Questions in mathematics

Questions in mathematics

[Done] What is the solution to the equation? \[ 5(8 + 7) = 5 \cdot x + 5 \cdot 7 \] A. \( x = 1 \) B. \( x = 5 \) C. \( x = 7 \) D. \( x = 8 \)

[Done] The waiter places a bowl of soup in front of Igor. In a counterclockwise direction, he passes the soup to Elan who then passes it to Abbey. Which two rotations about the center of the table describe passing the soup? A) first 80° and then 80° B) first 120° and then 120° C) first 144° and then 144° D) first 160° and then 160°

[Done] A survey of 80 sophomores at a certain western college showed that: - 36 take English - 32 take History - 32 take Political Science - 16 take both History and English - 16 take both Political Science and History - 14 take both Political Science and English - 6 take all three courses How many students: 1. Take English and neither of the other two? 2. Take none of the three courses? 3. Take History but neither of the other two? 4. Take Political Science and History but not English? 5. Do not take Political Science?

[Done] Movie tickets cost $7 for students and $9 for adults. A group of 8 people spent $66 on movie tickets. How many adult tickets were bought?

[Done] A sequence is defined recursively by \( f(1) = 16 \) and \( f(n) = f(n-1) + 2n \). Find \( f(4) \). 1) 32 2) 30 3) 28 4) 34

[Done] 22 . The figure is reflected across line m and then reflected across line n. What is the resulting transformation? A) glide reflection B) rotation C) reflection D) translation 24 . The waiter places a bowl of soup in front of Abbey. In a counterclockwise direction, she passes the soup to Kai who then passes it to Haifa. Which two rotations about the center of the table describe passing the soup? A) first 72° and then 108° B ) first 40° and then 60° C) first 80° and then 120° D) first 60° and then 90° 25. The waiter places a bowl of soup in front of Lacy. In a counterclockwise direction, she passes the soup 90°. The person receiving the soup passes it 30°. After the two passes, the soup is in front of which person? A) Garret B) Darcy C) Igor D) Haifa 28. What are the coordinates of the vertices of the triangle under the translation (x, y) ---> (x - 1, y - 3) A) (0, -8), (-1, -1), (-5, -4) B) (-8, 0), (-1, -1), (-4, -5) C) (5, -4), (0, 0), (5, 4) D) (-4, 5), (0, 0), (4, 5) 29. What is the reflection image of P(0, 0) after two reflections, first across x = -3 and then across y = 4? A) (-8, -6) b) (4, -3) C) (4, -6) D) (-6, 8)

[Done] The commission for selling a house is $11,825, which is 5.5% of the selling price. What is the selling price of the house?

[Done] What is \((x-5)(x+5)\)?

[Done] Preparing for a visit to London, a New York resident exchanged 3,500 U.S. dollars for British pounds. If the exchange rate was 125 U.S. dollars for 1 British pound, how many British pounds did the traveler receive?

[Done] Find the exact value of \(\cos(135^\circ + 30^\circ)\).