Answer:
x= -7
Step-by-step explanation:
Answer:
6x² – 10y² + 2xy + 10
Step-by-step explanation:
We'll begin calculating the sum of
x² + 3y² – 6xy and 2x² – y² + 8xy + 8
This can be obtained as follow:
... x² + 3y² – 6xy
+ 2x² – y² + 8xy + 8
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3x² – 2y² + 2xy + 8
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Next, we shall determine the sum of:
–3x² + 4y² + 3 and 4y² – 5
This can be obtained as follow:
–3x² + 4y² + 3
+ 4y² – 5
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–3x² + 8y² – 2
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Finally, we shall subtract the sum of:
–3x² + 4y² + 3 and 4y² – 5
from the sum of:
x² + 3y² – 6xy and 2x² – y² + 8xy + 8
This can be obtained as follow:
.. 3x² – 2y² + 2xy + 8
– (–3x² + 8y² – 2)
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
6x² – 10y² + 2xy + 10
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
Answer:
No
Step-by-step explanation:
Simplified ratios are not written in units.
The sequence is an arithmetic sequence with
a₁ = -4
d = a₂ - a₁
d = -1 - (-4)
d = -1 + 4
d = 3
an = x
Sn = 437
General formula in arithmetic sequence
Formula to find nth term
an = a₁ + d(n - 1)
Formula to find sum of sequence (sn)
Sn = n/2 (a₁ + an)
We have to make an equation system based on the problem
plug the numbers into the formula
First equation
an = a₁ + d(n - 1)
x = -4 + 3(n - 1)
x = -4 + 3n - 3
x = 3n - 7
Second equation
Sn = n/2 (a₁ + an)
n/2 (a₁ + an) = 437
n/2 (-4 + x) = 437
n(x - 4) = 874
xn - 4n = 874
Solve the equation system by subtitution method
Subtitute x with 3n - 7 in the second equation
xn - 4n = 874
(3n - 7)n - 4n = 874
3n² - 7n - 4n = 874
3n² - 11n - 874 = 0
(3n + 46)(n - 19) = 0
n = -46/3 or n = 19
Because the number of terms shouldn't be negative, -46/3 isn't required, so the value of n is 19.
Solve for x, back to the first equatin
x = 3n - 7
x = 3(19) - 7
x = 57 - 7
x = 50
The solution is 50
