I wish I could help but I didn’t learn that
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
A) 2^(x+3)= 4^(2x)
make base number the same
2^(x+3)= 2^2 (2x)
set the exponents equal to eachother
x+3=2 (2x)
x+3=4x
-x both sides
3=3x
÷3 both sides
x=1
b) 16^(1/5)×2^(x)=8^(3/4)
make base same number
2^4 (1/5)×2^(x)=2^3 (3/4)
2^(4/5)×2^(x)=2^(9/4)
set exponents
4/5 +x=9/4
-4/5 both sides
x= 29/20
Answer:
y=2
Step-by-step explanation:
A parallel line are lines that never intersect.
-They are generally formed when a line when lines are perfectly horizontal to the x axis or the vertical to the y-axis.
=>y=2 is the only parallel line .
=>y=x+2 is not parallel as the (x+2) is not a constant
=>y=2x-1 is not parallel as the (2x-1) is not a constant
=>y=2x+1 is not parallel as the (2x+1) is not a constant
