Random sampling. its where you pick or make a smaple at random
Answer:
C. Kalena made a mistake in Step 3. The justification should state: -x²
+ x²
Step-by-step explanation:
Given the function x(x - 1)(x + 1) = x3 - X
To justify kelena proof
We will need to show if the two equations are equal.
Starting from the RHS with function x³-x
First we will factor out the common factor which is 'x' to have;
x(x²-1)
Factorising x²-1 using the difference of two square will give;
x(x+1)(x-1)
Note that for two real number a and b, the expansion of a²-b² using difference vof two square will give;
a²-b² = (a+b)(a-b) hence;
Factorising x²-1 using the difference of two square will give;
x(x+1)(x-1)
Factorising x(x+1) gives x²+x, therefore
x(x+1)(x-1) = (x²+x)(x-1)
(x²+x)(x-1) = x³-x²+x²-x
The function x³-x²+x²-x gotten shows that kelena made a mistake in step 3, the justification should be -x²+x² not -x-x²
We have
x² + 24x = 17 (1)
Note that
(x + 12)² = x² + 24x + 144
By adding 144 to the left side of equation (1), it becomes a perfect square.
Therefore
x² + 24x = (x+12)² - 144 (2)
Substitute (2) into (1).
(x + 12)² - 144 = 17
(x + 12)² = 17 +144
(x + 12)² = 161
Answer:
We added 144 to the left side of equation (1) in order to make it a perfect square.
I rejected -5 as the base cannot be a negative value as it is impossible.
