Let
In order to prove this by induction, we first need to prove the base case, i.e. prove that P(1) is true:
So, the base case is ok. Now, we need to assume 
and prove 
.
states that
Since we're assuming , we can substitute the sum of the first n terms with their expression:
Which terminates the proof, since we showed that
as required
Answer:
D. 1 4 × 1 3 E. 4 12 × 3 6
Step-by-step explanation:
D. 1 4 × 1 3 E. 4 12 × 3 6
Answer:
It's -8
Step-by-step explanation:
DISTRIBUTE :
4x + 2( x - 2 ) = 4x + x - 12
4x + 2x - 4 = 4x + x - 12
COMBINE LIKE TERMS :
4x + 2x - 4 = 4x + x - 12
6x - 4 = 4x + x - 12
COMBINE LIKE TERMS :
6x - 4 = 4x + x - 12
6x - 4 = 5x - 12
ADD 4 TO BOTH SIDES :
6x - 4 = 5x - 12
6x - 4 + 4 = 5x - 12 + 4
ADD THE NUMBERS/ SIMPLIFY :
6x = 5x - 8
SUBTRACT 5x FROM BOTH SIDES :
6x = 5x - 8
6x - 5x = 5x - 8 - 5x
SIMPLIFY :
x = -8
I graphed the given points and based on my graph.
<span>
x
y </span>→ EXPONENTIAL<span><span>
</span>
<span>
-2
21
</span><span> 1 4
</span><span> 0 1
</span><span> 1 0
</span></span><span>
x y </span>→ LINEAR<span><span>
</span>
<span>
-2 6
</span>
<span>
-1
-2
</span><span> 0 2
</span><span> 1
6
</span></span>
<span>
x y </span>→ QUADRATIC<span><span>
</span>
<span>
-2
12
</span>
<span>
-1
-2
</span><span> 0
-8
</span><span> 1
-6
</span></span><span>
<span><span>
x
y </span></span></span>→ EXPONENTIAL<span><span><span>
</span>
<span>
-2
16
</span>
<span>
-1 8
</span><span> 0 4
</span><span> 1 2
LINEAR FUNCTIONS always maintain a constant slope. In the above linear function, the slope is 4.
EXPONENTIAL and QUADRATIC FUNCTIONS have different slope in every point.
Exponential functions can be identified by the immediate increase or decrease in the value of y resulting to a minimal increase or decrease in the value of x.
Quadratic functions can be identified as such due to the similar points it has after having the vertex.
</span></span></span>
Answer:
It might be 235.62
Step-by-step explanation:
