Answer:
a = -86.
Step-by-step explanation:
By the Factor Theorem, if x + 4 is a factor then P(-4) = 0, so:
P(-4) = 2(-4)^3 - 11(-4)^2 + a(-4)- 40 = 0
-128 - 176 - 4a - 40 = 0
-4a = 128 +176 + 40
-4a = 344
a = -86.
Answer:
7
Step-by-step explanation:
the reciprocal of 
To find reciprocal, flip the top and the bottom.
So would be 
.
Multiply like normal.
Answer:
The vertex of this parabola, 
, can be found by completing the square.
Step-by-step explanation:
The goal is to express this parabola in its vertex form:
,
where 
, 
, and 
are constants. Once these three constants were found, it can be concluded that the vertex of this parabola is at 
.
The vertex form can be expanded to obtain:
.
Compare that expression with the given equation of this parabola. The constant term, the coefficient for 
, and the coefficient for 
should all match accordingly. That is:
.
The first equation implies that is equal to 
. Hence, replace the "
" in the second equation with 
to eliminate 
:
.
.
Similarly, replace the "" and the "" in the third equation with and 
, respectively:
.
.
Therefore, 
would be equivalent to 
. The vertex of this parabola would thus be:
.
The absolute value is the value of the number without the sign. So in this case it's 3 and -3
Answer:
x is 3
Step-by-step explanation:
6 (x + 1) = 24
6 (x) + 6(1) = 24
6x + 6 = 24
Subtract 6 on both sides
6x + 6 - 6 = 24 - 6
6x + 0 = 18
6x = 18
x = 18/6
x = 3
