Final Exam Prep D The expression ( 2 3 x ) 2 is equivalent to

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1 Final Exam Prep 018 Name: Date: 1. Simplify: 50r s 6. If one factor of 6x + 5x 6 is 3x, the other factor is 3x x + 3. x + 3 x 3. What is 3 expressed in simplest radical form? Written in factored form, the trinomial 3x + 5x is equivalent to (3x + 1)(x ). (3x 1)(x + ). (3x + )(x 1) (3x )(x + 1) 3. The expression written in simplest radical form is The solution to the quadratic equation x + 5x 1 = 0 is 5 ± ± ± 33 5 ± 33. The expression ( 3 x ) is equivalent to 9x. 3x. 1 x + 9x 1 x + 6x 9. What is the solution set of the equation x x 1 = 0? 5. Factor: 5x 9. { ± 3 } { ± 1 }. { ± 5 } { ± 5 } page 1

2 10. If (x 3) = 5, then x is equal to 3 ± 5. 3 ± 5 1. In the accompanying diagram, parallel lines and D are cut by transversal GH at E and F, respectively. If m EF = (3x + 60), find the value of x.. 5 ± 3 ± The roots of the equation x + 7x 3 = 0 are 1 and 3. 1 and 3. 7 ± 73 7 ± In the accompanying diagram, parallel lines and D are intersected by transversal EF at points G and H, respectively. If the measure of angle EG is 3x and the measure of angle HF is 8, find the value of x. 1. Solve for x: 3 x = Solve for x: x = 5 page Final Exam Prep 018

3 16. In the accompanying diagram, parallel lines and D are intersected by transversal EF at points G and H, respectively. If m FG = x + 5 and m FHD = 3x 5, find x. 18. In the accompanying diagram, D, m = 80, and m D = 0. What is m? In the accompanying diagram, O is a straight line, m O = 5x, m OD = 3x + 30, and m DO = x Find the value of x. 17. In the accompanying diagram, transversal RS intersects parallel lines MN and PQ at and, respectively. If m RN = 3x + and m RQ = 7x 16, find the value of x. 0. In the accompanying diagram, D is an exterior angle of. If m = 0, m = x, and m D = 3x. What is the value of x? page 3 Final Exam Prep 018

4 1. In the accompanying diagram of, the measure of exterior angle D is 110 and m = 50. Find m. 3. In the diagram of PQR shown below, PR is extended to S, m P = 110, m Q = x, and m QRS = x + 5x. What is m Q? In the accompanying diagram of, side is extended to If m = x + 30, m = x + 10, and m D = x + 30, what is the value of x?. Which set of numbers can not represent the lengths of the sides of a triangle? {6, 8, 11}. {7, 5, 6}. {7, 18, 11} {9, 1, 19} 5. If the lengths of two sides of a triangle are 6 and 8, the length of the third side may be page Final Exam Prep 018

5 6. In the accompanying diagram of, DEF is formed by joining the midpoints of the sides of. If DE = 9, FE = 18, and DF = 13, what is the perimeter of? 8. In shown below, L is the midpoint of, M is the midpoint of, and N is the midpoint of If MN = 8, ML = 5, and NL = 6, the perimeter of trapezoid MN is In the accompanying diagram of, F, E,, E EF, F = 8, F = 1, FE = 9, and = x. What is the value of x? 9. In the diagram shown of right triangle, m = 90, m = 5, and = 8. What is the length of? If the hypotenuse of a right triangle is 6 and one leg is 5, the other leg is page 5 Final Exam Prep 018

