jugoslav

The possible lengths OP are 5, 11.

AB / CE = AF / FC = BF / FE

AB and CD are parallel

Let the midpoint of arc AB be G         

CG is a diameter

1/3 = 3/9

3/9 + 5/9 = 8/9

He sold 1/9 of the fruits.

In the diagram, angle U = 30, arc XY is 170, and arc VW is 110. Find arc WY, in degrees.

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arcVX + arcWY = 360 - (arcXY + arcVW)

∠U = 1/2(arcWY - arcVX)

Darius sold 50 milkshakes while working at Cool Treats. 40% of the milkshakes were vanilla. The rest were chocolate. After Darius sold some more vanilla milkshakes, the percentage of chocolate milkshakes decreased to 5%. How many more vanilla milkshakes did Darius sell?

decreased to and decreased by have a different meaning

...the percentage of chocolate milkshakes decreased to 5% (from 60%)

So, Darius sold 95% vanilla milkshakes and 5% chocolate milkshakes.

5% / 30 = 95% / x            x = 570

Darius sold 550 more vanilla milkshakes.

This question doesn't make much sense because the length of line segments MP, PQ, and QM depend on the height of trapezoid ABCD. I'll make some changes in red ink.

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Let ABCD be a trapezoid with midsegment MN, and suppose the diagonals split MN into three segments MP, PQ, and QN. If AB = 8, CD = 12, and AD = BC = 10, find the lengths of the midsegment MN and the three segments MP, PQ, and QN.

The ratio of apples Andrew, Ben, and Declan had was 3 : 8 : 4. When Ben gave 21 apples to Andrew and Declan, all of them have the same number of apples in the end. How many apples did Ben have at first?

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A : B : D = 3 : 8 : 4

3x + 4x +21 = 2(8x - 21)

x = 7

8x = 56

Ben had 56 apples  

AH = 5

[ABCD] = 24

[AFCH] = 24 - (3 * 4) = 12

EF = 12 / 5 = 2.4

EH = 5 - sqrt(3² - 2.4²) = 3.2

[EFGH] = 2.4 * 3.2 = 7.68 units squared

YZ = XZ

8x - 5 = 6x + 10         x = 7.5

XY = 10x - 10

XY = 65

YZ = XZ

8x - 5 = 6x + 10         x = 7.5

XY = 10x - 10

XY = 65