Answer:
The answer is 2,150
Step-by-step explanation:
Answer:
Step-by-step explanation:
The given expression is
To factor this polynomial, we just need to extract the common factor. Or you can see as the greatest common factor.
What is the greatest common factor between 8 and 16?
16: 1, 2, 4, 8, 16.
8: 1, 2, 4, 8.
You can observe that the greatest common factor is 8, so we extract it from both numbers
Notice that we placed the GCM in the front as a product, if we don't do that, it would be completely wrong, because we can change the equivalence of the expression. Now, notice that each variable have different coefficients, that is because if you extract the GCM, you need to placed its quotients as coefficients.
Therefore, the factor of the polynomial is
Step-by-step explanation:
h = -490t² + 1470t
When h = 980:
980 = -490t² + 1470t
Simplifying:
0 = -490t² + 1470t - 980
0 = t² - 3t + 2
Factoring:
0 = (t - 1) (t - 2)
t = 1, 2
There are two solutions because the rocket first reaches the height of 980 cm as it's going up at 1 second, then it reaches that height again as it's coming down at 2 seconds.
Answer:
If (K + 1)^2 = 2n + (n^2)/2, then the answer is Yes, else No.
Step-by-step explanation:
Sum of first K + 1 odd numbers (S): 1 + 3 + 5 + ... + (2K - 3) + (2K - 1) + (2K + 1).
(1 + 3 + 5 + ... + (2K - 3) + (2K - 1) + (2K + 1)) + ((2K + 1) + (2K - 1) + (2K - 3) + ... + 5 + 3 + 1 ) = (2K + 2) + (2K + 2) + (2K + 2) + ... + (2K + 2) + (2K + 2) + (2K + 2) (repeat K + 1 times) = (2K + 2)(K + 1) = 2S
2S = (2K + 2)(K + 1)
S = (2K + 2)(K + 1)/2
S = (2K^2 + 4K + 2)/2
S = K^2 + 2K + 1
S = (K + 1)^2
(4n + n^2)/2 = 2n + (n^2)/2
