Answer:
in steps
Step-by-step explanation:
The question did not state if alpha>beta or alpha<beta, so the answer will have 2 answers for each questions
3x²-9x+2=0
x = (-(-9) ± √(-9)²-4*(3)*(2)) / (2*3)
x = (9 + √57) / 6 or x = (9 - √57) / 6 (alpha and beta) or (beta and alpha)
(I) alpha (a) ×beta (b) + alpha² × beta = ab (1+a)
= ((9 + √57) / 6) ((9 - √57) / 6) (1 + (9 ± √57))
= ((9² - (√57)²)/36) (10 ± √57)
= (24/36) (10 ± √57)
= 2/3 (10 ± √57) or (11.7 or 1.63)
(ii) alpha²-alpha×beta+beta² = a² -2ab + b² +ab = (a - b)² + ab
if a is alpha
= ((9 + √57) / 6) - ((9 - √57) / 6)) + ((9 + √57) / 6) ((9 - √57) / 6))
= √57/3 + 2/3
= (√57 + 2) / 3
if a is beta
((9 - √57) / 6) - ((9 + √57) / 6)) + ((9 - √57) / 6) ((9 + √57) / 6))
= - √57/3 + 2/3
= - (√57 + 2) / 3
Answer:
4. Infinitely many
Step-by-step explanation:
5x + 3(x − 1) = 10x − 2x − 3
5x+3x-3=8x-3
5x+3x-8x=3-3
0=0
x∈R
y=6x-3
put a point on (0,-3) this is your y intercept
go up 6 and over 1 this should land you at (1,0) do this again and your at (2,6)
go back to the y intercept now go down 6 and over 1, this should land you (-1,-6)
continue to do this until you graph is filled
Answer:
x must equal 5 and y must equal 2
therefore,
5a + 2b = 23 and
5a - 2b = 7.
I'm gonna take 5a + 2b = 23 and add 7 to each side:
5a + 2b + 7 = 30
and substitute 5a -2b in for 7 on the left side:
5a + 2b + (5a-2b) = 30
10a = 30
a = 3
Now we know a. Now take
5a -2b = 7
and substitute in 3 for a
5*(3) - 2b = 7
15 -2b = 7
8 = 2b
b = 4
a = 3 and b = 4
Step-by-step explanation:
System of equations:
The intersection point for this is <em>(4,11)</em>.
