Rearrange the equation into slope intercept form
7x+3y=18
3y=-7x+18
y=-7x/3+18/3 so the slope of the reference line is -7/3
To be perpendicular to this line the slope must be the negative reciprocal of this...mathematically m1*m2=-1. So the slope of our perpendicular line is:
-7m/3=-1
-7m=-3
m=3/7 so our line so far is:
y=3x/7+b, using point (6,8) we can solve for b, the y-intercept
8=3(6)/7+b
8=18/7+b
56/7-18/7=b
38/7=b so our line is:
y=3x/7+38/7 or if you prefer
y=(3x+38)/7
First, find any zero of the polynomial. Since you didn't ask for work, I'll assume it's okay if I use my calculator. Your given polynomial has only one real root which is x=-4.
Now we use the rule that x-a divides the polynomial where a is a zero of said polynomial.
So x+4 divides 2x^3+2x^2-19x+20.
<span>(2x^3+2x^2-19x+20) / (x+4 equals 2x^2-6x+5).
If we factor out a two, we can use the quadratic formula.
2(x^2-3x+2.5) so we have x = (-(-3)+/-(9-4*1*2.5)^(1/2))/2*1)=(3+i)... or (3-i)/2 Where i is the square root of negative one. final answer:
2x^3+2x^2-19x+20=0
then x=-4, (3+i)/2, or (3-i)/2
</span>we have two imaginary number.
I hope it helped you
Answer:
( - 7 + √17 ) / 2, ( - 7 - √17 ) / 2
Step-by-step explanation:
x^2 = - 7x - 8
x^2 + 7x + 8 = 0
Here,
a = 1
b = 7
c = 8
D = b^2 - 4ac
= 7^2 - 4 ( 1 ) ( 8 )
= 49 - 32
D = 17
x = - b ± √D / 2a
= - 7 ± √17 / 2 ( 1 )
x = ( - 7 + √17 ) / 2, ( - 7 - √17 ) / 2
