Answers
Lets try one way to solve this system. First, we want to isolate one of the unkown, lets choose y, so we need to remove x from an equation. In order to remove x from an equation, thats what we are going to do :
Line 1:
(3x² - 5y²) * 2 = 22 * 2
6x² - 10y² = 44
We simply multiplied Line 1 by the number 2, this doesn't change anything on the nature of Line 1.
Line 2:
(2x² + 4y²)*3 = 22*3
6x² + 12y² = 66
We simply multiplied Line 2 by the number 3, this doesn't change anything on the nature of Line 2.
Solving your system of equations is exactly the same thing as solving this new system of equation :
6x² - 10y² = 44
6x² + 12y² = 66
It is exactly the same. But it is easier now, because we can remove x from the equation simply by subtracting line 2 from line 1 :
L1 - L2 :
(6x² - 10y²) - (6x² + 12y²) = 44 - 66
6x² - 10y² - 6x² - 12y² = - 22
- 22y² = - 22
y² = 1
y = + 1 or y = - 1
We know have the value of y, we just have to replace it in the equation to solve the entire system :)
3x² - 5y² = 22
since y² will always be equal to one, wether y = 1 or y = - 1, we can write :
3x² - 5 = 22
3x² = 22 + 5
3x² = 27
x² = 27/3
x² = 9
x = + 3 or x = - 3
So the solutions are the following couples in the form (x,y) :
S = { (3 ; 1) , (-3;1) , (3 ; - 1) , (-3 ; -1))
Good Luck
Related Questions
why (0.0) (3.4) (6.8) (6,12) not a function
Answers
Answer:
Step-by-step explanation:
Look at the first elements of the four points: {0, 3, 6, 6}. The element 6 appears twice and is associated with two different second elements: {8, 12}. That tells us immediately that this is not a function.
10, 18, 26, 34, 42, ...
What is the 15th term of this Arithmetic Sequence
Answers
Answer:
a₁₅ = 122
Step-by-step explanation:
Arithmetic sequence formula:
[tex]a_n=a_1+(n-1)d[/tex]
where aₙ is the nth term, a₁ is the first term, n is the index, and d is the rate of change.
For your given sequence:
[tex]10, 18, 26,34,42,...[/tex]
a₁ is 10
n is 15 (15th term)
d is 8 (each term increases by 8 over the last)
Plug those 3 variables in, and solve for a₁₅:
[tex]a_n=a_1+(n-1)d\\a_1_5=10+(15-1)8\\a_1_5=10+(14)8\\a_1_5=10+112\\a_1_5=122[/tex]
x3+y3+z3=k What does this equation mean please?
Answers
Answer:
Sum of cubes problem
Step-by-step explanation:
The equation x3+y3+z3=k is sum of cubes problem. While seemingly straightforward, the equation becomes exponentially difficult to solve when framed as a "Diophantine equation" a problem that stipulates that, for any value of k, the values for x, y, and z must each be whole numbers.
Answer:
it means x to the third power, plus y to the third power, plus z to the third power, equals some number (k).
Step-by-step explanation:
7x-15y=2 , x+2y=3 By subtition method
Answers
Answer:
([tex]\frac{49}{29},\frac{19}{29}[/tex])
Explanation:
7x - 15y = 2 (1)
x + 2y = 3 (2)
x + 2y = 3
x + 2y - 2y = 3 - 2y
x = 3 - 2y (3)
Substitute (3) to (1)
7x - 15y = 2
7(3 - 2y) - 15y = 2
21 - 14y -15y = 2
21 - 21 - 29y = 2 - 21
-29y = -19
y = [tex]\frac{19}{29}[/tex] (4)
Plug (4) into (2)
x + 2y = 3
x + 2[tex]\frac{19}{29}[/tex] = 3
x + [tex]\frac{38}{29}[/tex] = 3
x = 3 - [tex]\frac{38}{29}[/tex]
[tex]x = \frac{87}{29}-\frac{38}{29} =\frac{49}{29}[/tex]
([tex]\frac{49}{29},\frac{19}{29}[/tex])
Suzanne has 15 books and will buy 3 more each month. Jack has 57 books and will sell 4 books each month. After how many months will they have the same number of books? How many will that be?
Answers
They would both have the same number of books after 6 months.
The number of books they would have is 33.
