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Hatshy [7]
3 years ago
14

A(1, 3), B(5, 3), and D(1, -2) are three vertices of rectangle ABCD. The coordinates of vertex C are

Mathematics
1 answer:
pochemuha3 years ago
7 0

Answer:

b

Step-by-step explanation:

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If there are 10 values in a data set, in order from smallest to largest, what is
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Step-by-step explanation:

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Perform the operation. Enter your answer in scientific notation.<br> 9 x 10^*8 - 5.3 x 10^*8 =
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3 years ago
A train heads south out of Bloomington an hour after a northbound train
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Answer:

  • northbound: 2.5 hours
  • southbound: 1.5 hours

Step-by-step explanation:

When the second train leaves the station, the trains are already 63 miles apart. The rate of increase of their separation is (57 +63) = 120 miles per hour. The remaining 243-63 = 180 miles of separation will be achieved in ...

  (180 mi)/(120 mi/h) = 1.5 h

The northbound train will have traveled 2.5 hours; the southbound train will have traveled 1.5 hours when the trains are 243 miles apart.

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The graph of the equation below is a circle. What is the length of the radius of the circle? (x - 4)^2 + (y + 12)^2 = 17^2
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The correct answer is:  [D]:  "17" .
______________________________________________________
The radius is:  " 17" .
______________________________________________________
Note:
______________________________________________________
The formula/equation for the graph of a circle is:
______________________________________________________
   (x − h)²  +<span> </span> (y − k)² =  r²  ;

in which:  

          " (h, k) " ; are the coordinate of the point of the center of the circle;

           "r" is the length of the "radius" ; for which we want to determine;
_______________________________________________________
We are given the following equation of the graph of a particular circle:
_______________________________________________________

          →  (x − 4)²  +  (y + 12)² =  17² ;

which is in the correct form:

→  " (x − h)²  +  (y − k)² =  r²  " ;

 in which:  " h = 4 " ;

                  " k = -12" ;

                   "r = 17 " ;  which is the "radius" ; which is our answer.

          →  { Note that: "k = NEGATIVE  12" } ;

→  Since the equation <u>for this particular circle</u> contains the expression:             _________________________________________________________    
                      →     "...(y + k)² ..." ;  
         
[as opposed to the standard form:  "...(y − k)² ..." ] ; 
_________________________________________________________
→  And since the coordinates of the center of a circle are represented by:
            " (h, k) " ;  
 
→  which are:  " (4, -12) " ;  (<u>for this particular circle</u>) ; 
_________________________________________________________
→  And since:  " k = -12 " ;  (<u>for this particular circle</u>) ;
_________________________________________________________
then: 

 " [y − k ] ²  =  [ y − (k) ] ²  =  " [ y − (-12) ] ² " ;
                                    
                                         =  " ( y + 12)² "  ;
                                    
{NOTE:  Since:  "subtracting a negative" is the same as "adding a positive" ;

           →   So;  " [ y − (-12 ] " = " [ y + (⁺ 12) ] " = " (y + 12) "
___________________________________________________  
Note:  The above explanation is relevant to confirm that the equation is, in fact, in "proper form"; to ensure that the:  radius, "r" ;  is:  "17" .
___________________________________________________
           →    Since:  "r  =  17 " ;  

           →  The radius is:  " 17 " ;

          which is:  Answer choice:  [D]:  "17" .
___________________________________________________
8 0
3 years ago
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