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   The center of the circle with equation x^2+y^2=4x-12y-39 is the point (h,k). What is h+k?     

                              x² + y²  =  4x – 12y – 39     

   rearrange to       x² – 4x + y² + 12y  =  – 39     

   group as             (x² – 4x     ) + (y² + 12y     )  =  – 39     

   complete sqs      (x² – 4x + 4) + (y² + 12y + 36)  =  – 39 + 4 + 36     

                              (x – 2)²   +   (y + 6)²  =  1     

                              h + k  =  (– 2) + (+6)  =  4     

   _.     

   What is the area of triangle ABC if AB = BC = 12 and angle ABC = 128?     

   Drop a perpendicular from the apex down to side AC. Call the intersection point "D".     

   Since this is an isoceles triangle, the perpendicular bisects both AC and angle ABC.     

   DC / BC  =  sin (64^o)     

   DC / 12   =  0.89879     

   DC  =  12 • 0.89879     

   DC  =  10.78548       this is half the base     

   BD / BC  =  cos (64^o)     

   BD / 12   =  0.43837     

   BD  =  12 • 0.43837     

   BD  =  5.26044          this is the height     

   Area  =  (1/2) • base • height     

   Area  =  10.78546 • 5.26044     

   Area  =  56.736     round to  57     

   _,     

   The six faces of a three-inch wooden cube are each painted red.     

   The cube is then cut into one-inch cubes along the lines shown in the diagram.     

   How many of the one-inch cubes have red paint on at least one face?     

   All of them except the one buried in the very center.  ==>  26     

   _,

A toilet paper company sells rolls of toilet paper where the cardboard portion in the middle has a diameter of 1.8 inches and a height of 3.75 inches. How many square inches of cardboard would there be in a package of 24 rolls of toilet paper? Round your answer to the nearest roll.     

      A_{ONE ROLL}  =  Circumference times Length     

                       =  (3.1416) (1.8 inch) (3.75 inch)     

                       =  21.2058 in²     

      A_{24 ROLLS}   =  (24) (21.2058 in²)     

                       =  508.9392 in²  rounds to  509 in²     

   _.     

   Divide £10 in the ratio of 3:2     

   3 + 2  =  5     

   10 / 5 =  2     

   3 x 2  =  6     

   2 x 2  =  4     

   ans    =  6 : 4     

   _.     

   an igloo has a volume of 3.6m. find the height     

   Volume_SPHERE  =  (4/3) π r³     

               2 • 3.6  =  (4/3) • 3.1416 • r³     —>     r³  =  7.2 / 4.1888     

                                                                           r³  =  1.7189     

                                                                           r    =  1.1979     

                                                                           assuming the igloo     

                                                                           is a hemisphere     

   .     

   diana is walking to a campsite the campsite is 5/8 mi away and they are walking 2 and 1/2 mi/h     

   how many minutes will it take her to get to the campsite?     

       ⁵/₈ mi                ⁵/₈ mi                5 mi         2 hr     

    –––––––––   =   –––––––––   =   –––––  x  –––––   =   ²/₈ hr   =   ¹/₄ hr   =   15 min     

     2¹/₂ mi/hr           ⁵/₂ mi/hr               8            5 mi     

   _.     

   what is 3.48 x 10 to the power of -5     

   3.48 x 10^–5  =  0.0000348     

   The minus five means move the decimal point five places to the left.     

   _.     

   how do I write a quadratic equation with only one nonzero root?     

   Make both terms the same.   examples:   (x – 5)(x – 5)  =  x² – 10x + 25     

                                                                     (x + 8)(x + 8)  =  x² + 16x + 64     

   I think it's just semantics whether you say there's only      

   one root, or say there are two roots that are the same.     

   ^.     

   Find the coefficient of z in the product  (-3z^2 - 7z + 4)(6z^2 + 6z - 1).     

   (–3z² – 7z + 4) (6z² + 6z – 1)    —>    (– 7z) • (– 1) =  +   7z  —>    7     

   (–3z² – 7z + 4) (6z² + 6z – 1)    —>    (+ 4) • (+ 6z) =  + 24z  —>  24     

                                                                                          total  —>  31     

   _.     

     Three vertices of a rectangle in the standard (x,y) coordinate plane have the    

     coordinates (-2,3), (4,3) and (4,2).  What are the coordinates of the fourth vertex?     

     (–2, 2)       The right hand side is (4,2) to (4,3), i.e., 1 unit long.     

                       So, the left hand side has to be 1 unit long, too.     

   _.     

   Solve for x. Round to the nearest tenth     

   sine = opposite over hypotenuse     

   sin (29^o)  =  12 / x     

   0.48480962  =  12 / x     

   0.48480962 • x  =  12     

                         x  =  12 / 0.48480962     

                         x  =  24.752  rounds to  24.8     

   _.     

   The graph of the equation y=-2+5 will intersect the y-axis when y equals what value?     

   y=3 is a straight horizontal line.     

   It intersects the y-axis at y = 3.     

   Anything it intersects is at y= 3.     

   _.     

   your mom has offered you 2 options for your allowance. she will either give you $60 a month until     

   you turn 18 or a penny for for the number of days old you are every month until you are 18.     

   To get $60.00 at 1¢ per day, you need to be 6,000 days old.     

   6,000 days / 365 days/yr  =  16.438 yr     

   So, when you're less than ~ 16¹/₂ years old, the $60.00 is the better deal.     

   But, when you're ~ 16¹/₂ years old or older, the pennies is the better deal.     

   Of course, you'd have to shlep 6,000 pennies down to the bank every time.     

   _.     

   what is 0 divided by 0     

   It is largely agreed that, in lower mathematics, 0 / 0 equals 1.     

   But, in calculus, they call 0 / 0 "undefined" or "indeterminate"     

   by which I think they mean they don't know what to do with it.     

   .     

   6,_,_,_,42 answer     

   6,  15,  24,  33,  42       d = 9      

   _.     

   the perimeter of rectangle is 52 inches the length is 9 inches.What is its width? let w= the rectangle's width     

   (2 • L) + (2 • W)  =  P_ERIMETER     

   (2 • 9) + (2 • W)  =  52     

              18 + 2W  =  52     

                      2W  =  34     

                        W  =  17     

   _.