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Hint |
3) In the big 3 x 3 square, what is the ratio of the shaded four
triangles to the unshaded octagon in the middle of the square?
The octagon is not regular but is a truncated square. All line
segments are intended to be straight.
Please note: The unshaded figure inside the 3x3 square has cutoff corners making it an octagon (they are small cutoffs). Also, all the small squares are of the same size.
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- You have to look close, but what looks like a white square in the middle of the 3x3 larger square actually has litle sides that cut off the corners, making it an octagon.
- Consider the squares in the lower right corner. The shaded triangle that is inside that 2x2 square is _______ of the area of the 2x2 square.
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- At this point we must assume the small squares of that 2x2 square are the same size as the squares in the larger 3x3 square.
- Therefore the 4 shaded triangles are ______ squares in area
- The larger 3x3 square is ______ squares in area.
- Therefore the unshaded octagon is ______ squares in area.
- The ratio of shaded areas to the unshaded areas is ______
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4) The line given by the equation y = 3x - 3 is translated 3 units up and then reflected across the line y = 0. What is the equation of the new line?
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- To translate an equation up 3 units (in y) is to add 3 units to y: _____________
- To reflect an equation across the y axis (y=0) is to negate the x value: _____________
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5) A circular cone can be created by joining the two straight
edges of the shown section of a circle with central angle 135 degrees and radius 5 centimeter. What is the diameter of the created cone? (The diameter of a cone is the diameter of the circular opening where it is the widest.)
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- The length of the circle section is
_______ cm.
- When you make this into a cone, this length becomes the circumference of the base, so the diameter is:
_________ cm.
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