Bosco

At the city museum child museum child admission is 5.70 and adult admission is 9.30 on Saturday three times as many adult tickets as child tickets were sold for a total of 1075.20 how many child tickets were sold that day     

9.30  =  cost of one adult ticket     

5.70  =  cost of one child ticket     

A  =  number of adult tickets sold  =  3C     

C  =  number of child tickets sold     

(A • 9.30)   + (C • 5.70)  =  1075.20     

(3C • 9.30) + (C • 5.70)  =  1075.20     

27.90A + 5.70A  =  1075.20     If the decimal points throw you off, remove them all,

                                                 just remember to put one back in the final answer.     

33.60C  =  1075.20     

         C  =  32                           Child tickets sold that Saturday     

_.     

When Lara was 13 years old, she weighed 38 kg.     
Two years later, her weight increased by 10%.     
Find Lara's weight when she was 15 years old.     

At age 13 Lara weighed 38 kg     

Her weight increased by10%                   10% of 38 kg     

                                                                  0.10 x 38 kg = 3.8 kg     

To find Lara's weight after the increase,     

add the increase to her original weight      38 kg + 3.8 kg  =  41.8 kg     

_.     

     The figure below consists of a rectangle and a right triangle.     

     What is the area of the shaded region?     

     A_rectangle  =  7 • 8     

     A_rectangle  =  56     

     A_triangle  =  (1/2) • 4 • 4     

     A_triangle  =  8     

     A_shadedarea  =  A_rectangle – A_triangle     

     A_shadedarea  =  56 – 8     

     A_shadedarea  =  48     

_.     

Josie's friend is skinnier than a fashion model.     

A.  No.  Hyperbole is exaggerated statements or claims not meant to be taken literally.     

              Josie's friend could easily be skinnier than a fashion model.     

B.  No.  Personification is the attribution of a personal nature or human characteristics     

             to something nonhuman.  Neither Josie nor Josie's friend is nonhuman.     

             All that leaves is C. Neither for the answer.     

_.     

               y  =  (180 – 75)     

               y  =  105     

     (4x–17)  =  180 – 105     

              4x  =  92     

                x  =  23     This is not the size of the angle, it's only what x equals.     

                                  The angle equals 180 – 105 = 75.     

_.     

3 yards of cotton and 12 yards of denim cost 45 dollars. On the other hand, 5 yards of cotton and 8 yards of denim cost 51 dollars. What is the price of a yard of each?     

3C + 12D  =  45     (eq 1)     

5C +   8D  =  51     (eq 2)     

multiply both sides of     

(equation 2) by 3                        15C +  24D  =  153     

multiply both sides of     

(equation 1) by 2                          6C + 24D  =     90     

subtract                                         9C            =     63     

                                                                  C  =  7     

substitute 7 back into     

(equation 1)                               (3)(7) + 12D  =  45     

                                                      21  +  12D  =  45     

                                                                 12D  =  24     

                                                                     D  =  2     

.    

The 3rd angle in the big triangle  =  180 – (70 + 74)     

                                                     =  36     

                                                 y  =  180 – (36 + 78)     

                                                 y  =  66^o     

                                                 x  =  180 – (66 + 90)     

                                                 x  =  24^o     

_.     

Find the vertex of the parabola y = 2x^2 + 10x + 8     

                                                  y  =  2x² + 10x + 8     

take the 1st derivative               y'  =  4x + 10     

set it equal to zero                     4x + 10  =  0     

                                                           4x  =  –10     

                                                             x  =  –2.5     this is the x-coordinate     

find y when x = 2.5                     y  =  (2)(–2.5²) + (10)(–2.5) + 8     

                                                   y  =  12.5 – 25 + 8     

                                                   y  =  –4.5     this is the y-coordinate     

the vertex is at                           (–2.5 , –4.5)     

_.     

Felicia has a ladder that is 11 ft long. She wants to lean the ladder against a vertical wall so that the top of the ladder is 9.5 ft above the ground. For safety reasons, she wants the angle the ladder makes with the ground to be no greater than 75°. Will the ladder be safe at this height? Show all your work and draw a diagram to support your answer.     

The wall is the opposite end of a right triangle.     

The ladder is the hypotenuse of that triangle.     

sine = opposite / hypotenuse     

sine of angle with ground  =  9.5 / 11     

                                          =  0.86364     

sine^–1 (0.86364)  =  59.7^o  call it 60^o   so, yes the ladder will besafe     

_.     

The ceiling of Xavier’s living room is a square that is 12 ft long on each side. To decorate for a party, he plans to hang crepe paper around the perimeter of the ceiling and then from each corner to the opposite corner. Xavier can buy rolls that each contain 10 ft of crepe paper. What is the minimum number of rolls he should buy? Show all your work.     

Needed for perimeter  =  4 • 12  =  48 ft     

Needed for diagonals  =  2 • 12 • sqrt(2)  =  33.94 ft     call it 34 ft     

Total crepe paper needed  =  48 + 34  =  82 ft     

Xavier needs to buy 9 rolls of crepe paper to have enough.     

_.