Use the sum-product pattern
2
−
−
1
2
x
2
−
x
−
12
x2−x−12
2
+
3
−
4
−
1
2
x
2
+
3
x
−
4
x
−
12
x2+3x−4x−12
2
Common factor from the two pairs
2
+
3
−
4
−
1
2
x
2
+
3
x
−
4
x
−
12
x2+3x−4x−12
(
+
3
)
−
4
(
+
3
)
x
(
x
+
3
)
−
4
(
x
+
3
)
x(x+3)−4(x+3)
3
Rewrite in factored form
(
+
3
)
−
4(+3)x
(x+3)−4(x+3)
x(x+3)−4(x+3)
(−4)(+3)
(x−4)(x+3)
(x−4)(x+3)
I'm just going to take a chance and say 1.A, and 2.D.
Its B step 2 Its right multiply it and yea its b
Let the numbers be a and b and b>a
2a=3b and 3(b-a)=2(b-a)+13
Solving the first for a:
2a=3b
a=3b/2, now using this value of a in the second equation gives you:
3(b-3b/2)=2(b-3b/2)+13 upon performing indicated operations.
3b-9b/2=2b-6b/2+13 making all terms have a common denominator of 2
(6b-9b)/2=(4b-6b+26)/2 multiplying the whole equation by 2
6b-9b=4b-6b+26 combining like terms
-3b=-2b+26 adding 2b to both sides
-b=26 dividing both sides by -1
b=-26, since a=3b/2
a=3(-26)/2
a=-39
So the numbers are -39 and -26
check...
2a=3b becomes:
2(-39)=3(-26)
-78=-78
3(b-a)=2(b-a)+13 becomes:
3(-26--39)=2(-26--39)+13
3(13)=2(13)+13
39=26+13
39=39
correct :P
It's a pretty simple suvat linear projectile motion question, using the following equation and plugging in your values it's a pretty trivial calculation.
V^2=U^2+2*a*x
V=0 (as it is at max height)
U=30ms^-1 (initial speed)
a=-g /-9.8ms^-2 (as it is moving against gravity)
x is the variable you want to calculate (height)
0=30^2+2*(-9.8)*x
x=-30^2/2*-9.8
x=45.92m
With these questions it's best to just memorise the suvat equations and either draw or imagine the actions involved, that was you can tell what piece of given information translates to which variable. For example; I know that I am looking for max height, so when a ball is at its highest point, it can't be moving up anymore (thus V = 0). I also know that it is moving upwards against gravity, so gravity will be decelerating the ball (therefore a=-g). In a paper, it may as for assumptions with this question, a good answer would be no air resistance or movement due to any other external forces. I hope I helped :)
