Step One
Begin by getting one side of the question equal to zero.
32x -4 = 4x^2 + 60 Add - 32x + 4 from both sides.
0 = 4x^2 + 60 - 32x + 4 Collect like terms.
0 = 4x^2 - 32x + 64
Step Two
For this question, you could divide both sides by 4. It just makes the steps later on easier.
0 = x^2 - 8x + 16
Step Three
Calculate the discriminate.
The discriminate is b^2 - 4*a*c
a = 1; b = -8; c = 16
b^2 - 4*a*c = (-8)^2 - 4*(1)(16) = 64 - 64 = 0
There is only 1 root. It is real and it is rational.
A <<<<< Answer
The formula in getting the arithmetic sequence:
an = a1<span> + (n – 1)d.
</span>
We can substitute the values in order for us to know how many terms the sequence has.
an = 7373
a1 = 1313
d = 303
an = a1<span> + (n – 1)d
</span>7373 = 1313 + (n-1) 303
7373 = 1313 + 303n - 303
-303n = 1313 - 303 - 7373
303n = -1313 + 303 + 7373
303n = 6363
n = 21
So, there are 21 terms in the sequence given.
-x² + 8x - 6 = 0
x = <u>-(8) +/- √((8)² - 4(-1)(-6))</u>
2(-1)
x = <u>-8 +/- √(64 - 20)</u>
-2
x = <u>-8 +/- √(44)
</u> -2<u>
</u>x = <u>-8 +/- 2√(11)
</u> -2
x = <u>-8 + 2√(11)</u> x = <u>-8 - 2√(11)
</u> -2 -2<u>
</u>x = 4 - √(11) x = -8 + √(11)
Answer:
y = -6 + 2x
Step-by-step explanation: