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Amiraneli [1.4K]
3 years ago
13

Solve the quadratic equation. 2x2 + 35 = 17x

Mathematics
1 answer:
atroni [7]3 years ago
8 0
Get it to equal 0

minus 17x from both sides

2x²-17x+35=0

tricky part
get something like
(2x-a)(x-b)
we know the signs  are negative since the middle term is negative and last term is positive

so a and b are either 1 and 35 or 5 and 7

(2x-1)(x-35), nope
(2x-35)(x-1) nope
(2x-5)(x-7), nope
(2x-7)(x-5), yep

(2x-7)(x-5)=0
set to zero
2x-7=0
2x=7
x=7/2

x-5=0
x=5


x=7/2 and 5
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Answer:

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Step-by-step explanation:

Part A>

The apotherm of a regular polygon is the distance of the line segment from the centre of the polygon to the midpoint of a side.

2 radii of this decagon joined to the endpoints of a side form an isosceles triangle with equal sides = 14 cm.

The apotherm is the altitude of this triangle.  The  vertex of the triangle  has an angle of 360 / 10 = 36 degrees and the apotherm bisects this angle.

So using trigonometry on the right triangle formed:

cos 18 = x / 14   where x is the apotherm.

x = 14 cos 18

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Part B.

Using trigonometry on the right triangle again:

sin 18 = x/2 / 14     (where x is the length of a side of the hexagon)

x/2 = 14 sin 18

x = 2 * 14 sin 18

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As a decagon has 10 sides the perimeter = 8.652 * 10

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https://www.mathsteacher.com.au/year8/ch06_ratios/03_inc/Image13125.gif

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