Answer:
(
4
x
−
1
)
(
x
−
3
)
Step-by-step explanation:
Factor by grouping.
Answer:

Step-by-step explanation:
Let v be the speed after the collision of both the cars.
Now, momentum is given by: mass × velocity, then by equating the total momentum before and after the collision of the two cars, we get

⇒
⇒
⇒
Thus, they are moving at the velocity of 
The easiest way to find the vertex is to convert this standard form equation into vertex form, which is y = a(x - h)^2 + k.
Firstly, put x^2 - 10x into parentheses: y = (x^2 - 10x) + 30
Next, we want to make what's inside the parentheses a perfect square. To do that, we need to divide the x coefficient by 2 and square it. In this case, the result is 25. Add 25 inside the parentheses and subtract 25 outside of the parentheses: y = (x^2 - 10x + 25) + 30 - 25
Next, factor what's inside the parentheses and combine like terms outside of the parentheses, and your vertex form is: y = (x - 5)^2 + 5.
Now going back to the formula of the vertex form, y = a(x - h)^2 + k, the vertex is (h,k). Using our vertex equation, we can see that the vertex is (5,5).
Answer:
The number of home runs that Lu hit is 4 and the number of home runs that Karrine hit is 6
Step-by-step explanation:
Let
x ----> represent the number of home runs Lu hit
y ---> represent the number of home runs Karrine hit
we know that
Together they hit 10 home runs
so
----> equation A
Karrine hit 4 more home runs than half the number of home runs Lu hit
so
---> equation B
substitute equation B in equation A

solve for x


Find the value of y

therefore
The number of home runs that Lu hit is 4 and the number of home runs that Karrine hit is 6