(x+4)(x+6)=0
x = -4, x=-6
The answer is C.
Answer:
115.48![m^{2}](https://tex.z-dn.net/?f=m%5E%7B2%7D)
Step-by-step explanation:
This shape can be split into two distinct shapes
Two halves of a semi circle, and a rectangle in between
Circle:
Putting both halves of the semi circle together will give you a full circle. The diameter of the circle is given (7m).
The area of a circle is A = π ![r^{2}](https://tex.z-dn.net/?f=r%5E%7B2%7D)
The radius, r, is half of the diameter, so 7 / 2 = 3.5m
A = π ![r^{2}](https://tex.z-dn.net/?f=r%5E%7B2%7D)
A = π * ![3.5^{2}](https://tex.z-dn.net/?f=3.5%5E%7B2%7D)
A = 38.38![m^{2}](https://tex.z-dn.net/?f=m%5E%7B2%7D)
Rectangle:
The area of a rectangle is A = h b
The height, h, is known at 7m
The base, b, can be found by removing the length from the dot to the end of the semi circles. This length is the radius of the semi circles, 3.5m
Removing the radius from the total length given
18 - 3.5 - 3.5 = 11m
The base is 11m
A = h b
A = 7 * 11 = 77![m^{2}](https://tex.z-dn.net/?f=m%5E%7B2%7D)
Total Area = Circle area + Rectangle area
Total Area = 38.38 + 77 = 115.48![m^{2}](https://tex.z-dn.net/?f=m%5E%7B2%7D)
The answer would be B) Sexual Reproduction
Answer: The correct option is (c) ![\dfrac{49}{100}.](https://tex.z-dn.net/?f=%5Cdfrac%7B49%7D%7B100%7D.)
Step-by-step explanation: We are given to solve the following quadratic equation by the method of completing the square:
![5x^2-7x+2=0~~~~~~~~~~~~~~~~~~~(i)](https://tex.z-dn.net/?f=5x%5E2-7x%2B2%3D0~~~~~~~~~~~~~~~~~~~%28i%29)
Also, we are to find the constant added on both sides to form the perfect square trinomial.
We have from equation (i) that
![5x^2-7x+2=0\\\\\Rightarrow x^2-\dfrac{7}{5}x+\dfrac{2}{5}=0\\\\\\\Rightarrow x^2-2\times x\times \dfrac{7}{10}+\left(\dfrac{7}{10}\right)^2+\dfrac{2}{5}=\left(\dfrac{7}{10}\right)^2\\\\\\\Rightarrow \left(x-\dfrac{7}{10}\right)^2=\dfrac{49}{100}-\dfrac{2}{5}\\\\\\\Rightarrow \left(x-\dfrac{7}{10}\right)^2=\dfrac{49-40}{100}\\\\\\\Rightarrow \left(x-\dfrac{7}{10}\right)^2=\dfrac{9}{100}\\\\\\\Rightarrow x-\dfrac{7}{10}=\pm\dfrac{3}{10}\\\\\\\Rightarrow x=\pm\dfrac{3}{10}+\dfrac{7}{10}.](https://tex.z-dn.net/?f=5x%5E2-7x%2B2%3D0%5C%5C%5C%5C%5CRightarrow%20x%5E2-%5Cdfrac%7B7%7D%7B5%7Dx%2B%5Cdfrac%7B2%7D%7B5%7D%3D0%5C%5C%5C%5C%5C%5C%5CRightarrow%20x%5E2-2%5Ctimes%20x%5Ctimes%20%5Cdfrac%7B7%7D%7B10%7D%2B%5Cleft%28%5Cdfrac%7B7%7D%7B10%7D%5Cright%29%5E2%2B%5Cdfrac%7B2%7D%7B5%7D%3D%5Cleft%28%5Cdfrac%7B7%7D%7B10%7D%5Cright%29%5E2%5C%5C%5C%5C%5C%5C%5CRightarrow%20%5Cleft%28x-%5Cdfrac%7B7%7D%7B10%7D%5Cright%29%5E2%3D%5Cdfrac%7B49%7D%7B100%7D-%5Cdfrac%7B2%7D%7B5%7D%5C%5C%5C%5C%5C%5C%5CRightarrow%20%20%5Cleft%28x-%5Cdfrac%7B7%7D%7B10%7D%5Cright%29%5E2%3D%5Cdfrac%7B49-40%7D%7B100%7D%5C%5C%5C%5C%5C%5C%5CRightarrow%20%20%5Cleft%28x-%5Cdfrac%7B7%7D%7B10%7D%5Cright%29%5E2%3D%5Cdfrac%7B9%7D%7B100%7D%5C%5C%5C%5C%5C%5C%5CRightarrow%20x-%5Cdfrac%7B7%7D%7B10%7D%3D%5Cpm%5Cdfrac%7B3%7D%7B10%7D%5C%5C%5C%5C%5C%5C%5CRightarrow%20x%3D%5Cpm%5Cdfrac%7B3%7D%7B10%7D%2B%5Cdfrac%7B7%7D%7B10%7D.)
So,
![x=\dfrac{3}{10}+\dfrac{7}{10},~~~~~~~~x=-\dfrac{3}{10}+\dfrac{7}{10}\\\\\\\Rightarrow x=\dfrac{10}{10},~~~~~~~~\Rightarrow x=\dfrac{-3+7}{10}\\\\\\\Rightarrow x=1,~-\dfrac{2}{5}.](https://tex.z-dn.net/?f=x%3D%5Cdfrac%7B3%7D%7B10%7D%2B%5Cdfrac%7B7%7D%7B10%7D%2C~~~~~~~~x%3D-%5Cdfrac%7B3%7D%7B10%7D%2B%5Cdfrac%7B7%7D%7B10%7D%5C%5C%5C%5C%5C%5C%5CRightarrow%20x%3D%5Cdfrac%7B10%7D%7B10%7D%2C~~~~~~~~%5CRightarrow%20x%3D%5Cdfrac%7B-3%2B7%7D%7B10%7D%5C%5C%5C%5C%5C%5C%5CRightarrow%20x%3D1%2C~-%5Cdfrac%7B2%7D%7B5%7D.)
Thus, the required solution is
and the value of the constant added is ![\dfrac{49}{100}.](https://tex.z-dn.net/?f=%5Cdfrac%7B49%7D%7B100%7D.)
Option (c) is correct.