Bosco

The functions f and h are defined as follows:     

f(x) = (x + 5)/(x - 7)  and h(x) = (x + 5)(x - 7).     

Explain why the functions f and h are not the same function.     

     At first glance, they look alike, sort of, but look closely at f(x)     

     and you'll see that there's a virgule between (x+5) and (x–7),     

     indicating division, but h(x) does not have a virgule.     

     f(x) is a division operation     

     h(x) is a multiplication operation     

_.     

   is -1.75 the same as -5/4, or is it -7/4     

   – 1.75  =  – ⁷/₄ which is another way of writing – 1 ³/₄     

_.     

Find the length AB.     

        sine = opposite over hypotenuse     

        sin(34)  =  29 / AB     

        AB  =  29 / sin(34)     

        AB  =  29 / 0.5592     

        AB  =  51.86     <<——  so the answer is A.     

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Find the area of the region enclosed by the graph of x^2 + y^2 = 4x - 6y + 6.     

                                                    x² + y²  =  4x – 6y + 6     

                                                    x² + y² – 4x + 6y  =  6     

                                                    x² – 4x + y² + 6y  =  6     

                                                   (x² – 4x    ) + (y² + 6y    )  =  6     

                                                   (x² – 4x + 4) + (y² + 6y + 9)  =  6 + 13     

                                                   (x – 2)² + (y + 3)²  =  19     

The standard equation of a circle is (x – h)² + (y – k)²  =  r²     

which means, in our equation, the radius squared equals 19.     

                                                   Area of a circle is π r²     

                                                   A  =  3.1416 • 19     

                                                   A  =  59.69     

_.     

Find the standard equation of the circle defined by the equation x^2 + y^2 +8x - 12y + 43 = 0     

As you may have deduced from the answer choices,

you are going to have to complete those squares.     

The standard equation of a circle is (x – h)² + (y – k)²  =  r²     

 Starting with                                      x² + y² + 8x – 12y + 43  =  0     

Rearrange and add parentheses      (x² + 8x     ) + (y² – 12y     ) + 43  =  0     

You need to add 16 to the x and 36 to the y.     

To keep the equation in balance you have to     

subtract the same amount that you add.     

                                                          (x² + 8x + 16) + (y² – 12y + 36) + 43 – 52  =  0     

                                                          (x + 4)² + (y – 6)² – 9  =  0     

Normally, you would take that 9 over to the right of the equals sign     

but this is the form in which the choices of answer were presented.     

_.     

The second side of a triangular deck is 6 feet longer than the shortest​ side, and the third side is 6 feet shorter than twice the length of the shortest side. If the perimeter of the deck is 48 ​feet, what are the lengths of the three​ sides?     

        Call "s" the shortest side.     Perimeter is the sum of all three sides.     

        48  =  (s) + (s + 6) + (2s – 6)     

        48  =  4s + 6 – 6     

        4s  =  48     –––>>     s  = 12     

        1st side                    =  12 ft     

        2nd side  =  (12+6)  =  18 ft     

        3rd side   =  (24–6)  =  18 ft     

_.     

Find the value of x in the triangle shown below.     
x=     

     Equal sides show the triangle to be isoceles.     

     So x and the other unlabeled angle are equal.     

     The sum of all angles of every triangle is 180^o.     

     x  =  (1/2)(180^o – 58^o)     

     x  =  (1/2)(122^o)     

     x  =  61^o     

The functions f and h are defined as follows:     

f(x) = (x + 5)/(x - 7)  and h(x) = (x + 5)(x - 7).     

Explain why the functions f and h are not the same function.     

Because     f(x) is (x+5) divided by (x–7)     

whereas     h(x) is (x+5) multiplied by (x–7)     

That's why they're not the same.     

_.     

A tree diagram has outcomes (H, H, H), (H, H, T), (H, T, H), (H, T, T), (T, H, H), (T, H, T), (T, T, H), (T, T, T).What is the probability of one of the coins landing on tails and two of them landing on heads? 1/4 3/8  1/2 3/4     

There are eight possible outcomes,     

of which three are 1 tails & 2 heads.     

So the likelihood is 3 / 8.     

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