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Harlamova29_29 [7]
3 years ago
11

Find an expression (where you have to multiply polynomials) to represent the shaded region of #33 and if you could also include

how that would be great!

Mathematics
1 answer:
Brrunno [24]3 years ago
4 0
First, find the area of the circle using the formula A=pi r^2. 
A=pi (2x+3)^2 = pi(4x^2 + 12x + 9) 
Second, find the area of the rectangle inside by multiplying the polynomials. 
(X+1)*(3x+2) = 3x^2 + 5x +2 
Third, subtract the area of the rectangle from the area of the circle to find the area of the shaded region. 
pi(4x^2 + 12x + 9) - 3x^2 + 5x +2 =area of shaded region 
Or 
(pi (2x+3)^2) - ((X+1)(3x+2)) = area of shaded region


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Answer:

94.2

Step-by-step explanation:

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3 years ago
Triangle A″B″C″ is formed by a reflection over x = 1 and dilation by a scale factor of 2 from the origin. Which equation shows t
andrew-mc [135]

Answer:

segment AB over segment A double prime B double prime = the square root of 13 over 2 times the square root of 13

Step-by-step explanation:

Triangle ABC has vertices at points A(-3,3), B(1,-3) and C(-3,-3).

1. Reflection over x = 1 maps vertices A, B and C as follows

  • A(-3,3)→A'(5,3);
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2. Dilation by a scale factor of 2 from the origin has the rule

(x,y)→(2x,2y)

So,

  • A'(5,3)→A''(10,6);
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  • C'(5,-3)→C''(10,-6)

See attached diagram for details

Note that

A''B''=2AB\\ \\A''C''=2AC\\ \\B''C''=2BC,\\ \\AB=\sqrt{(-3-1)^2+(3-(-3))^2}=\sqrt{16+36}=\sqrt{52}=2\sqrt{13}

so

\dfrac{AB}{A''B''}=\dfrac{2\sqrt{13}}{2\cdot 2\sqrt{13}}=\dfrac{\sqrt{13}}{2\sqrt{13}}

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