Answer:
y = x-2
Step-by-step explanation:
y = mx + b as an equation
m = slope
slope = (change in y) / (change in x) = (y₂-y₁)/(x₂-x₁) = (y₁-y₂)/(x₁-x₂) = (2-(-2))/(4-0) = 4/4 = 1
y = 1*x + b
plug a value in, e.g. (0, -2)
-2 = 1 * 0 + b
-2 = b
our equation is thus
y = x - 2
Answer:
404.7
Step-by-step explanation:
You multiply 10.65 by 38 to get 404.7
For this case we have that the variable "x" represents the number of hours that Leticia uses to take care of children on Saturday.
IF on Friday I use 4 hours ($ 8 each) and on Saturday "x" hours ($ 8 each) obtaining a profit of $ 72, we have the following equation:
![8 (4 + x) = 72](https://tex.z-dn.net/?f=8%20%284%20%2B%20x%29%20%3D%2072)
We apply distributive property:
![32 + 8x = 72\\8x = 72-32\\8x = 40\\x = \frac {40} {8}\\x = 5](https://tex.z-dn.net/?f=32%20%2B%208x%20%3D%2072%5C%5C8x%20%3D%2072-32%5C%5C8x%20%3D%2040%5C%5Cx%20%3D%20%5Cfrac%20%7B40%7D%20%7B8%7D%5C%5Cx%20%3D%205)
So, on Saturday she spent 5 hours.
Answer:
![8 (4 + x) = 72\\x = 5](https://tex.z-dn.net/?f=8%20%284%20%2B%20x%29%20%3D%2072%5C%5Cx%20%3D%205)
we have
![x^{2} -7x=-13](https://tex.z-dn.net/?f=x%5E%7B2%7D%20-7x%3D-13)
Complete the square. Remember to balance the equation by adding the same constants to each side
![x^{2} -7x+3.5^{2}=-13+3.5^{2}](https://tex.z-dn.net/?f=x%5E%7B2%7D%20-7x%2B3.5%5E%7B2%7D%3D-13%2B3.5%5E%7B2%7D)
![x^{2} -7x+12.25=-13+12.25](https://tex.z-dn.net/?f=x%5E%7B2%7D%20-7x%2B12.25%3D-13%2B12.25)
![x^{2} -7x+12.25=-0.75](https://tex.z-dn.net/?f=x%5E%7B2%7D%20-7x%2B12.25%3D-0.75)
Rewrite as perfect squares
![(x-3.5)^{2}=-0.75](https://tex.z-dn.net/?f=%28x-3.5%29%5E%7B2%7D%3D-0.75)
remember that
![i=\sqrt{-1}](https://tex.z-dn.net/?f=i%3D%5Csqrt%7B-1%7D)
Square root both sides
![(x-3.5)=(+/-)\sqrt{-0.75}](https://tex.z-dn.net/?f=%28x-3.5%29%3D%28%2B%2F-%29%5Csqrt%7B-0.75%7D)
![(x-3.5)=(+/-)\sqrt{-1*0.75}](https://tex.z-dn.net/?f=%28x-3.5%29%3D%28%2B%2F-%29%5Csqrt%7B-1%2A0.75%7D)
![(x-3.5)=(+/-)\sqrt{0.75}i](https://tex.z-dn.net/?f=%28x-3.5%29%3D%28%2B%2F-%29%5Csqrt%7B0.75%7Di)
![x1=3.5+\sqrt{0.75}i](https://tex.z-dn.net/?f=x1%3D3.5%2B%5Csqrt%7B0.75%7Di)
![x2=3.5-\sqrt{0.75}i](https://tex.z-dn.net/?f=x2%3D3.5-%5Csqrt%7B0.75%7Di)
Simplify
![\sqrt{0.75}=\frac{\sqrt{3}}{2}](https://tex.z-dn.net/?f=%5Csqrt%7B0.75%7D%3D%5Cfrac%7B%5Csqrt%7B3%7D%7D%7B2%7D)
![x1=3.5+\frac{\sqrt{3}}{2}i](https://tex.z-dn.net/?f=x1%3D3.5%2B%5Cfrac%7B%5Csqrt%7B3%7D%7D%7B2%7Di)
![x2=3.5-\frac{\sqrt{3}}{2}i](https://tex.z-dn.net/?f=x2%3D3.5-%5Cfrac%7B%5Csqrt%7B3%7D%7D%7B2%7Di)
therefore
<u>the answer is</u>
![x1=3.5+\frac{\sqrt{3}}{2}i](https://tex.z-dn.net/?f=x1%3D3.5%2B%5Cfrac%7B%5Csqrt%7B3%7D%7D%7B2%7Di)
![x2=3.5-\frac{\sqrt{3}}{2}i](https://tex.z-dn.net/?f=x2%3D3.5-%5Cfrac%7B%5Csqrt%7B3%7D%7D%7B2%7Di)