Study Guide and Review
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- Antony Maxwell
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1 Choose the term that best matches the statement or phrase. a square of a whole number A perfect square is a square of a whole number. a triangle with no congruent sides A scalene triangle has no congruent sides. decimals that do not repeat or terminate Decimals that do not repeat or terminate are called irrational numbers. the sides of a right triangle that are adjacent to the right angle The sides of a right triangle that are adjacent to the right angle are called legs. the angle measures are different, all the sides are different lengths as well. the side opposite the right angle in a triangle The side opposite the right angle is called the hypotenuse. sides of a figure that have the same length Sides of a figure that have the same length are congruent. the point at which two sides of a triangle intersect The vertex is the point at which two sides of a triangle intersect. used to indicate a positive square root A radical sign is used to indicate a positive square root. esolutions Manual - Powered by Cognero Page 1
2 Find the square root. = 13 = 5 = 1 = 22 Estimate the square root to the nearest integer. Do not use a calculator. The first perfect square less than 15 is 9. The first perfect square greater than 15 is 16. The square root of 15 is between the integers 3 and 4. Since 15 is closer to 16 than to 9, The first perfect square less than 52 is 49. The first perfect square greater than 52 is 64. The negative square root of 52 is between the integers 7 and 8. Since 54 is closer to 49 than to 64, to 7 than to 8. The first perfect square less than 90 is 81. The first perfect square greater than 90 is 100. The negative square root of 90 is between the integers 9 and 10. Since 90 is closer to 81 than to 100, closer to 9 than to 10. esolutions Manual - Powered by Cognero Page 2
3 The first perfect square less than 415 is 400. The first perfect square greater than 415 is 441. The square root of 415 is between the integers 20 and 21. Since 415 is closer to 400 than to 441, 20 than to 21. Name all of the sets of numbers to which the real number belongs. Write whole, integer, rational, or irrational. 18 Since 18 =, this number is a rational number. So, 18 is a whole number, an integer, and a rational number. is written as a fraction, so it is a rational number. cannot be written as a fraction, so it is an irrational number. Since, this number is a rational number. with <, >, or = to make a true statement. = Since,. esolutions Manual - Powered by Cognero Page 3
4 8 = 8.2 = Since 8, Since 11 is to the right of, 11 >. = Since,. Solve the equation. Round to the nearest tenth, if necessary. d 2 = 100 The solutions are 10 and esolutions Manual - Powered by Cognero Page 4
5 4y 2 = 5.76 The solutions are 1.2 and 1.2. GARDENS The formula A r 2 can be used to determine the area of a circle where A is the area and r is the distance from the center of the circle to the outside edge. If the area of a circular garden is 700 square feet, about how far is the distance from the center of the garden to the outside edge? Round to the nearest tenth. To find the distance from the center of the garden to the outside edge, you will need to find the radius of the circle. Substitute 700 for A in the equation A r 2. Since radius is a positive value, the distance from the center of the garden to the outside edge is about 14.9 feet. Find the value of x in the triangle. Then classify the triangle by its angles and by its sides. Angles: The triangle has all acute angles. Sides: The triangle has no congruent sides. The triangle is an acute scalene triangle. esolutions Manual - Powered by Cognero Page 5
6 Angles: The triangle has all acute angles. Sides: The triangle has two congruent sides. The triangle is an acute isosceles triangle. Angles: The triangle has a right angle. Sides: The triangle has two congruent sides. The triangle is a right isosceles triangle. Angles: The triangle has an obtuse angle. Sides: The triangle has no congruent sides. The triangle is an obtuse scalene triangle. esolutions Manual - Powered by Cognero Page 6
7 Classify the yield sign by its angles and by its sides. The yield sign has three congruent sides and therefore has three congruent angles. Because the sum of the angles and three congruent sides. The triangle is an acute equilateral triangle. Find the missing length of the triangle. Round to the nearest tenth, if necessary. Use the Pythagorean Theorem, substituting 30 for a and 40 for b. So, the missing length is 50 inches. Use the Pythagorean Theorem, substituting 5 for a and 6 for b. So, the missing length is about 7.8 feet. esolutions Manual - Powered by Cognero Page 7
8 Use the Pythagorean Theorem, substituting 7 for a and 20 for c. So, the missing length is about 21.2 centimeters. Use the Pythagorean Theorem, substituting 15 for a and 34 for c. So, the missing length is about 37.2 meters. esolutions Manual - Powered by Cognero Page 8
9 On a fast pitch softball diamond, the bases are 60 feet apart. What is the distance from home plate to second base in a straight line to the nearest tenth of a foot? Drawing a straight line from home plate to second base forms a right triangle with legs of 60 feet. Use the Pythagorean Theorem to find the hypotenuse, which is the distance between home plate and second base. The distance between home plate and second base is about 84.9 feet. Find the distance between the pair of points. Round to the nearest tenth, if necessary. G(0, 0), H(3, 4) Use the Distance Formula. The distance between G and H is 5 units. B( 2, 7), C( 5, 7) Use the Distance Formula. The distance between B and C is 3 units. esolutions Manual - Powered by Cognero Page 9
10 J(9, 5), K(0, 4) Use the Distance Formula. The distance between J and K is about 12.7 units. M( 8, 1), N(7, 6) Use the Distance Formula. The distance between M and N is about 16.6 units. esolutions Manual - Powered by Cognero Page 10
11 Find the perimeter of DEF. Round to the nearest tenth. To find the perimeter of DEF, find the sum of the side lengths. Use the distance formula to calculate each side length. The sum of the side lengths is or 15.4 units. So, the perimeter of DEF is 15.4 units. esolutions Manual - Powered by Cognero Page 11
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