This expression can be used to determine the number of books Suzanne would have after x months: 15 + 3x
This expression can be used to determine the number of books Jack would have after x months: 57 - 4x
In order to determine the month in which both people would have the same number of books, equate both expressions.
15 + 3x = 57 - 4x
Combine similar terms
3x + 4x = 57 - 15
7x = 42
Divide both sides b y 7
x = 6
Number of books they would have : 15 + 3(6) = 15 + 18 = 33
A similar question was answered here: https://brainly.com/question/21014980?referrer=searchResults
ben bolwed 138 and 208 in his first two games. What must he bowl in his third game to have an average of at least 170?
Answers
Answer:
at least 164
Step-by-step explanation:
Let the third score = x.
(138 + 208 + x)/3 ≥ 170
x + 346 ≥ 510
x ≥ 164
Answer: at least 164
Solve and graph each of the following. Show your work to receive full credit.5x – 6 – 8x ≤ 9
Answers
Answer: x> or equal to -5
Step-by-step explanation:
5x – 6 – 8x ≤ 9
Combine the lioe numbers
-3x-6≤ 9
+6 to both sides
-3x≤ 15
Divide by a -3 to both sides
X>or equal to -5
Hope that helps
List three negative numbers that are greater than - 9
Answers
Answer:
the answer to your question is -6 -5 -3 but there are more.
Answer:
there are infinite but you can take any numbers from the right one that are
-8,-7,-6,-5,-4,-3,-2,-1,0,1,2....
help with my math plz
Answers
Answer:
Step-by-step explanation:
The side is S= 5 cm , and the area is A= S² = 5²= 25
If the side would be doubled will be S= 5*2 = 10 cm, and the area A= 10²=100
Compare the area of S=5 to area of S=10 , 100 = 4*25
Conclusion:
If we double the side the area is 4 times greater.
1. £1000 is invested for 2 years at 5% per annum with compound interest. Work out the total amount in the account after 2 years.
Answers
Answer:
A = £1102.50
Step-by-step explanation:
Use the compound amount formula:
A = P(1 + r)^t, where P is the principal, r is the interest rate as a decimal fraction, and t is the number of years.
Here A = £1000·(1 + 0.05)^2, which evaluates to A = £1102.50
A backback originally costs $35 it is on sale for $22.75 find the percent of decrese
Answers
Answer $12.25
Step-by-step explanation: edmentum
Î"RST was _____________, then dilated, to create Î"ZXY. Rotated reflected translated dilated.
Answers
Answer:
5
Step-by-step explanation:
Yall i need help asap! please help
Answers
3) 1010000
4) 1582
I helped
plssss help picture down below
Answers
Answer:
it is (-4,1)
Step-by-step explanation:
Hope this helps:)
Use substitution to solve the system of equations algebraically.
x² + y² = 32
y = x
One solution to the system of equations is (4,4).
The other solution to the system of equations is
Answers
Answer:
(-4,-4)
Step-by-step explanation:
Since y=x,plug in x for y in equation 2
x²+x²=32
2x²=32
x²=16
x=√16=±4
So one solution is (4,4) and another is (-4,-4)
Answer:
i really cant tell you
Step-by-step explanation:
sorry
Please give me the answer
Answers
Answer:
8%
If you need the work comment on this post.
Graph a right triangle with the two points forming the hypothenuse, Using the sides, find the distance between the two points, to the nearest tenth if necessary (3. -7) and 8. -3)
Answers
Answer:
That distance is 6.4
Step-by-step explanation:
The legs of the triangle form a right angle. The bottom leg has length 8 - 3, or 5, and the vertical leg -3 - (-7), or 4. Applying the Pythagorean Theorem:
(vertical leg)^2 + (horizontal leg)^2 = (hypotenuse)^2, which here is
4^2 + 5^2 = (hypotenuse)^2
This works out to 16 + 25, or 41.
The distance between these two points is d = √41, or d = 6.4
What is the slope of the line ( part 2 )
Answers
Answer:
[tex]m=-\frac{1}{2}[/tex]
Step-by-step explanation:
Same as last time, take any 2 points you want:
(0, 3) and (4, 1)
Use the slope formula to calculate the slope:
[tex]m=\frac{1-3}{4-0}\\m=\frac{-2}{4}\\m=-\frac{1}{2}[/tex]
On small problems like these, you don't really even need to calculate it like that. You can just look at the graph, see that it goes down 1 and over 2 from one point to the next, and have your slope that way. Again, rise over run. It "rises" by -1, and runs by 2. -1 over 2, there's your slope.
what is the product of... see attachment below
Answers
The answer is -7 (option A)
Steps are in the attachment.
