Answer:
a) 64 : 13
b) 1.5×10⁹
c) China➛ 18.2%
India➛ 44.7%
US➛ 25.0%
Bulgaria➛ -19.1%
India, United States, China, Bulgaria
d) No, I do not agree. (see picture for justification)
Step-by-step explanation:
Please see the attached pictures for full solution.
1/2 (30*60*12)
is 10800 cubic inches volume of water
For each parabola, you have to do a system of equation with the line y = x - 5 and find which of them has one real solution.
For that you can solve the systems and find the roots, but you can also use the rule that to have one real solution the discriminant of the quadratiic equation (b^2 - 4ac) has to be zero.
1)
y = x - 5
y = x^2 + x - 4
=> x - 5 = x^2 + x - 4
=> x^2 + 1 = 0
It is easy to tell, by simple inspection, that this equation has not real solutions.
2)
y = x -5
y = x^2 + 2x - 1
=> x - 5 = x^2 + 2x - 1
=> x^2 + x + 4 = 0
discriminant = b^2 - 4ac = 1^2 - 4(1)(4) = 1 - 16 = - 15
A negative discriminant means that there are not real solutions.
3)
y = x - 5
y = x^2 + 6x + 9
x - 5 = x^2 + 6x + 9
=> x^2 + 5x + 14 = 0
=> b^2 - 4ac = 5^2 - 4(1)(14) = 25 - 56 = - 31 => no real solutions
4)
y = x - 5
y = x^2 + 7x + 4
x - 5 = x^2 + 7x + 4
=> x^2 + 6x + 9 = 0
=> b^2 - 4ac = 6^2 - 4(1)(9) = 36 - 36 = 0 => the system has one real solution.
By the way, that solution is easy to find because you can factor the equation as: (x + 3)^2 = 0 => x = - 3
Answer:
29 i think not sure ill reach back to you if i find a positive answer
Very arty photograph with the hands reflecting. I like it.
I prefer point point form, the line through (a,b) and (c,d) is
(c - a)(y - b) = (d - b)(x - a)
This is really the same as point slope form, without the awkward possibility of divsion by zero,
y - b = m (x -a ) where m = (d - b) / (c - a)
Join of (-1, 6) and (1,-4)
m = (-4 - 6)/(1 - -1) = -10/2 = -5
y - 6 = -5(x - -1)
Answer: y = -5x + 1
check: -5(-1)+1=5+1=6, good, -5(1)+1=-5+1=-4, good