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bagirrra123 [75]
3 years ago
10

For what value of a does the equation ax^2−3x−5=0 have 1 as one of its roots?

Mathematics
1 answer:
allsm [11]3 years ago
5 0
Answer: When a = 8, one of the roots of the equation will be 1.

To solve this problem, you could graph the equation with a 1 in the place of the a on a graphing calculator (there are some online).

Then, just keep changing the a value until the graph crosses the x-axis at 1. When, you enter an a value of 8, it will have a root of 1.
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I need to find the perimeter and area of the regular polygon.
mezya [45]
The area of a polygon is given by the formula Area = ap/2 where a is the length of the apothem and p is the perimeter. The apothem is a line from the center of the polygon perpendicular to a side.

Depending on the formula you know, you can find the length of a side in 1 of 2 ways. 

The first way uses a triangle. Using the radius of the polygon you can create 8 congruent triangles. The center angle will be 360 / 8 = 45 and two side lengths of 20. You can find the length of the base using the law of cosines.

c^2 = 20^2 + 20^2 - 2(20)(20)(cos 45)
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The second way is to use this formula:
r = s / (2 sin(180 / n))
20 = s / (2 sin(180/8)
(20)(2)sin(22.5) = s
(40)sin(22.5) = s
s = 15.31

We need to calculate the perimeter. As there are 8 sides (8)(15.31) = 122.48
Now we need to calculate the apothem using

a = S / (2 tan (180 / n)
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Area = 1131.72

perimeter = 122.48
area = 1131.72
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2 years ago
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