the credit remaining on a phone card in dollars is a linear function of the total calling time made with the card in minutes. The remaining credit after 30 minutes of calls is $15.20 and the remaining credit after 47 minutes of calls is $12.48 what is the remaining credit after 51 minutes of calls

he credit remaining on a phone card (in dollars) is a linear function of the

total calling time made with the card (in minutes), as shown in the figure below.

The remaining credit after 45 minutes of calls is $22.80 , and the remaining

credit after 64 minutes of calls is $19.76.

What is the remaining credit after 73 minutes of calls?

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Not sure what figure you are referring to, write an equation from the given values:

Assign the values as follows

x1 = 45; y1 = 22.80

x2 = 64; y2 = 19.76

:

Find the slope (m) using the formula: m = %28y2-y1%29%2F%28x2-x1%29

m = %2819.76-22.80%29%2F%2864-45%29 = %28-3.04%29%2F%2819%29

m = -.16

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Write the equation using the point/slope formula: y - y1 = m(x - x1)

y - 22.80 = -.16(x - 45)

y - 22.80 = -.16x + 7.2

y = -.16x + 7.2 + 22.80

y = -.16x + 30

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Use this equation to find the credit (y) when minutes (x) = 73

y = -.16(73) + 30

y = -11.68 + 30

y = $18.32; credit after 73 minute of calls

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That you can also see the original value of the phone card: x=0, y = $30

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Did this help you understand what's going on here? Any questions

Step-by-step explanation:

(sin 42)/31. = sinx)/37

sinx = 37 (sin42)/31

= 37× 0.66/31 = 0.787

x= 51.9

other angle opposite to y = 180-51.9-42

= 180- 93.9 =86.1

so

sin42)/31 = sin 86.1)/y

0.021 = 0.997 /y

y= 0.997/0.021 =47.47