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iren [92.7K]
3 years ago
7

Given the following rectangle and circle, at what approximate value of x are the two areas equal? x ≈ 5.8 x ≈ 3.4 The curves do

not intersect, so there is no solution. x ≈ 8.7
Mathematics
1 answer:
SIZIF [17.4K]3 years ago
6 0

The approximate value of x will be approximately equal to 3.4

<h3>Area of triangle and circle</h3>

The formula for calculating area of rectangle is expressed as:

A  = lw

  • l is the length
  • w is the width

Ar = (3x-1)(x+2)

Ar = 3x^2+6x-x-2

Ar = 3x^2 + 5x - 2

For the circle

Ac = πr²

Ac = 3.14(x-3)²

Ac = 3.14(x²-6x+9)

Ac = 3.14x² - 18.84x + 28.26

If the area are equal;

3x² + 5x - 2 = 3.14x² - 18.84x + 28.26

3.14x² - 3x² - 5x - 18.84x + 30.26 = 0
0.14x²-23.84x+30.26 = 0

On factorizing the equation, the approximate value of x will be approximately equal to 3.4

Learn more on area of rectangle here; brainly.com/question/25292087

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The most helpful representation would be option C.

Step-by-step explanation:

The horizontal distance traveled corresponds to one of the roots of the quadratic equation.

h(x) = -0.01(x-150)(x+4)

In this case, option c presents the roots of the polynomial, which answers are

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Since we are talking about positive distances, the first option gets discarded.

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Please helppppppppppp me so the problem its jessica said that the sum of −8+d is always positive when the value of d is greater
Alex_Xolod [135]
<h3>Answer: Sometimes true</h3>

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

Explanation:

-8+d is positive only when d > 8

Here's why

-8+d > 0

-8+d+8 > 0+8 .... add 8 to both sides

d > 8

So if Jessica said "d is greater than 8", then her claim would always be correct.

However, her claim is sometimes true.

Two counter examples could be when d = 1 and d = 2.

If d = 1, then -8+d = -8+1 = -7 which isn't positive.

If d = 2, then -8+d = -8+2 = -6 which also isn't positive.

Basically if d is anything smaller than 8, then you'll have -8+d be negative.

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Answer:

3

Step-by-step explanation:

f(-1)g(-1) \text{ is the same thing as } f(-1)\cdot g(-1). \\\text{Therefore, find f(-1) and g(-1)}

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g(-1)=3(-1)+2\\g(-1)=-3+2\\g(-1)=-1

Therefore:

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