6 31. In a circle, the coordinates of the endpoints of a diameter are (, 5) and (10, 1). What are the coordinates of the center of the circle? 37. The sum of 7 and 1 is 5 3. i 39. 5i 3 3i 5 3. ircle O has center (7, 3) and diameter. The coordinates of are (, ). What are the coordinates of? 38. Using the translation that maps (3, ) to its image (1, 0), what is the image of any point (x, y)? (16, 10). (1, ). (16, ) (1, 10) (x +, y + ). (x, y ). (x +, y ) (x, y + ) 33. What is the distance, in radical form, between the points (, 6) and (8, )? 39. The translation (x, y) (x, y + 3) maps the point (7, ) onto the point whose coordinates are (9, 5). (5, 5). (5, 1) ( 1, 6) 3. Find, in radical form, the length of the line segment joining points (1, 5) and (3, 9). 0. Which shape does not have rotational symmetry? trapezoid. regular pentagon 35. Express the product (3 + i)(1 3i) in a + bi form.. circle square 36. Simplify and express in a + bi form: (1 + 3i) (3 i) 1. letter is chosen at random from the word SPINNER. Find the probability that the letter chosen is an N. page 6 Final Exam Prep 018

7 . n urn contains three red marbles and four blue marbles. One marble is selected at random, its color is noted, and it is returned to the urn. nother marble is then selected. What is the probability the second marble drawn is red? 6. letter is chosen from the eight letters in the word SVNNH. What is the probability the letter is an or an N? If two cards are dealt randomly from a standard deck of 5 cards, what is the probability that they are both red queens? 7. In the accompanying diagram of right triangle, a right angle is at, = 6, and m = 7. Find the length of to the nearest tenth n urn contains four red marbles and five blue marbles. What is the probability of selecting at random, without replacement, two blue marbles? 8. The center pole of a tent is 8 feet long, and a side of the tent is 1 feet long as shown in the diagram below From a standard deck of 5 cards, one card is drawn. What is the probability that it will be either a club or a diamond? If a right angle is formed where the center pole meets the ground, what is the measure of angle to the nearest degree? page 7 Final Exam Prep 018

8 9. Which equation could be used to find the measure of one acute angle in the right triangle shown below? 51. n 8-foot rope is tied from the top of a pole to a stake in the ground, as shown in the diagram below. sin = 5. tan = 5. cos = 5 tan = 5 If the rope forms a 57 angle with the ground, what is the height of the pole, to the nearest tenth of a foot? communications company is building a 30-foot antenna to carry cell phone transmissions. s shown in the diagram below, a 50-foot wire from the top of the antenna to the ground is used to stabilize the antenna. 5. In the diagram below of right triangle JTM, JT = 1, JM = 6, and m JMT = 90. What is the value of cot J? Find, to the nearest degree, the measure of the angle that the wire makes with the ground page 8 Final Exam Prep 018

9 53. s shown in the accompanying diagram, a kite is flying at the end of a 5-meter string. If the string makes an angle of 65 with the ground, how high, to the nearest meter, is the kite? 55. Joe is holding his kite string 3 feet above the ground, as shown in the accompanying diagram. The distance between his hand and a point directly under the kite is 95 feet. If the angle of elevation to the kite is 50, find the height, h, of his kite, to the nearest foot. 5. The angle of elevation from a ship at point to the top of a lighthouse, point, is 3. When the ship reaches point, 300 meters closer to the lighthouse, the angle of elevation is 56. Find to the nearest meter, the height to the lighthouse, [Show or explain the procedure used to obtain your answer.] page 9 Final Exam Prep 018

10 56. The accompanying diagram shows a flagpole that stands on level ground. Two cables, r and s, are attached to the pole at a point 16 feet above the ground. The combined length of the two cables is 50 feet. If cable r is attached to the ground 1 feet from the base of the pole, what is the measure of the angle, x, to the nearest degree, that cable s makes with the ground? 57. tree casts a shadow that is 0 feet long. The angle of elevation from the end of the shadow to the top of the tree is 66. Determine the height of the tree, to the nearest foot. 58. While sailing a boat offshore, Donna sees a lighthouse and calculates that the angle of elevation to the top of the lighthouse is 3, as shown in the accompanying diagram. When she sails her boat 700 feet closer to the lighthouse, she finds that the angle of elevation is now 5. How tall, to the nearest tenth of a foot, is the lighthouse? page 10 Final Exam Prep 018

11 Problem-ttic format version..35 c Educide Software Licensed for use by Melissa Walker Terms of Use at Final Exam Prep 018 1/17/ rs. 3.. D 5. (5x 3)(5x + 3) D D (7, 3) i 9 + i D

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