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3 years ago

What is an equation of the line that passes through 7,3 and a slope of 4/7

Mathematics

1 answer:

Cerrena [4.2K]3 years ago

5 0

Answer:

y=(4/7)x-1

Step-by-step explanation:

y=mx+b

3=(4/7)(7)+b

3=4+b

b=-1

y=(4/7)x-1

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"A line that goes through (4, 7) and (-2, 1)"

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Y= x + 3
1. Find the gradient(slope)

1 - 7 / - 2 - 4
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3 years ago

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4 years ago

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The 5th term in a geometric sequence is 40. The 7th term is 10. What is (are) the possible value(s) of the 4th term?

Lena [83]

Answer:

possible values of 4th term is 80 & - 80

Step-by-step explanation:

The general term of a geometric series is given by

$a(n)=ar^{n-1}$

Where a(n) is the nth term, r is the common ratio (a term divided by the term before it) and n is the number of term

Given, 5th term is 40, we can write:

$ar^{5-1}=40\\ar^4=40$

Given, 7th term is 10, we can write:

$ar^{7-1}=10\\ar^6=10$

We can solve for a in the first equation as:

$ar^4=40\\a=\frac{40}{r^4}$

Now we can plug this into a of the 2nd equation:

$ar^6=10\\(\frac{40}{r^4})r^6=10\\40r^2=10\\r^2=\frac{10}{40}\\r^2=\frac{1}{4}\\r=+-\sqrt{\frac{1}{4}} \\r=\frac{1}{2},-\frac{1}{2}$

Let's solve for a:

$a=\frac{40}{r^4}\\a=\frac{40}{(\frac{1}{2})^4}\\a=640$

Now, using the general formula of a term, we know that 4th term is:

4th term = ar^3

Plugging in a = 640 and r = 1/2 and -1/2 respectively, we get 2 possible values of 4th term as:

$ar^3\\1.(640)(\frac{1}{2})^3=80\\2.(640)(-\frac{1}{2})^3=-80$

possible values of 4th term is 80 & - 80

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4 years ago