Answer:
The solution is (3 , 1)
Step-by-step explanation:
To solve the system of the equation you can use the elimination method or substitution method.
We will use the substitution method
From the first equation x + 2y = 5⇒get x = 5 - 2y
In the second equation 3x + 5y = 14⇒we will substitute x by 5 - 2y
3(5 - 2y) + 5y =14
15 - 6y + 5y = 14
-6y + 5y = 14 - 15
-y = -1
y = 1
Substitute the value of y in x = 5 - 2y
x = 5 - 2(1) = 5 -2 =3
∴ The solution of the system of equations is (3 , 1)
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
$19,802.5 I hope this helps and I'm sorry I didn't reply sooner.
I'm pretty sure it's a prime number.
Answer:
D
Step-by-step explanation:
A) more like parallel line
B) That is angle bisecting
C) Neither Angle or line bisector
