Hank's reasoning is being questioned for assuming that all sequences start with 1 and that the y-intercept of a linear function is always at x=0.
Given that,
Hank's reasoning is being discussed.
The claim is that Hank's reasoning is incorrect.
The reasoning involves sequences that begin with the term number 1, where x=1.
By convention,
The first term of a sequence starts with n = 1 instead of n = 0.
This is so n = 1 matches with 1st,
n = 2 matches with 2nd, and so on.
In contrast,
The y-intercept always occurs when x = 0.
So y = 3x+5 has a y-intercept of 5 when you plug in x = 0.
An arithmetic sequence:
f(n) = 2n+7 has its first term when n = 1.
So, the first term would be f(1) = 2(1)+7=9 instead of 7 as Hank claims.
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The complete question is:
Hank's reasoning is incorrect because all sequences begin with the term number 1, which translates to x=1.
The y-intercept of a linear function is when x=0.
By convention, the first term of a sequence starts with n = 1 instead of n = 0. This is so n = 1 matches with 1st, n = 2 matches with 2nd, and so on.
In contrast, the y intercept always occurs when x = 0. So something like y = 3x+5 has a y intercept of 5 when you plug in x = 0.
An arithmetic sequence like f(n) = 2n+7 has its first term when n = 1. So the first term would be f(1) = 2(1)+7 = 9 instead of 7 as Hank claims.
Answer:
2^(8p) =2^(5p+15)
Step-by-step explanation:
16 ^ 2p = 32 ^ (p+3)
Rewrite each number as a power of 2
16 = 2^4
32 = 2^5
2^4 ^ 2p =2^5 ^ (p+3)
We know a^b^c = a^(b*c)
2^(4 * 2p) =2^(5 * (p+3))
2^(8p) =2^(5p+15)
b.
c.
d. –51?
To find the distance between the points (a, a) and (b, b), we can use the distance formula. The distance formula calculates the distance between two points in a coordinate plane.
The distance between two points (x1, y1) and (x2, y2) is given by the formula:
Distance = √((x2 - x1)² + (y2 - y1)²)
In this case, since the points are (a, a) and (b, b), we substitute a for both x1 and y1, and b for both x2 and y2:
Distance = √((b - a)² + (b - a)²)
Simplifying this expression further:
Distance = √((b - a)² + (b - a)²) = √(b² - 2ab + a² + b² - 2ab + a²) = √(2a² + 2b² - 4ab)
Therefore, the distance between the points (a, a) and (b, b) is √(2a² + 2b² - 4ab).