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3 years ago

Ian has 20 football cards, and Jason has 44 baseball cards. They agree to trade such that jason

Mathematics

1 answer:

Alina [70]3 years ago

8 0

Answer:

12 trades

Step-by-step explanation:

Let's call 'x' the number of trades they will do.

After each trade, the number of cards Ian has increase by 1 (he gives 1 but receives 2), and the number of cards Jason has decrease by 1 (he receives 1 but gives 2), so after x trades, the number of cards Ian has is 20 + x, and Jason has 44 - x.

To find the number of trades when they will have the same amount of cards, we have that:

20 + x = 44 - x

2x = 24

x = 12 trades

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What is the area of rhombus ABCD? Enter your answer in the box. Do not round at any steps. put the answer in units²

AlladinOne [14]

Answer:

Therefore the Area of Rhombus ABCD is 36 unit².

Step-by-step explanation:

Given:

ABCD is a Rhombus

A = (-1,0)

B = (5,-3)

C = (-1,-6)

D = (-7 ,-3)

To Find:

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Solution:

We know that Area of Rhombus is given as

$\textrm{Area of Rhombus}=\dfrac{1}{2}\times d_{1}\times d_{2}$

Where ,

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We have,

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Using Distance Formula we get

$l(AC) = \sqrt{((x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2} )}$

Substituting coordinates A and C we get

$l(AC) = \sqrt{((-1-(-1))^{2}+(-6-0)^{2} )}=\sqrt{36}\\l(AC)=6\ unit$

Similarly for BD we have,

$l(BD) = \sqrt{((5-(-7))^{2}+(-3-(-3))^{2} )}=\sqrt{144}\\l(BD)=12\ unit$

Now Substituting AC and BD in Formula we get

$\textrm{Area of Rhombus}=\dfrac{1}{2}\times AC\times BD$

$\textrm{Area of Rhombus}=\dfrac{1}{2}\times 6\times 12=36\ unit^{2}$

Therefore the Area of Rhombus ABCD is 36 unit².

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Step-by-step explanation:

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