_________
Hope it helps ✌
Find the unit rate.
12 laps in 30minutes
Answers
Answer:
0.4/1
Step-by-step explanation:
We want a unit rate where
1 is in the denominator,
so we divide top and bottom by 30
what is 3 x 7 = x 3 ?
Answers
Answer:
7
Step-by-step explanation:
21=3x
x=7
Answer:
x = 7
Step-by-step explanation:
3 x 7 = x 3
21 = 3x
x = 21/3 = 7
Type the expression that results from the following series of steps:
Start with z and add 5.
Answers
Annelise buys a car that is one year old for $13600.
The value of this car has reduced by 15% of the value when it was new.
Calculate the value of the car when it was new.
Answers
Answer:
$16000Step-by-step explanation:
Initial value is x, current value is $13600, price reduction by 15%.
x - 15% = 13600x - 0.15x = 136000.85x = 13600x = 13600/0.85x = 16000Use the distributive property to
expand the expression below.
6(2a – 3) = [?]a - [ ]
Answers
Answer:
12a - 18
Step-by-step explanation:
6 x 2 = 12 (then add the "a" = 12a
6 x 3 = 18
put the minus in the middle then get
12a- 18
1 dm = _______ cm what answer of this
Answers
Answer:
1dm = 10cm
Simple as it is
Answer:
The term “Deci” means one-tenth, and therefore decimetre means one-tenth of a meter. Since a meter is made up of 100 cm, one-tenth of 100 cm is 10 cm. Thus one decimeter measures 10 cm.
Step-by-step explanation:
hope it's help!
#letusstudy
#Staysafe!
#brainly
-4x + 60 < 72 or 14x + < -31
Answers
x=31/14
Step-by-step explanation:
I did the second one btw
(−4/3)⋅(−1/3)⋅1.2 answer plz
Answers
Answer:
= .533
Step-by-step explanation:
(−4/3)•(−1/3)= .44
.44•1.2=.533
On a coordinate plane,△FGH is formed with the vertices at point F(0,−2), point G(1,0) , and point H(2,−3) . Which expression can be used to determine the perimeter, in units, of△FGH ?
A
(0−1)2+(−2−0)2−−−−−−−−−−−−−−−−√+(1−2)2+(0−(−3))2−−−−−−−−−−−−−−−−−−√+(2−0)2+(−3−(−2))2−−−−−−−−−−−−−−−−−−−√
B
(0−(−2))2+(1−0)2−−−−−−−−−−−−−−−−−−√+(1−0)2+(2−(−3))2−−−−−−−−−−−−−−−−−−√+(2−(−3))2+(0−(−2))2−−−−−−−−−−−−−−−−−−−−−√
C
(0+1)2−(−2+0)2−−−−−−−−−−−−−−−−√−(1+2)2−(0+(−3))2−−−−−−−−−−−−−−−−−−√−(2+0)2−(−3+(−2))2−−−−−−−−−−−−−−−−−−−√
D
(0+(−2))2−(1+0)2−−−−−−−−−−−−−−−−−−√+(1+0)2−(2+(−3))2−−−−−−−−−−−−−−−−−−√+(2+(−3))2−(0+(−2))2−−−−−−−−−−−−−−−−−−−−−√
Answers
Answer:
the answer i think is B
Step-by-step explanation:
Answer: B
Step-by-step explanation:
THEN c. If a || band line c is parallel to line a, then line b and c are?
Answers
Answer: parallel
Step-by-step explanation:
For two lines to be parallel they must have the same slope.
Because a is parallel to b they must have the same slope. Let's call that slope x.
Because c is parallel to b they must have the same slope. Because the slope of b is x, the slope of c must be x.
Because the slope of both a and c are x, they must be parallel.
does anyone know what the answers are to this question? thank you sm if you help!! :)
Answers
v’ should be equal to 4
I’m not exactly sure but please do feel free to correct any mistakes I made.