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Mnenie [13.5K]
3 years ago
15

A costume designer is preparing costumes for 22 dancers . She pays 373.78 for all of the materials. She also buys gloves for all

of the dancers. Each pair of gloves cost 4.30.How much is a costume designer experience for each dancer.
Mathematics
1 answer:
Zolol [24]3 years ago
8 0

Answer:

  $21.29 per dancer

Step-by-step explanation:

The materials cost $373.78 for all 22 dancers, so the cost per dancer is ...

  $373.78 / 22 = $16.99

Adding the $4.30 cost of gloves to that brings the total for each dancer to ...

  $16.99 +4.30 = $21.29 . . . . for each dancer

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This problem can be readily solved if we are familiar with the point-slope form of straight lines:
y-y0=m(x-x0) ...................................(1)
where 
m=slope of line
(x0,y0) is a point through which the line passes.

We know that the line passes through A(3,-6), B(1,2)

All options have a slope of -4, so that should not be a problem.  In fact, if we check the slope=(yb-ya)/(xb-xa), we do find that the slope m=-4.

So we can check which line passes through which point:

a. y+6=-4(x-3)
Rearrange to the form of equation (1) above,
y-(-6)=-4(x-3)  means that line passes through A(3,-6) => ok

b. y-1=-4(x-2) means line passes through (2,1), which is neither A nor B
   ****** this equation is not the line passing through A & B *****

c. y=-4x+6  subtract 2 from both sides (to make the y-coordinate 2)
   y-2 = -4x+4, rearrange
   y-2 = -4(x-1)  
   which means that it passes through B(1,2), so ok

d. y-2=-4(x-1)
   this is the same as the previous equation, so it passes through B(1,2), 
   this equation is ok.

Answer: the equation y-1=-4(x-2) does NOT pass through both A and B.
   
8 0
3 years ago
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