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Math Equations and Geometry Questions Explained

Learn how to calculate total costs, solve equations, and understand geometric similarity and proportions with step-by-step examples and explanations. Perfect for math students seeking clarity.

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Math Equations and Geometry Questions Explained

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  1. If the rate of tax is 7%, find the total cost of a television that sells for $750. Warm up Tax: ($750) (0.07) = $52.50 Final Cost: $750 + $52.50 = $802.50 Boiled shrimp sells for $9.25 a pound. Write an equation that describes the total cost (T) is someone buys (P) pound of shrimp. T=$9.25P

  2. Similarity – sides are proportional and angles are congruent. 10 8 5 4 6 3 Scale factor is 2 : 1

  3. A tree is 32 feet tall. The tree casts a shadow of length 24 feet. If the shadow of a motel is 60 feet in length, how tall is the motel?

  4. Tree: 32 24 Motel: x 60 A tree is 32 feet tall. The tree casts a shadow of length 24 feet. If the shadow of a motel is 60 feet in length, how tall is the motel?

  5. A 42-foot tree casts a 27-foot shadow. At the same time, a flagpole casts a shadow 9 feet long. What is the flagpole’s height?

  6. Tree: 42 27 Flagpole: x 9 A 42-foot tree casts a 27-foot shadow. At the same time, a flagpole casts a shadow 9 feet long. What is the flagpole’s height?

  7. Which of the following is a true statement?A. ∆PQR =∆STUB. ∆PQR ≈ ∆STUC. ∆PQR is both similar & congruent to ∆STUD. ∆PQR is neither similar nor congruent to ∆STU. R U 3 4 8 6 S T 3 P 9 Q Answer: D

  8. A 32 B 40 C x E 54 D

  9. A 6 B 12 C 7 E x D

  10. The sheet of paper on the left is a reduced copy of the original. What is the length of the copy to the nearest tenth of an inch? 8.5 in. 6 in. 11 in. x in.

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