Patty lives on a chicken farm and can collect 80 eggs in 2 hours. At that rate how long will it take her to collect 360 eggs?
2 answers:
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Check the picture below
now, we know is a parallelogram, so the diagonals will bisect
looking at the picture, the interior angles are not right-angles, and thus is not a rectangle, and is not a square either, due to the same reason
is it a rhombus? well, a rhombus, is a parallelogram, that's "slanted" per se, but regardless of how slanted it may be, the sides are all equal
now, we don't need to check the length of both pairs, just one of the segments of each pair, let's check only then JK and KL, the ones in red in the picture, since each pair of segments are twin, if JK = KL, then that means all sides are equal
![\bf \textit{distance between 2 points}\\ \quad \\ \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) J&({{-7 }}\quad ,&{{ -2}})\quad % (c,d) K&({{ 0}}\quad ,&{{ 4}})\\\\ K&({{ 0}}\quad ,&{{ 4}})\quad % (c,d) L&({{ 9}}\quad ,&{{ 2}}) \end{array}\qquad % distance value d = \sqrt{({{ x_2}}-{{ x_1}})^2 + ({{ y_2}}-{{ y_1}})^2} \\\\\\ JK=\sqrt{[0-(-7)]^2+[4-(-2)]^2}\implies JK=\sqrt{(0+7)^2+(4+2)^2} \\\\\\ JK=\sqrt{7^2+6^2} \\\\\\ KL=\sqrt{(9-0)^2+(2-4)^2}\implies KL=\sqrt{9^2+(-2)^2}](https://tex.z-dn.net/?f=%5Cbf%20%5Ctextit%7Bdistance%20between%202%20points%7D%5C%5C%20%5Cquad%20%5C%5C%0A%5Cbegin%7Barray%7D%7Blllll%7D%0A%26x_1%26y_1%26x_2%26y_2%5C%5C%0A%25%20%20%28a%2Cb%29%0AJ%26%28%7B%7B-7%20%7D%7D%5Cquad%20%2C%26%7B%7B%20-2%7D%7D%29%5Cquad%20%0A%25%20%20%28c%2Cd%29%0AK%26%28%7B%7B%200%7D%7D%5Cquad%20%2C%26%7B%7B%204%7D%7D%29%5C%5C%5C%5C%0AK%26%28%7B%7B%200%7D%7D%5Cquad%20%2C%26%7B%7B%204%7D%7D%29%5Cquad%20%0A%25%20%20%28c%2Cd%29%0AL%26%28%7B%7B%209%7D%7D%5Cquad%20%2C%26%7B%7B%202%7D%7D%29%0A%5Cend%7Barray%7D%5Cqquad%20%0A%25%20%20distance%20value%0Ad%20%3D%20%5Csqrt%7B%28%7B%7B%20x_2%7D%7D-%7B%7B%20x_1%7D%7D%29%5E2%20%2B%20%28%7B%7B%20y_2%7D%7D-%7B%7B%20y_1%7D%7D%29%5E2%7D%0A%5C%5C%5C%5C%5C%5C%0AJK%3D%5Csqrt%7B%5B0-%28-7%29%5D%5E2%2B%5B4-%28-2%29%5D%5E2%7D%5Cimplies%20JK%3D%5Csqrt%7B%280%2B7%29%5E2%2B%284%2B2%29%5E2%7D%0A%5C%5C%5C%5C%5C%5C%0AJK%3D%5Csqrt%7B7%5E2%2B6%5E2%7D%0A%5C%5C%5C%5C%5C%5C%0AKL%3D%5Csqrt%7B%289-0%29%5E2%2B%282-4%29%5E2%7D%5Cimplies%20KL%3D%5Csqrt%7B9%5E2%2B%28-2%29%5E2%7D)
now... another characteristic of a rhombus is, the diagonals, meet at right-angle, that means KM ⟂ JL
and that simply means, if you get the slope of KM and the slope of JL, the product of their slope is -1
then multiply both slopes, if their product is -1, that means, they're perpendicular to each other, and it IS a rhombus only, then.
now, we know is a parallelogram, so the diagonals will bisect
looking at the picture, the interior angles are not right-angles, and thus is not a rectangle, and is not a square either, due to the same reason
is it a rhombus? well, a rhombus, is a parallelogram, that's "slanted" per se, but regardless of how slanted it may be, the sides are all equal
now, we don't need to check the length of both pairs, just one of the segments of each pair, let's check only then JK and KL, the ones in red in the picture, since each pair of segments are twin, if JK = KL, then that means all sides are equal
now... another characteristic of a rhombus is, the diagonals, meet at right-angle, that means KM ⟂ JL
and that simply means, if you get the slope of KM and the slope of JL, the product of their slope is -1
then multiply both slopes, if their product is -1, that means, they're perpendicular to each other, and it IS a rhombus only, then.
We want to change the digit in the number 5,341 into 5,841, and to find the difference between the numbers.
Refer to the figure shown below.
The number 3 is in the 3rd place (hundreds) of the number 5,341 as a digit.
It is replaced by 8 to form the number 5,841.
This means that 300 is replaced by 800 because, in the third place, we count by hundreds in the 3rd place.
The difference between 800 and 300 is 500.
Subtraction of 5,341 from 5,841 also yields 500.
Answer:
The digit is in the 3rd place (hundreds).
The difference between the numbers is 500.
Refer to the figure shown below.
The number 3 is in the 3rd place (hundreds) of the number 5,341 as a digit.
It is replaced by 8 to form the number 5,841.
This means that 300 is replaced by 800 because, in the third place, we count by hundreds in the 3rd place.
The difference between 800 and 300 is 500.
Subtraction of 5,341 from 5,841 also yields 500.
Answer:
The digit is in the 3rd place (hundreds).
The difference between the numbers is 500.