(x + 4) (x + 2)
=x^2 +2x + 4x + 8
=x^2 + 6x + 8
the other factor is (x + 2)
Let q be the number of 25 cent coins.
Let d be the number of 10 cent coins.
0.25q+0.10d= 3.95...(1)
q-d=6...(2)
(2)-> q-d= 6
q-d+d= 6+d
q= 6+d...(2a)
(2a)-> (1) 0.25q+0.10d=3.95
0.25(6+d)=0.10d= 3.95
1.95+0.25d+0.10d= 3.95
0.35d= 3.95-1.5
0.35d/0.35= 2.45/0.35
d= 7...(3)
(3)->(2) q-d= 6
q-7= 6
q=6+7
q= 13
There are 13 quarters and 7 dimes.
Substitute this into the parabolic equation,
We're told the line 
intersects 
twice, which means the quadratic above has two distinct real solutions. Its discriminant must then be positive, so we know
We can tell from the quadratic equation that has its vertex at the point (3, 6). Also, note that
and
so the furthest to the right that extends is the point (5, 2). The line passes through this point for 
. For any value of 
, the line passes through either only once, or not at all.
So 
; in set notation,
Elsa's answer is incorrect since there is a solution of the given equation. In the given logarithmic problem, we need to simplify the problem by transposing log2(3x+5) in the opposite side. The equation will now be log2x-log2(3x+5)=4. Using properties of logarithm, we further simplify the problem into a new form log (2x/6x+10)=4. Then transform the equation into base form 10^4=(2x/6x+10) and proceed in solving for x value which is equal to 1.667.
Answer:
He made 7 3-point shots.
Step-by-step explanation:
x+y=19
2x+3y=45
y=19-x
2x+3*(19-x)=45
2x+57-3x=45
-x=45-57
-x=-12
x=12
y=19-12
y =7
