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Tasya [4]
3 years ago
6

Write an equation for the line that contains the points (-5,50) and (-15,0).

Mathematics
1 answer:
gtnhenbr [62]3 years ago
3 0

Answer:

y=5

Step-by-step explanation:

The equation of a line can be written as y − y 0 = m ⋅ ( x − x 0 ) where ( x 0 , y 0 ) is any point that lies on the line. The gradient, m , of the line can be found using any two non-identical points that lie on the line. m = y 2 − y 1 x 2 − x 1 = 5 − 5 − 3 − 0 = 0 A gradient of zero indicates that the line is horizontal. The equation of the line can thus be simplified to y = y 0 In this case, both points have a y coordinate of 5. The equation of this line is therefore y = 5 .

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A triangle has two sides of length 1 and 8. What is the smallest possible whole-number length for the third side?
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Answer:

8

Step-by-step explanation:

For the smallest possible length, this has to be one of the shorter sides. Let the length of this side be x.

So, by the triangle inequality theorem, 1+x>8, which means x>7.

So, the smallest possible whole number length is 8.

7 0
3 years ago
Simplify (-4 + 5i) + 2(1 + 3i). Enter your answer in the form a + bi.
luda_lava [24]

(-4 + 5i) + 2(1 + 3i)

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4 years ago
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The third, fifth and eighth terms of an AP are the first 3 consecutive terms of a GP. Given that the first term of the AP is 8,
marshall27 [118]

Answer:

Common Difference = 2.

Step-by-step explanation:

An AP can be written as  a1,  a1 + d,  a1 + 2d,  a1 + 3d,  a1 + 4d,  a1 + 5d, a1 + 6d , a1 + 7d.    

 where a1 = first term and d is the common difference.

Here first term = a1 = 8

3rd term = a1 + 2d = 8 + 2d

5th term = a1 + 4d = 8 + 4d

8th term = 8 + 7d

First 3 terms of a GP are  a , ar and ar^2

So from the given information:

a = 8 + 2d

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Dividing the second equation by the first  we have

r = (8 + 4d)/(8 + 2d)

Dividing the third by the second:

r = (8 + 7d) / (8 + 4d)

Therefore, eliminating r we have:

(8 + 4d)/(8 + 2d)  =   (8 + 7d)/(8 + 4d)

(8 + 4d)^2 = (8 + 2d)(8 + 7d)

64 + 64d + 16d^2 =  64 + 72d^ + 14d^2

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2d = 0 or d^2 = 4, so

d =  0, 2.

The common difference can't be zero so it must be 2.

8 0
4 years ago
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