X(x - 2) = 4 [upon multiplying and moving the 4 becomes x² - 2x - 4 = 0] x(2x + 3) = 12 [upon multiplying and moving the 12 becomes 2x² - 3x - 12 = 0] 3x(x + 8) = -2 [upon multiplying and moving the -2 becomes 3x² + 24x + 2 = 0]
So, to factor out the equation x²+12x+35, first multiply the first and last numbers.
1×35=35
So, you need to find the multiples of 35 that add up to 12.
So, you find 7 and 5. These two numbers are the magic numbers that will be used as the correct factored form of x²+12x+35, because:
>7×5=35
>7+5=12
So, using these two numbers, you get your factored form as:
(x+5)(x+7)
Step-by-step explanation:
We have,
Mass of ball is 9 kg
Initial speed, u = 5 m/s
Final speed, v = -2 m/s (negative as it bounces off)
(a) The change in velocity of the bowling ball is :
(b) Change of momentum of the ball is :
|p| = 630 kg-m/s
(c) Impulse momentum theorem states that the change in momentum of the ball is equal to the impulse exerted on the ball. So, impulse is 630 kg-m/s.
(d) Impulse is also given by :
1st:
f(x) = x^2.
f(x +1): Anywhere we see x we replace it with (x+1)
f(x+1) = (x+1)^2 , Expand
(x+1)^2 = (x+1)(x+1) = x^2 + 2x + 1= C.
2nd:
Noting general equation, y = mx + c
m = slope, c = vertical intercept.
From the graph, slope = (2,0) and (0, -4)
= (-4 -0) / (0 - 2) = -4/-2 = 2.
Vertical intercept, c = -4.
y = mx + c , y = 2x + (-4), y = 2x - 4 = D.
3rd:
f(x) = x^2 - x, f(-4). we would substitute x = -4.
f(-4) = (-4)^2 - (-4) = 16 + 4 = 20 = D.
Cheers.
All you have to do is line it up with the numbers
