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3 years ago

Gerry thinks that the points (4,2) and (−1,4) form a line perpendicular to a line with slope 4. Do you agree? Why

Mathematics

1 answer:

faust18 [17]3 years ago

4 0

Answer:

The answer to your question is these lines are not perpendicular.

Step-by-step explanation:

Data

A (4, 2)

B (-1, 4)

slope = m = 4

Perpendicular lines mean that these lines cross and form an angle of 90°. Also, the slope of perpendicular lines is negative reciprocals.

Process

1.- Find the slope of the second line and compare it to the slope given.

slope = $\frac{y2 - y1}{x2 - x1}$

Substitution

slope = $\frac{4 - 2}{-1 - 4}$

Simplification and result

slope = $\frac{-2}{5}$

-2/5 is not a negative reciprocal of 4, so these lines are not perpendicular.

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Can someone explain what geometric sequences are?

Fed [463]

Explanation:

A sequence is a list of numbers.

A geometric sequence is a list of numbers such that the ratio of each number to the one before it is the same. The common ratio can be any non-zero value.

Examples

1, 2, 4, 8, ... common ratio is 2
27, 9, 3, 1, ... common ratio is 1/3
6, -24, 96, -384, ... common ratio is -4

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General Term

Terms of a sequence are numbered starting with 1. We sometimes use the symbol a(n) or an to refer to the n-th term. The general term of a geometric sequence, a(n), can be described by the formula ...

a(n) = a(1)×r^(n-1) . . . . . n-th term of a geometric sequence

where a(1) is the first term, and r is the common ratio. The above example sequences have the formulas ...

a(n) = 2^(n -1)
a(n) = 27×(1/3)^(n -1)
a(n) = 6×(-4)^(n -1)

You can see that these formulas are exponential in nature.

Sum of Terms

Another useful formula for geometric sequences is the formula for the sum of n terms.

S(n) = a(1)×(r^n -1)/(r -1) . . . . . sum of n terms of a geometric sequence

When |r| < 1, the sum converges as n approaches infinity. The infinite sum is ...

S = a(1)/(1-r)

8 0

3 years ago

I have a question here.

taurus [48]

9514 1404 393

Answer:

P(F|A) = 35%

Step-by-step explanation:

P(F|A) = P(F&A)/P(A) = 7%/20% = 0.35

P(F|A) = 35%

_____

The given numbers will let you fill in a table for all of the categories of workers. However, it turns out this question can be answered using only the numbers given in the problem statement.