Here we're discussing the "nth partial sum of a geom series."
1 - r^n
The formula for that is s(n) = a(1) ---------------
1-r
We can subst. the given values and see where that takes us:
1 - (-2)^6 1 - 64
105 = a(1)*---------------- = ----------*a(1) = -21*a(1)
1-(-2) 3
105
Solving this for a(1): a(1) = --------- = -5 (answer)
-21
Answer:
Step-by-step explanation:
The vertex form of a parabola is given by y = a(x - h)^2 + k, where (h, k) is the vertex.
Given vertex at (2,-3), h = 2, k = -3
y = a(x - 2)^2 + (-3) = a(x - 2)^2 - 3
The parabola passes through (0,5) so
5 = a(0 - 2)^2 - 3
5 = 4a - 3
4a = 8
a = 2
The parabola equation in vertex form:
y = 2(x - 2)^2 - 3
Let z be any number (like x would be)
if we set z equal to 2x-6y, then we get z = 2x-6y
The system
2x-6y = 8
2x-6 = 3
turns into this new system
z = 8
z = 3
but z is a single number. It can't be both 8 and 3 at the same time. So there are no solutions
Answer:
x=4
Step-by-step explanation:
2/3 x + 5/6 = x - 1/2
Multiply each side by 6 to clear the fractions
6(2/3 x + 5/6) = 6(x - 1/2)
Distribute
4x +5 = 6x-3
Subtract 4x from each side
4x+5 -4x = 6x-3-4x
5 = 2x-3
Add 3 to each side
5+3= 2x-3+3
8 =2x
Divide by 2
8/2 =2x/2
4 =x
She/he could use 2 12x3 in of wood and 1 4x2 so now we will take all of the numbers and see what we get when we calculat them so when we take the 2 12x3 we will get 72 and then we will add 72 to 4x2 after we multiply them so when we multiply the 4x2 we will get 8 and now will we add 72 to the 8 and we will get a 80 for your answer hope that is the right answer if it is not sorry