Amanda and Alexis live 4 miles apart. They decide to start walking toward each other’s houses at the same time. Amanda walks at
1 answer:
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Step-by-step explanation:
The simplest method is "brute force". Calculate each term and add them up.
∑ = 3(1) + 3(2) + 3(3) + 3(4) + 3(5)
∑ = 3 + 6 + 9 + 12 + 15
∑ = 45
∑ = (2×1)² + (2×2)² + (2×3)² + (2×4)²
∑ = 4 + 16 + 36 + 64
∑ = 120
∑ = (2×3−10) + (2×4−10) + (2×5−10) + (2×6−10)
∑ = -4 + -2 + 0 + 2
∑ = -4
4. 1 + 1/4 + 1/16 + 1/64 + 1/256
This is a geometric sequence where the first term is 1 and the common ratio is 1/4. The nth term is:
a = 1 (1/4)ⁿ⁻¹
So the series is:
5. -5 + -1 + 3 + 7 + 11
This is an arithmetic sequence where the first term is -5 and the common difference is 4. The nth term is:
a = -5 + 4(n−1)
a = -5 + 4n − 4
a = 4n − 9
So the series is:
By the binomial theorem,
Each term containing a factor 6 is divisible by 3, since 3 divides 6. The remaining 1 and 2 sum to 3, which is also divisible by 3.
Answer:
The vertex of the parabola is the maximum value, i.e.,(-1,0). The function is increasing x<-1. the function is decreasing x>-1. the domain of the function is all real numbers. the range of the function is all real numbers less than or equal to 0.
Step-by-step explanation:
The given function is
....(1)
The general vertex form of the parabola is
.....(2)
Where, (h,k) is vertex and a is stretch factor.
On comparing (1) and (2), we get
The vertex of the parabola is (-1,0). Since a=-1<1 so it is a downward parabola.
The axis of symmetry is x=-1. So, before -1 the function is increasing and after -1 the function is decreasing.
The vertex of a downward parabola is the point of maxima. So, the rang of the function can not exceed 0.
Therefore the vertex of the parabola is the maximum value, i.e.,(-1,0). The function is increasing x<-1. the function is decreasing x>-1. the domain of the function is all real numbers. the range of the function is all real numbers less than or equal to 0.