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Aneli [31]
3 years ago
6

What is the slope of the line that contains the points (9,-4) and (1,-5)?

Mathematics
2 answers:
marissa [1.9K]3 years ago
6 0

Answer:

B

Step-by-step explanation:


cupoosta [38]3 years ago
4 0

Answer:   \bold{D.\ \dfrac{1}{8}}

<u>Step-by-step explanation:</u>

Plug the given coordinates (x₁, y₁) = (9, -4) and (x₂, y₂) = (1, -5) into the slope formula to find the slope (m):

m=\dfrac{y_2-y_1}{x_2-x_1}\\\\m=\dfrac{-5-(-4)}{1-9}\\\\.\quad =\dfrac{-5+4}{-8}\\\\.\quad =\dfrac{-1}{-8}\\\\.\quad =\dfrac{1}{8}


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The sum of three numbers in <br> g.p. is 21 and the sum of their squares is 189. find the numbers.
sashaice [31]
Let the three gp be a, ar and ar^2
a + ar + ar^2 = 21 => a(1 + r + r^2) = 21 . . . (1)
a^2 + a^2r^2 + a^2r^4 = 189 => a^2(1 + r^2 + r^4) = 189 . . . (2)
squaring (1) gives
a^2(1 + r + r^2)^2 = 441 . . . (3)
(3) ÷ (2) => (1 + r + r^2)^2 / (1 + r^2 + r^4) = 441/189 = 7/3
3(1 + r + r^2)^2 = 7(1 + r^2 + r^4)
3(r^4 + 2r^3 + 3r^2 + 2r + 1) = 7(1 + r^2 + r^4)
3r^4 + 6r^3 + 9r^2 + 6r + 3 = 7 + 7r^2 + 7r^4
4r^4 - 6r^3 - 2r^2 - 6r + 4 = 0
r = 1/2 or r = 2
From (1), a = 21/(1 + r + r^2)
When r = 2:
a = 21/(1 + 2 + 4) = 21/7 = 3
Therefore, the numbers are 3, 6 and 12.
3 0
3 years ago
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