 each day.
3230 calories - 190 calories × a
3230 - 190a
The number of days that they would be consuming the same number of calories =
Kilani = Adrian
1200 + 100a = 3230 - 190a
Collect like terms
190a + 100a = 3230 - 1200
290a = 2030
a = 2030/290
a = 7 days
Therefore, the would be consuming the same number of calories in 7 days
Which of these numbers is irrational?
O A. v3
OB. 0.25
O C. 1
O D. V9
Answers
Answer:
A
Step-by-step explanation:
the square root of 3 is an irrational number.