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Ira Lisetskai [31]
3 years ago
14

Three farmers buy a total of 2,249 acres of land at an auction, Farmer Mel buys land that is 3 times as many acres as Farmer Cas

sius's land. Farmer Cassius buys land that is 3 times as many acres as Farmer Anne's land. How many acres of land does each farmer buy?​
Mathematics
1 answer:
fgiga [73]3 years ago
8 0

Answer:

Farmer Anne's land = 173 acres

Farmer Cassius = 519 acres

Farmer Mel = 1,557 acres

Step-by-step explanation:

Total acre = 2,249

Let

Farmer Anne's land = x

Farmer Cassius = 3x

Farmer Mel = 3(3x) = 9x

x + 3x + 9x = 2,249

13x = 2,249

x = 173

Farmer Anne's land = x = 173 acres

Farmer Cassius = 3x

= 3(173)

= 519 acres

Farmer Mel = 3(3x) = 9x

= 9(173)

= 1,557 acres

Therefore,

Farmer Anne's land = 173 acres

Farmer Cassius = 519 acres

Farmer Mel = 1,557 acres

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Marissa bought four bottles of water Each bottle of water is 0.95 cents Write an equation with the same product as the total cos
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Determine which of the lines are parallel and which of the lines are perpendicular. Select all of the statements that are true.
slega [8]

Answers:

Line A is parallel to line D.

Line A is perpendicular to line C.

Line C is perpendicular to line D.

=====================================================

Explanation:

Let's use the slope formula to calculate the slope of the line through (-1,-17) and (3,11)

(x_1,y_1) = (-1,-17) \text{ and } (x_2,y_2)  = (3,11)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{11 - (-17)}{3 - (-1)}\\\\m = \frac{11 + 17}{3 + 1}\\\\m = \frac{28}{4}\\\\m = 7\\\\

The slope of line A is 7

-------------

Now let's find the slope of line B.

(x_1,y_1) = (0,4) \text{ and } (x_2,y_2)  = (7,-5)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{-5 - 4}{7 - 0}\\\\m = -\frac{9}{7}\\\\

-------------

Now onto line C.

(x_1,y_1) = (7,1) \text{ and } (x_2,y_2)  = (0,2)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{2 - 1}{0 - 7}\\\\m = \frac{1}{-7}\\\\m = -\frac{1}{7}\\\\

-------------

Lastly we have line D.

(x_1,y_1) = (-1,-6) \text{ and } (x_2,y_2)  = (1,8)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{8 - (-6)}{1 - (-1)}\\\\m = \frac{8 + 6}{1 + 1}\\\\m = \frac{14}{2}\\\\m = 7\\\\

------------------------------

Here's a summary of the slopes we found

\begin{array}{|c|c|} \cline{1-2}\text{Line} & \text{Slope}\\\cline{1-2}\text{A} & 7\\\cline{1-2}\text{B} & -9/7\\\cline{1-2}\text{C} & -1/7\\\cline{1-2}\text{D} & 7\\\cline{1-2}\end{array}

Recall that parallel lines have equal slopes, but different y intercepts. This fact makes Line A parallel to line D.

Lines A and C are perpendicular to one another, because the slopes 7 and -1/7 multiply to -1. In other words, -1/7 is the negative reciprocal of 7, and vice versa. These two lines form a 90 degree angle.

Lines C and D are perpendicular for the same reasoning as the previous paragraph.

Line B unfortunately is neither parallel nor perpendicular to any of the other lines mentioned.

You can use a graphing tool like Desmos or GeoGebra to verify these answers.

6 0
1 year ago
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