CoolStuffYT

5X/7=15

Multiply by 7 on both sides

5X = 105

Divide by 5 on both sides

X=21

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CPHILL! You're back! I haven't been on this site in a while either...

Multiply by 12xy to remove all denominators

12y+12x=xy

So we have xy-12x-12y=0

Add 144

xy-12x-12y+36 = (x-12)(y-12)=144

Note that we can't have 12*12 but we can have 16*9

So x-12 = 16 and y-12 = 9 and x=28, y = 21.

x+y=49

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Since J is between H and K, then HJ + JK = HK.

That means 4x+7+5x-8=53.

Solving gets 9x-1 = 53, so 9x = 54, so x = 6.

That means the length of JK is 5*6-8 = 22.

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Say the side length of hexagon = 1, so perimeter = 6. The circumference of circle must be 6, so the radius is 2 * pi * r = 6 and r = 3/pi.

The area of the hexagon is 3sqrt(3)/2 by the formula (or draw 6 equliateral triangles). The areae of circle is 9/pi.

The ratio of hexagon to circle is (3sqrt(3)/2)/(9/pi) = (3sqrt(3) * pi) / (18) = (sqrt(3) * pi) / 6.

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The arc is 120/360 = 1/3 around the circle. So the chord makes a triangle with 30-30-120 angles and sides radius, radius, 8 in.

Split this in the middle of the 120 angle to form two 30-60-90 triangles. The side lengths for the triangle are 4/sqrt(3), 4. The area is 8/sqrt(3), and since there are two the area is 16/sqrt(3) = 16sqrt(3)/3.

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Teh largest 3-digit base 10 number is 999. You take the biggest number and put it in all values.

The largest 3-digit base 14 integer is DDD. This in base 10 is 14^2 * 13 + 14 * 13 + 13 = 2743.

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45 > 12t + 3t - 24 - 6

45 > 15t - 30

75 > 15t

5 > t

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There were 20% * 100 = 20 more boys, and 18% * 50 = 9 more girls, so in total 29 more students got on the honor roll. From 150 to 179, the percentage is 29/150 = 19.3%.

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Start simplifying on each side of numerator and denominator. For example, the first numerator is factored to (3x-7)(x+3).

Then cancel out terms.