The slope is the rise over the run. How high you go over how far you go. The slope of a line can be all real numbers.
Answer:
25+ -8
Step-by-step explanation:
17
Answer:
Yes, the line intersects the parabola two times at the points (0,0) and (-1,-1)
Step-by-step explanation:
Hi there!
We have the following system of equations:
y = x
y = -x²
If the curves intersect, then there is at least a pair (x,y) that satisfies both equations. That will only happen for those values of x for which:
-x² = x
The only two values that satisfy that equality are 0 and -1.
When x = 0, y is also 0 for both functions. In the same way, when x = -1 y is also -1 for both functions. Then, the curves will intersect at the points (0, 0) and (-1, -1).
Please, see the attached graphic for a better understandign of the problem.
Have a nice day!
Answer:
Step-by-step explanation:
<u>We can observe general terms of n:</u>
- aₙ = n + 1 + 2n + 2 + 3n + 3 + ... + (n - 1)n + (n - 1)
<u>Rewrite it as:</u>
- aₙ = (n + 1) + 2(n + 1) + 3(n + 1) + ... (n - 1)(n + 1) =
- (n + 1)(1 + 2 + 3 + ... + n - 1) =
- (n + 1)(1 + n - 1)(n - 1)/2 =
- (n - 1)n(n + 1)/2
<u>We need to find the least n for which aₙ > 500:</u>
- (n - 1)n(n + 1)/2 > 500 ⇒ (n - 1)n(n + 1) > 1000
<u>If n = 10:</u>
- a₁₀ = 9*10*11 = 990 < 1000
<u>If n = 11:</u>
- a₁₁ = 10*11*12 = 1320 > 1000
So the least n is 11