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enot [183]
3 years ago
9

Directions: Complete all 3 questions. Make sure you include a graph, work and conclusion.

Mathematics
1 answer:
Simora [160]3 years ago
8 0

Prove that the quadrilateral whose vertices are I(-2,3), J(2,6), K(7,6), and L(3, 3) is a rhombus.

I think in these problems the first step is to express each side as a vector.  A vector is the difference between points.  When two sides have the same vector (or negatives) it means they're parallel and congruent.  So in a rhombus IJKL the vectors IJ and LK should be the same, as should JK and IL.  That much assures a parallelogram; we check IJ and JK are congruent to complete the crowing of the rhombus.

Let's calculate these vectors:

IJ = J - I = (2,6) - (-2,3) = (2 - -2, 6 - 3) = (4, 3)

LK = K - L = (7, 6) - (3, 3) = (4, 3)

IJ = LK, so far so good

(Note: If you haven't got to vectors yet you can just show the two sides are the same length, 5, and have the same slope, 3/4, both of which can be read off the vectors.)

JK = K - J = (7,6) - (2,6) = (5,0)

IL = L - I = (3, 3) - (-2, 3)  = (5, 0)

Those are the same too.    

Now we have to show IJ ≅ JK

The length of IJ is the cliche √4²+3² = 5, the same as JK, so IJ ≅ JK

We showed all four sides are congruent and we have two pair of parallel sides, so we have a rhombus.

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Doña Gertrudis recolecta en promedio 75 litros de leche de cabra por día y utiliza alrededor de 5 litros para hacer un kilogramo
Nimfa-mama [501]

Answer:

825 pesos a day on average

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Step-by-step explanation:

In ENGLISH:

Doña Gertrudis collects on average 75 liters of goat milk per day and uses around 5 liters to make one kilogram of cheese. The cheeses he makes weigh 200 grams each and he sells them for 132 pesos a dozen. How much money do you get per day on average from the sale of your cheeses? How many kilograms does the dozen cheeses weigh?

<u>Solution:</u>

75 Liters / 5 Liters = 15

15 * 1 kg = 15 kg of cheese per day

15kg in grams is 15*1000 = 15,000 grams

Each cheese block is 200 grams, so number of blocks of cheese:

15,000/200 = 75 blocks of cheese

1 dozen (12) = 132 pesos, so 1 would be:

132/12 = 11 pesos PER BLOCK

SO, 75 blocks of cheese = 75 * 11 = <u>825 pesos (per day on average)</u>

<u></u>

Dozen cheese weight in kg,

200 grams * 12 = 2400 grams

In kg,

2400/1000 = <u>2.4 kg</u>

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3 years ago
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Answer:

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Step-by-step explanation:

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