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   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)     

   _.     

You have two coordinates. Let's call (-1,-3) as P and (2,-2) as Q.

• First let's find the slope of the line PQ
• \(\text{Slope}= \frac{y_Q-y_P}{x_Q-x_P}=\frac{(-2)-(-3)}{(2)-(-1)}=\frac{-2+3}{2+1}=\frac{1}{3}\), we can interpret this as, for every 3 units of x, y changes 1 unit.

Now we can represent the line PQ as \(y=\frac{1}{3}x+b\), where b is the y-intercept of the line (when x=0).

To find the value of b, we can take one of the coordinates and add into our function, example:

• \(\begin{align} y &= \frac{1}{3}x+b\\ -2 &= \frac{1}{3}\cdot 2 + b\\ b &= -2 - \frac{2}{3}\\ b &= -\frac{8}{3} \end{align}\)

Then we can conclude that we can express the line PQ that passes through P and Q as \(y=\frac{1}{3}x-\frac{8}{3}\)

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     

   _.     

   The legs of a right triangle measure 6 inches and 9 inches.     

   If Xis the angle between the 6-inch leg and the hypotenuse, sinX=     

   a² + b² + c²     —>     hypotenuse²  =  6² + 9²     

                                                            =  36 + 81     

                                                            =  117     

                                       hypotenuse  =  sqrt(117)     

   sine equals opposite over hypotenuse     

   sin(x)  =  9 / sqrt(117)         The convention is not to leave a radical in the denominator.     

   sin(x)  =  9 • sqrt(117) / (sqrt(117)(sqrt(117)     

   sin(x)  =  9 • sqrt(117) / 117                             9 will evenly divide 117     

   sin(x)  =  sqrt(117) / 13     

   _.

   A 30 foot ladder leaning against a vertical wall makes an angle of 81degree with the ground.     

   How far from the base of the wall is the foot of the ladder?     

   cosine = adjacent over hypotenuse     

          cos ( 81^o )  =  x / 30 ft     

     0.156434465  =  x / 30 ft     

                         x  =  (0.156434465) • 30 ft     

                         x  =  4.693 ft     

   _.     

Given points P(-2,7) and Q(4,y) in a coordinate plane, for what value of y is the slope of the line through P and Q equal to 2/3?     

             y₂ – y₁     

   m  =  –––––––     

             x₂ – x₁     

    2         y₂ – 7     

   ––  =  –––––––     

    3        4 – (–2)     

   crossmultiply     

   (3)(y₂ – 7)  =  (2)(4 + 2)     

    3y₂ – 21    =  8 + 4     

              3y₂  =  33     

                y₂  =  11     

   _.

   The proper divisors of 12 are 1, 2, 3, 4 and 6.     

   A proper divisor of an integer N is a positive divisor of N that is less than N.     

   What is the sum of the proper divisors of the sum of the proper divisors of 280?     

   The proper divisors of 280 are    1,   2,   4,   5,   7,     

                                                       8, 14, 20, 28, 35,     

                                                     40, 56, 70, & 140           Sum  =  440     

   The proper divisors of 440 are    1,   2,   4,   5,   8,     

                                                     10, 11, 20, 22, 40,     

                                                     44, 55, 88, 110, & 220    Sum  =  640     

   _.     

Three times the result of subtracting a certain number from 7 gives the same answer as adding eleven to the number. find the number     

     x + 11  =  3 • (7 – x)     

     x + 11  =  21 – 3x     

   4x + 11  =  21     

           4x  =  10     

             x  =  2.5     

   check answer     

     x + 11  =  3 • (7 – x)     

  2.5 + 11  =  3 • (7 – 2.5)     

        13.5  =  3 • 4.5     

        13.5  =  13.5   True     

   _.     

   Lindsay has 20 pip cleaners, each measuring 8 inches.     

   She attaches them end to end to build a frame.     

   Determine the greatest area that can be enclosed by the frame.     

   It helps when you know that the area of a     

   rectangle is maximized when it's a square.     

   So use 1/4 of the pipe cleaners for each side of the square.     

   That forms a square that's (5 x 8 = 40) inches on each side.     

   The area of a square =  s² where s is the length of one side.     

   A  =  (40 inches)²  =  1600 in²     

   _.     

   how do u find a surface area of a sphere     

   Use the formula   A  =  4 π r²   where r is the radius.     

   _.   

Inversely proportional means that 

y = k/x        when x = 1 and y = 2  this becomes 

2 = k/1      which shows k = 2 

so the relationship is then    y = 2/x 

     then when x = 2     

              y =  2/2

              y =1 

   A guy wire to a tower is 180 ft long and makes an angle of 34 degrees.     

   If the ground it level, how far from the base of the tower is the anchor point?     

   cosine =  adjacent over hypotenuse     

   cos( 34^o )  =  x / 180 ft     

       0.8290  =  x / 180 ft     

                x  =  (0.8290) • 180 ft     

                x  =  149.22 ft     

   .     

   calculate 1oo to the power of .3 and how is this accomplished on a scientific calculator?     

   I get  3.98 • • •  a little more than that.     

   You have to use the y^x key.  The sequence for this problem is:   100   y^x   .3   =     

   _.     

   The variables x and y are inversely proportional.  If x = 1, then y = 2.  And if x = 2, then y = ___.     

   When two variables are inversely proportional, their product is always equal to a constant.     

   Given that when x = 1, then y = 2     

   In this problem, xy = 2 . . . and xy in this proportion must always equal 2.     

   When x changes to 2, then xy must still equal 2 ( y = 2 / x ) and so  y = 1     

   _.     

   The population of a town increased from 3550 in 2005 to 4400 in 2009.     

   Find the absolute and relative (percent) increase.     

   Absolute increase              4400 – 3550  =  850     

   Relative increase               850 / 3550  =  0.239  =  23.9%     

   _.     

   The store is selling lemons at $0.53 each.     

   Each lemon yields about 2 tablespoons of juice.     

   How much will it cost to buy enough lemons to make two 9-inch lemon pies, each requiring half a cup of lemon juice?     

   Two pies, requiring half a cup each, equals 1 cup of juice is needed.     

   My Betty Crocker cookbook says there are 16 tablespoons in 1 cup.     

   At 2 tbsp per lemon, you will have to buy 16 / 2 lemons = 8 lemons.     

                                               8 lemons • 0.53 $ / lemon  =  $ 4.24     

                                               plus sales tax, if applicable     

   _.