Bosco

   The first two terms of a geometric sequence are 9 and 3. What is the fourth term of the sequence?     

   You can use r = ¹/₃ for the common ratio, and then the geometric sequence is 9, 3, 1, ¹/₃     

   _.     

   x2-2x-15     

   What's the question?     

   If you want it factored . . .  x² – 2x – 15  =  (x – 5)(x + 3)     

   _.     

   If the area of a rectangle can be represented by x2 - 25, which could represent its length and width?     

   This could be many rectangles.     

   Here are a couple of examples:     

   rectangle is 10 x 20        10 = 15 – 5   20 = 15 + 5     

                       A = 200       (15 – 5)(15 + 5) = 225 – 25 = 200     

   rectangle is 45 x 55        45 = 50 – 5   55 = 50 + 5     

                       A = 2475     (50 – 5)(50 + 5) = 2500 – 25 = 2475     

   _.     

   Factoring: Difference of two squares:  169y2-144     

   The difference of squares factors as  a² – b²  =  (a + b)(a – b).     

   Your specific example factors as 169y² – 144  =  (13y + 12)(13y – 12).     

   _.     

   how do you find the geometric probability of a square in a square?     

   Without seeing the squares I can't say for sure.     

   But a good guess would be to do the following.     

   Calculate the areas of the inner square and of the outer square.     

   Divide the area of the inner square by the area of the outer square.     

   Say a square has sides 6" long, and inside it another square that has sides 4" long.     

   The area of the inner square is 16 sq in, and the area of the outer square is 36 sq in.     

   A missle hitting the large square has a 16 / 36 chance of landing in the small square.     

   You can reduce the fraction to its lowest terms,        in this example, 4 / 9     

   or complete the division to get the percemtage.        in this example, 44%     

   _.     

   Find the vertex of the graph of the equation y=-2x^2+18x-15.     

                                                y  =  –2x² + 18x – 15     

   Take the first derivative     

   and set it equal to zero     

   and solve for x.                     y'  =  –4x + 18     

                                                         –4x + 18  =  0     

                                                         –4x          =  –18     

                                                                     x  =  4.5     

   Substitute 2.5 back into     

   the original equationn           y  =  –2x² + 18x – 15     

                                                y  =  –2(4.5²) + 18(4.5) – 15     

                                                y  =  –40.5     + 81         – 15     

                                                y  =  25.5     

   Put the two together, vertex at (4.5 , 25.5)     

   _.     

Marsha deposited 10,000​ dollars into a savings account 3 years ago.     

The simple interest rate is ​2%. How much money did she earn in​ interest?     

What would be her new account​ balance?     

             Amt Money at          Interest          Amt Money at     

             Begin of Year           Earned          End of Year     

1^st yr      10,000.00               200.00            10,200.00     

2^nd yr     10,200.00               204.00            10,404.00     

3^rd yr      10,404.00               208.08            10,612.08     

              interest $612.08    balance $10,612.08     

_.     

   With the average square feet per person being 3.5, will 3,000 poeple    

   be able to fit in a building that measures 100 x 100 ft?     

   100 x 100  =  10,000 sq ft available in the building.     

   10,000 sq ft / 3,000 people  =  3.33 sq ft per person,     

   If they absolutely need 3.5 each, 3.33 is not enough.     

   _.     

   Manuel Fraser's bank granted him a single-payment loan of $9,650.00.     

   He agreed to repay the loan in 146 days at an ordinary interest rate of 7.75 percent.     

   What is the maturity value of the loan?     

   The proportion of a year's interest will be 146 / 365     

   Maturity value will  =  (9,650.00) + (0.0775)(9,650.00)(146/365)     

                                  =   9650.00 + 299.15     

                                  =   9949.15     

   _.