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Veronika [31]
3 years ago
10

Karen and Dale and Tom sent a total of 84 messages during the weekend. Dale sent six fewer messages and Karen and Tom sent four

times as many as Karen. How many did they send each.
Mathematics
1 answer:
yuradex [85]3 years ago
3 0

Answer:

Karen: 15; Dale: 9; Tom: 60

Step-by-step explanation:

"Karen and Dale and Tom sent a total of 84 messages during the weekend."

k + d + t = 84

"Dale sent six fewer messages than Karen"

d = k - 6

"Tom sent four times as many as Karen."

t = 4k

Substitute k - 6 for d and 4k for t in the first equation.

k + d + t = 84

k + k - 6 + 4k = 84

6k - 6 = 84

6k = 90

k = 15

d = k - 6 = 16 - 6 = 9

t = 4k = 4(15) = 60

Answer: Karen: 15; Dale: 9; Tom: 60

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Write the equation of the line that passes through the point (-5,5) and has a slope of -8/5
Free_Kalibri [48]

Answer:

The equation of the line that passes through the point (-5,5) and has a slope of -8/5 will be:

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Step-by-step explanation:

Given

  • \left(x_1,\:y_1\right)=\left(-5,5\right)
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Point-Slope Form equation is

\left(y-y_1\right)=m\left(x-x_1\right)

\left(y-5\right)=\frac{-8}{5}\left(x-\left(-5\right)\right)

\mathrm{Apply\:rule}\:-\left(-a\right)=a

y-5=\frac{-8}{5}\left(x+5\right)

\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{-a}{b}=-\frac{a}{b}

y-5=-\frac{8}{5}\left(x+5\right)

y-5+5=-\frac{8}{5}\left(x+5\right)+5

y=-\frac{8}{5}x-3

Therefore, the equation of the line that passes through the point (-5,5) and has a slope of -8/5 will be:

                                           y=-\frac{8}{5}x-3

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3 years ago
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