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N76 [4]
3 years ago
5

Explain how to use a cordinate plane to find the area of a rectangle with vertices (-4,9) (-4-3) (-1,-3) and(-1,9) . What is the

area?

Mathematics
1 answer:
PolarNik [594]3 years ago
7 0

Answer:

The Area of the rectangle is 36

Step-by-step explanation:

One can use the vertices of the rectangle in coordinate form, by observing that (please see image attached):

(1) the distance between x-coordinates that share the same y-value give the length of the segments that define the horizontal sides of the rectangle,

(2) and the distance between y-coordinates that share the same x-value give the length of the segments that define the vertical sides of the rectangle,

Therefore, as an example of statement (1) above, the distance between the x-coordinates of : (-4,-3) and (-1,-3) which share the same "y-value" -3, is:

| -1 - (-4)| = |-1+4| = |3| = 3 which is the length of the horizontal side of the rectangle (the base of the rectangle).

As an example of statement (2), the distance between the y-coordinates of: ((-1,-3, and (-1,9) which share the same "x-value" -1, is:

| 9-(-3)| = |9+3|=|12|=12 which is the length of the vertical side of the rectangle (the height of the rectangle).

So, the area of the rectangle which is defined as the product of its base times its height, is given by:

Area=base\,*\.height\,= 3\,*\,12\,= 36

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seropon [69]

Answer:  Choice B) \frac{5\sqrt{11}+5\sqrt{3}}{8}\\\\

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

Work Shown:

\frac{5}{\sqrt{11}-\sqrt{3}}\\\\\\\frac{5(\sqrt{11}+\sqrt{3})}{(\sqrt{11}-\sqrt{3})(\sqrt{11}+\sqrt{3})}\\\\\\\frac{5\sqrt{11}+5\sqrt{3}}{(\sqrt{11})^2-(\sqrt{3})^2}\\\\\\\frac{5\sqrt{11}+5\sqrt{3}}{11-3}\\\\\\\frac{5\sqrt{11}+5\sqrt{3}}{8}\\\\\\

This shows why choice B is the answer.

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

Explanation:

  • In the second step, I multiplied top and bottom by (\sqrt{11}+\sqrt{3})
  • This is so we can apply the difference of squares rule in step 3. The difference of squares rule is (x-y)(x+y) = x^2-y^2.
  • In step 4, the square roots cancel out with the squaring operation. The two operations are inverses of one another, which is why they cancel.

So in general, if the denominator is \sqrt{a}-\sqrt{b} and you want to rationalize the denominator, then you should multiply top and bottom by \sqrt{a}+\sqrt{b}. The same applies in reverse as well.

This leads to the denominator becoming (\sqrt{a}-\sqrt{b})(\sqrt{a}+\sqrt{b}) = (\sqrt{a})^2-(\sqrt{b})^2 = a-b

Keep in mind that a \ge 0 and b \ge 0

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Step-by-step explanation:

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the equation 4(x+9)=76 models this situation which choice shows the sequence of operations neede to slove this problem using bot
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Answer:

Step-by-step explanation:

Here you go mate

Use PEMDAS

Parenthesis,Exponent,Multiplication,Division,Addition,Subtraction

Step 1

4(x+9)=76  Equation/Question

Step 2

4(x+9)=76  Remove parenthesis by multiplying 4

4x+36=76

Step 3

4x+36=76  Subtract 36 from sides

4x=40

Step 4

4x=40  Divide sides by 4

answer

x=10

Hope this helps

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The answer is...

Step-by-step explanation:

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