Ahh, basic shapes. Split up the weird shapes into easier ones. #1 can be truned into 2 trapezoids. #2 can be turned into 2 circles. #3 is a triangle and a trapezoid. #4 is 2 right triangles. #5 is a rectangel and a traingle. Finally, #6 is 3 traigles and a rectangle. Do you see how we broke the hard shapes into easier shapes?
Answer:
54 - 10y
Step-by-step explanation:
Distribute each of the 3 parenthesis
= 12y + 24 - 32y + 32 - 10y - 2 ← collect like terms
= 54 - 10y
Answer:
The mean is also increased by the constant k.
Step-by-step explanation:
Suppose that we have the set of N elements
{x₁, x₂, x₃, ..., xₙ}
The mean of this set is:
M = (x₁ + x₂ + x₃ + ... + xₙ)/N
Now if we increase each element of our set by a constant K, then our new set is:
{ (x₁ + k), (x₂ + k), ..., (xₙ + k)}
The mean of this set is:
M' = ( (x₁ + k) + (x₂ + k) + ... + (xₙ + k))/N
M' = (x₁ + x₂ + ... + xₙ + N*k)/N
We can rewrite this as:
M' = (x₁ + x₂ + ... + xₙ)/N + (k*N)/N
and (x₁ + x₂ + ... + xₙ)/N was the original mean, then:
M' = M + (k*N)/N
M' = M + k
Then if we increase all the elements by a constant k, the mean is also increased by the same constant k.
Answer: all real numbers
Step-by-step explanation:
7a + 1 = 8a - a + 1
7a + 1 = 7a + 1
a = all real numbers
