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3 years ago

Find the slope of a line through a pair of points (2,-3) and (8,4)

1 answer:

4 0

Slope of any line (m) can be calculated as follows:
m = (y2-y1) / (x2-x1)
from the given points:
(x1,y1) = (2,-3)
(x2,y2) = (8,4)
substituting in the equation, we can get the slope as follows:
m = (4--3) / (8-2) = (4+3) / (8-2) = 7/6

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a worker A finishes a project on his own in 12 days. the worker completes the same work alone in 16 days. the two workers starte

ankoles [38]

Answer:

Worker B needs 9 days to finish the rest of the work

Step-by-step explanation:

Proportions

Worker A finishes a project on his own in 12 days and worker B does the same in 16 days.

Worker A does 1/12 of the project in one day and worker B does 1/16 of the project in one day. When working together, they do

$\frac{1}{12}+\frac{1}{16}=\frac{7}{48}$

After 3 days they have completed:

$3*\frac{7}{48}=\frac{7}{16}$

parts of the project, this means it still remains:

$1-\frac{7}{16}=\frac{9}{16}$

parts of the project and it is done by B alone. Since B does $\frac{1}{16}$ per day, he now takes

$\displaystyle \frac{\frac{9}{16}}{\frac{1}{16}}=9$

days to complete the project.

Worker B needs 9 days to finish the rest of the work

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3 years ago

Factorize this expression completely using (a-b)² formula 3a²- 36a + 108

Novosadov [1.4K]

Answer:

$3a^2 - 36a + 108 = (\sqrt{3}a - 6\sqrt{3} )^2$

Step-by-step explanation:

$3a^2 = (\sqrt{3} a)^2\\108 = 9 \times 4 \times 3= 3^2 \times 2^2 \times 3 = (3\times2 \sqrt{3} )^2 = (6\sqrt{3})^2$

$so, a = \sqrt{3} a \ , \ b = 6\sqrt{3} \\\\(a - b)^2 = a^2 -2ab + b^2\\\\-36a = -2ab\\\\-36a = -2 \times \sqrt{3} a \times 6\sqrt{3}$

Therefore ,

$3a^2 - 36a + 108 = (\sqrt{3}a )^2 - 2(\sqrt{3}a \times 6\sqrt{3} ) + (6\sqrt{3} )^2 = (\sqrt{3}a - 6\sqrt{3} )^2$

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