Bosco

Use the substitution method . . . 13x - 2y = 70 2x - 2y = 4     

13x – 2y = 70     

  2x – 2y =   4     —>  –2y =  4 – 2x     

                                    2y  =  2x – 4    <—  substitute this into the other equation     

13x – (2x – 4 )  =  70     

 13x – 2x + 4     =  70     

                  11x  =  66     

                      x  =  6     

            2x – 2y  =  4     

            12 – 2y  =  4     

                  –2y  =  –8     

                      y  =  4     

check answer     

Does  (13)(6) – (2)(4)  equal 70 ?      

               78   –   8  =  70   true     

_.     

How many y-intercepts does the graph of the parabola x = -y^2 + 4y - 4 - 2y + 7 have?     

                                                               x = -y^2 + 4y - 4 - 2y + 7     

simplify equation, combine terms          x  =  –y² + 2y +3     

when the curve crosses the y-axis,     

that means that x = 0, so set x to 0        –y² + 2y + 3  =  0     

it will factor                                            (–y + 3)(y + 1)  =  0     

                                                               (–y + 3)  =  0     ——>>  y = +3     

                                                               (  y + 1)  =  0     ——>>  y = –1     these two values are the y-intercepts     

So the answer to "how many" is 2     

_.     

Point  A lies somewhere within or on the square which has opposite corners at (0,0) and (2,2) . Point B  lies somewhere within or on the square which has opposite corners at points (4,2) and (5,3) . What is the greatest possible value of the slope of the line containing points A and B ? Express your answer as a common fraction.     

                          m  =  (y₂ – y₁) / (x₂ – x₁)     

                          m  =  (3 – 0) / (4 – 2)     

                          m  =  3 / 2     

                          m  =  1.5     

                          Just draw both squares on some graph paper and it's obvious that the steepest line is     

                          one drawn from the bottom right corner of the large square to the top left corner of the     

                          small square.     

_.     

The admission fee at an amusement park is $1.25 for children and $6.40 for adults. On a certain day, 325 people entered the park, and the admission fees collected totaled 1050 dollars. How many children and how many adults were admitted?     

A_dults + C_hildren  =  325      ——>>     A  =  325 – C     

6.40A + 1.25C  =  1050     substitute (325 – C) for A in this equation     

(6.40)(325 – C) + (1.25)(C)  =  1050     

        2080 – 6.40C + 1.25C  =  1050     

                               – 5.15C  =  – 1030     

                                         C  =  200     

                                         A  =  325 – C     

                                         A  =  325 – 200     

                                         A  =  125     

check answer     

Does (6.40)(125) + (1.25)(200)  =  1050 ?     

                    800  +  250             =  1050  true     

_.     

Tim is 4 years older than one-third of Juan's age.     

In 10 years, Juan will be 6 years older than twice as old as Tim is now.     

How old is each now?      

  T  =  4 + (1/3) J           —>>     3T  =  12 + J     (eq 1)     

  J + 10  =  6 + (2) T      —>>     2T  =    4 + J     (eq 2)     

  subtract (eq 2) from (eq 1)         T  =  8     

  substitute 8 for T in (eq 1)        24  =  12 + J     

                                                     J  =  12     

  check answers     

  8  =?  4 + 4         12 + 10  =?  6 + 16     

  8  =  8   true                22  =  22   true     

_.     

A quiz has four multiple-choice questions; each question is either true or false. How many different solution keys are possible?     

Each question has two possible answers, True or False     

Q1 has 2 possible answers – so, if there's only one question, there are 2 possible solution keys     

Q2 has 2 possible answers – so, with the previous question, there are 4 possible solution keys     

Q3 has 2 possible answers – with the previous 2 questions, that makes 8 possible solution keys     

Q4 has 2 possible answers – with the other 3 questions, there can be a possible 16 solution keys     

_.     

  Select the three expressions below that result in a negative solution. Group of answer choices     

  A)  (-7) + (-9)       B)   -3 - 6       C)   9 + (-8)       D)  (-2) - (-8)       F)  9 + (-12)      

  A)   =  – 16     

  B)   =  – 9     

  C)   =  + 1     

  D)   =  + 6     

  F)   =  – 3     

What happened to E) ?     

_.     

    A rectangular piece of paper with length 35cm and width 16cm has two semicircles cut out of it, as shown below.     

    Find the area of the paper that remains. Use the value 3.14 for π.     

    A  =  (35 • 16) – (2)(¹/₂ • 3.14)(8²)     

    A  =  560 – 200.96     

    A  =  359.04 cm²     

_.