Step-by-step explanation:
![{x}^{2} + 25 = 0 \\ \therefore {x}^{2} = - 25 \\ \therefore {x} = \sqrt{ - 25} \\ \therefore {x} = \pm\sqrt{ - 1 \times 25} \\ \therefore {x} = \pm \sqrt{ 25} \times \sqrt{ - 1} \\ \therefore {x} = \pm5 \: i \\ \therefore {x} = \{ - 5i, \: \: 5i \} \: \\ is \: the \: solution \: set.](https://tex.z-dn.net/?f=%20%7Bx%7D%5E%7B2%7D%20%20%2B%2025%20%3D%200%20%5C%5C%20%20%5Ctherefore%20%7Bx%7D%5E%7B2%7D%20%20%3D%20%20-%2025%20%5C%5C%20%5Ctherefore%20%7Bx%7D%20%20%3D%20%20%5Csqrt%7B%20-%2025%7D%20%20%5C%5C%20%20%5Ctherefore%20%7Bx%7D%20%20%3D%20%20%20%5Cpm%5Csqrt%7B%20-%201%20%5Ctimes%2025%7D%20%20%5C%5C%20%5Ctherefore%20%7Bx%7D%20%20%3D%20%5Cpm%20%20%5Csqrt%7B%20%2025%7D%20%20%5Ctimes%20%20%5Csqrt%7B%20-%201%7D%20%20%5C%5C%20%5Ctherefore%20%7Bx%7D%20%20%3D%20%20%5Cpm5%20%5C%3A%20i%20%20%5C%5C%20%5Ctherefore%20%7Bx%7D%20%20%3D%20%5C%7B%20-%205i%2C%20%5C%3A%20%20%5C%3A%205i%20%5C%7D%20%5C%3A%20%5C%5C%20%20is%20%5C%3A%20the%20%5C%3A%20solution%20%5C%3A%20set.)
Integers are whole numbers so the answer is -3
Answer:
350 square feet
Step-by-step explanation:
We are given that
Width of strip=6 in
Dimension of rectangle=![20 ft\times 230 ft](https://tex.z-dn.net/?f=20%20ft%5Ctimes%20230%20ft)
We know that
Area of rectangle ,A=xy
Differentiate
![dA=\frac{\partial A}{\partial x}x+\frac{\partial A}{\partial y}y](https://tex.z-dn.net/?f=dA%3D%5Cfrac%7B%5Cpartial%20A%7D%7B%5Cpartial%20x%7Dx%2B%5Cfrac%7B%5Cpartial%20A%7D%7B%5Cpartial%20y%7Dy)
We have ![\frac{\partial A}{\partial x}=y=230 ft](https://tex.z-dn.net/?f=%5Cfrac%7B%5Cpartial%20A%7D%7B%5Cpartial%20x%7D%3Dy%3D230%20ft)
![\frac{\partial A}{\partial y}=x=120](https://tex.z-dn.net/?f=%5Cfrac%7B%5Cpartial%20A%7D%7B%5Cpartial%20y%7D%3Dx%3D120)
![dx=\frac{12}{12}=1 ft](https://tex.z-dn.net/?f=dx%3D%5Cfrac%7B12%7D%7B12%7D%3D1%20ft)
1 ft=12 in
Because 6 in added in both side of breadth
dy=![\frac{12}{12}=1 ft](https://tex.z-dn.net/?f=%5Cfrac%7B12%7D%7B12%7D%3D1%20ft)
Because 6 in added on both sides of length of rectangle
Substitute the values
![dA=230\times 1+120\times 1=350 ft^2](https://tex.z-dn.net/?f=dA%3D230%5Ctimes%201%2B120%5Ctimes%201%3D350%20ft%5E2)
Hence, the number of square feet of paint in the strip=350 square feet
Answer:
Option A is correct
The function
has real zeroes at x =-10 and x =-6
Explanation:
Given: The real zeroes or roots are x = -10, and x = -6
To find the quadratic function of degree 2.
where α,β are real roots. ....[1]
Here, α= -10 and β= -6
Sum of the roots:
α+β = -10+(-6) = -10-6 = -16
Product of the roots:
αβ = (-10)(-6)= 60
Substitute these value in equation [1] we have;
![x^2-(-16)x+60 = x^2+16x+60](https://tex.z-dn.net/?f=x%5E2-%28-16%29x%2B60%20%3D%20x%5E2%2B16x%2B60)
Therefore, the quadratic function for the real roots at x =-10 and x =-6 ;
![x^2+16x+60](https://tex.z-dn.net/?f=x%5E2%2B16x%2B60)