Answer:
Step-by-step explanation:
The equation for an arithmetic sequence is
where n is the position of the number in the sequence, a1 is the first number in the sequence, and d is the difference between the numbers in the sequence.
Our first number is 2, so a1 = 2; to get from 2 to 5 we add 3, to get from 5 to 8 we add 3. That means that d = 3. Filling in the standard form of the equation:
which simplifies to
and a bit more to
(which should tell you that arithmetic sequences are lines!)
Finding the 13th number simply requires that we replace n with 13 and solve:
so
Answer:
x = 16 -5/2y
Step-by-step explanation:
2x + 5y = 32
2x = 32 -5y
/2 /2
x = 16 -5/2y
Answer:
f(-3) = -20
Step-by-step explanation:
We observe that the given x-values are 3 units apart, and that the x-value we're concerned with is also 3 units from the first of those given. So, a simple way to work this is to consider the sequence for x = 6, 3, 0, -3. The corresponding sequence of f(x) values is ...
34, 10, -8, ?
The first differences of these numbers are ...
10 -34 = -24
-8 -10 = -18
And the second difference is ...
-18 -(-24) = 6
For a quadratic function, second differences are constant. This means the next first-difference will be ...
? -(-8) = -18 +6
? = -12 -8 = -20
The value of the function at x=-3 is -20.
_____
The attachment shows using a graphing calculator to do a quadratic regression on the given points. The graph can then be used to find the point of interest. There are algebraic ways to do this, too, but they are somewhat more complicated than the 5 addition/subtraction operations we needed to find the solution. (Had the required x-value been different, we might have chosen a different approach.)
Answer:
28 cm
Step-by-step explanation:
Triangle ABC is obtained by joining the mid points of the sides of triangle XYZ.
So, perimeter of triangle ABC will be equal to half of the perimeter of triangle XYZ.
He should add exact since money is involved
he could also estimate since they are so close together, but he would be off only 2 cents
A
