9514 1404 393
Answer:
the correct choice is marked
Step-by-step explanation:
The line has a rise of 2 for a run of 1, so a slope of 2. The line crosses the y-axis at y=-2, so the y-intercept is -2. The slope-intercept equation for the line is ...
y = mx + b . . . . . . for slope m and y-intercept b
y = 2x -2
Answer:
3,740,000,000
Step-by-step explanation:
Answer:
The equation is
Let n represent the number
4n + (-2) = 5n + 8
4n - 2 = 5n + 8
Solve for n
Group like terms
4n - 5n = 8 + 2
-1n = 10
n = 10/-1
n = -10
The number is -10
Answer:
In Exercises 1-15 use mathematical induction to establish the formula for n ≥ 1.
1. 1
2 + 22 + 32 + · · · + n
2 =
n(n + 1)(2n + 1)
6
Proof:
For n = 1, the statement reduces to 12 =
1 · 2 · 3
6
and is obviously true.
Assuming the statement is true for n = k:
1
2 + 22 + 32 + · · · + k
2 =
k(k + 1)(2k + 1)
6
, (1)
we will prove that the statement must be true for n = k + 1:
1
2 + 22 + 32 + · · · + (k + 1)2 =
(k + 1)(k + 2)(2k + 3)
6
. (2)
The left-hand side of (2) can be written as
1
2 + 22 + 32 + · · · + k
2 + (k + 1)2
.
In view of (1), this simplifies to: