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andrew11 [14]
3 years ago
6

Sara is working on a Geometry problem in her Algebra class. The problem requires Sara to use the two quadrilaterals below to ans

wer a list of questions.
Part A: For what one value of x are the perimeters of the quadrilaterals the same? (Hint: The perimeter of a quadrilateral is the sum of its sides.)


Part B: For what one value of x are the areas of the quadrilaterals the same? (Hint: The area of a quadrilateral is the product of its base and height.)
Mathematics
1 answer:
zloy xaker [14]3 years ago
7 0
Part A:

Given a square with sides 6 and x + 4. Also, given a rectangle with sides 2 and 3x + 4

The perimeter of the square is given by 4(x + 4) = 4x + 16

The area of the rectangle is given by 2(2) + 2(3x + 4) = 4 + 6x + 8 = 6x + 12

For the perimeters to be the same

4x + 16 = 6x + 12
4x - 6x = 12 - 16
-2x = -4
x = -4 / -2 = 2

The value of x that makes the <span>perimeters of the quadrilaterals the same is 2.



Part B:

The area of the square is given by

Area=(x+4)^2=x^2+8x+16

The area of the rectangle is given by 2(3x + 4) = 6x + 8

For the areas to be the same

x^2+8x+16=6x+8 \\  \\ \Rightarrow x^2+8x-6x+16-8=0 \\  \\ \Rightarrow x^2+2x+8=0 \\  \\ \Rightarrow x= \frac{-2\pm\sqrt{2^2-4(8)}}{2}  \\  \\ = \frac{-2\pm\sqrt{4-32}}{2} = \frac{-2\pm\sqrt{-28}}{2}  \\  \\ = \frac{-2\pm2i\sqrt{7}}{2} =-1\pm i\sqrt{7}

Thus, there is no real value of x for which the area of the quadrilaterals will be the same.
</span>
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therefore, it will be
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Next, distribute the negative to the four and add normally.

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5 0
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Answer:

If the question does not limit man to produce only one model of club, then the maximized profit of every condition produced under 50 sets daily will be all model A exclusive. such as $60 x 50 (model A) , even just produce 49 set that day, the maximal profit is still $60 x 49.

Step-by-step explanation:

If the question does not limit man to produce only one model of club, then the maximized profit of every condition produced under 50 sets daily will be all model A exclusive. such as $60 x 50 (model A) , even just produce 49 set that day, the maximal profit is still $60 x 49.

Re-consider the logic of the question ....

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kupik [55]
<h3>Answer: Circumference is approximately 75.36 feet</h3>

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

Work Shown:

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pi = 3.14 approx

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G(x) = 3x + 1<br><br>f(x) = 2x - 5<br><br> Find g (f (x))​
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Answer:

g(f(x)) = 6x - 14

General Formulas and Concepts:

<u>Pre-Algebra</u>

  • Distributive Property

<u>Algebra I</u>

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Step-by-step explanation:

<u>Step 1: Define</u>

g(x) = 3x + 1

f(x) = 2x - 5

<u>Step 2: Find</u>

  1. Substitute:                    g(f(x)) = 3(2x - 5) + 1
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