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wlad13 [49]
2 years ago
5

A group of 8 friends went to lunch and spent a total of $76, which included the food bill and a tip of $16. They decided to spli

t the bill and tip evenly among themselves. Which equations and solutions describe the situation? Select two options. The equation StartFraction 1 over 8 EndFraction (x + 16) = StartFraction 76 over 8 EndFraction represents the situation, where x is the food bill. The equation StartFraction 1 over 8 EndFraction (x + 16) = 76 represents the situation, where x is the food bill. The solution x = 60 represents the total food bill. The solution x = 60 represents each friend’s share of the food bill and tip. The equation 8 (x + 16) = 76 represents the situation, where x is the food bill.
Mathematics
1 answer:
Margarita [4]2 years ago
6 0

1) The scenario is represented by the equation 1/8(x+16)=76/8, where x is the food bill.

2) The total food bill is represented by the equation x=60.

Both of these responses are correct.

Step-by-step instructions:

Because there are eight buddies in the group, the total money spent by them is $76 (including the $16 tip).

Our equation can be as follows if x is the food bill:

76/8 = (x+16)/8

Solving the Problem

9.5 = (x+16)/8

9.5*8 Equals x+16

x=76 -16 x=76 -16 x=76 -16 x=

60 = x

The cost of food is x=60.

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<u>Answer:</u>

1) The equation of the line parallel to  x-5y=6 and through (4,-2) is 5y = x -14

2) The equation of the line perpendicular to y= -2/5x + 3 and through (2,-1) is  2y = 5x -12

<u>Solution:</u>

<u><em>1) find the equation of the line parallel to  x-5y=6 and through (4,-2).</em></u>

Given, line equation is x – 5y = 6  

We have to find the line equation that is parallel to given line and passing through the point (4, -2)

Now, let us find slope of the given line.

\text { Slope }=\frac{-x \text { coefficient }}{y \text { coefficient }}=\frac{-1}{-5}=\frac{1}{5}

Now, we know that, slope of parallel lines are equal.

So, slope of required line is 1/5 and it passes through (4, -2)

Now, using point slope form

y-y_{1}=m\left(x-x_{1}\right) \text { where } m \text { is slope and }\left(x_{1}, y_{1}\right) \text { is point on line. }

y-(-2)=\frac{1}{5}(x-4) \rightarrow 5(y+2)=x-4 \rightarrow 5 y+10=x-4 \rightarrow x-5 y=14

Hence, the line equation is 5y = x -14

<u><em> 2) find the equation of the line perpendicular to y= -2/5x + 3 and through (2,-1)</em></u>

\text { Given, line equation is } y=-\frac{2}{5} x+3 \rightarrow 5 y=-2 x+15 \rightarrow 2 x+5 y=15

We have to find the line equation that is perpendicular to given line and passing through the point (2, -1)

Now, let us find slope of the given line.

\text { Slope }=\frac{-x \text { coefficient }}{y \text { coefficient }}=\frac{-2}{5}=-\frac{2}{5}

Now, we know that, product of slopes of perpendicular lines equals to -1.

So, slope of required line \times slope of given line = -1

slope of required line = -1 \times \frac{5}{-2}=\frac{5}{2}

And it passes through (2, -1)

Now, using point slope form

\begin{array}{l}{\text { Line equation is } y-(-1)=\frac{5}{2}(x-2) \rightarrow 2(y+1)=5(x-2)} \\\\ {\rightarrow 2 y+2=5 x-10 \rightarrow 5 x-2 y=12}\end{array}

Hence, the line equation is 2y = 5x -12

4 0
3 years ago
A company has 14 employees with a salary of ​$21,000​, 11 employees with a salary of ​$22,800​, 17 employees with a salary of ​$
kodGreya [7K]

Answer:

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Step-by-step explanation:

First need to add the total number of employees:

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Now multiply the salary for each number of employees then add to have the total:

14x21000+11x22800+17x24800+3x32200+5x38500+1x148300= 1403800

Now to obtain the mean value just divide the total salary by the total number of employees:

1403800/51= 27525.4902

the mean salary is $27,525.49

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Answer:

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Step-by-step explanation:

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/A     /A

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