Mathematics

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• Three parallels
  The vertices of an equilateral triangle lie on 3 different parallel lines. The middle line is 5 m and 3 m distant from the end lines. Calculate the height of this triangle.
• An animal shelter
  An animal shelter spends $5.50 per day to care for each bird and $8.50 per day to care for each cat. Nicole noticed that the shelter spent $283.00 caring for birds and cats on Wednesday. Nicole found a record showing that there were a total of 40 birds and
• Land boundary
  The land has the shape of a right triangle. The hypotenuse has a length of 30m. The circumference of the land is 72 meters. What is the length of the remaining sides of the land boundary?
• Parallels and one secant
  There are two different parallel lines a, b and a line c that intersect the two parallel lines. Draw a circle that touches all lines at the same time.
• Circular railway
  The railway is to interconnect in a circular arc the points A, B, and C, whose distances are | AB | = 30 km, AC = 95 km, BC | = 70 km. How long will the track from A to C?
• Flowerbed
  We enlarge the circular flower bed, so its radius increased by 3 m. The substrate consumption per enlarged flower bed was (at the same layer height as before magnification) nine times greater than before. Determine the original flowerbed radius.
• A rectangle 2
  A rectangle has a diagonal length of 74cm. It’s sides are 5:3. Find its lengths.

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