Answer:
B, -4/5
Step-by-step explanation:
:)
Answer:
![(2x^2+2x+1)-(7x^2+2x+15)=-5x^2-14](https://tex.z-dn.net/?f=%282x%5E2%2B2x%2B1%29-%287x%5E2%2B2x%2B15%29%3D-5x%5E2-14)
Step-by-step explanation:
To explain how to approach this question, I am going to place letters in the blank spaces:
![(ax^2+bx+c)-(dx^2+ex+f)=-5x^2-14](https://tex.z-dn.net/?f=%28ax%5E2%2Bbx%2Bc%29-%28dx%5E2%2Bex%2Bf%29%3D-5x%5E2-14)
First, compare the <u>coefficients</u> of the x² terms on both sides of the equation: ![a - d = -5](https://tex.z-dn.net/?f=a%20-%20d%20%3D%20-5)
Therefore, we need to choose any two numbers in place of a and d whose difference is -5:
⇒ a = 2 and d = 7 as 2 - 7 = -5.
Similarly, upon comparing the <u>coefficients</u> of the x terms, we can see that there is no x term on the right side of the equation. Therefore, we need to choose numbers in place of b and e for which the difference is zero. So b and e should be the <u>same number</u>:
⇒ b = 2 and e = 2 as 2 - 2 = 0.
Finally, compare the constant term on both sides of the equation: ![c - f = -14](https://tex.z-dn.net/?f=c%20-%20f%20%3D%20-14)
Therefore, we need to choose any two numbers in place of c and f whose difference is -14:
⇒ c = 1 and f = 15 as 1 - 15 = -14.
Plug in the numbers in place of the letters on the left side of the equation:
![(2x^2+2x+1)-(7x^2+2x+15)=-5x^2-14](https://tex.z-dn.net/?f=%282x%5E2%2B2x%2B1%29-%287x%5E2%2B2x%2B15%29%3D-5x%5E2-14)
<u>Check</u>
Remove the brackets:
![2x^2+2x+1-7x^2-2x-15=-5x^2-14](https://tex.z-dn.net/?f=2x%5E2%2B2x%2B1-7x%5E2-2x-15%3D-5x%5E2-14)
Collect like terms:
![2x^2-7x^2+2x-2x+1-15=-5x^2-14](https://tex.z-dn.net/?f=2x%5E2-7x%5E2%2B2x-2x%2B1-15%3D-5x%5E2-14)
Combine like terms:
![-5x^2-14=-5x^2-14](https://tex.z-dn.net/?f=-5x%5E2-14%3D-5x%5E2-14)
Hence proving that the left and right sides of the equation are the same.
Distance from Supermarket to Bank = 3 miles.
Distance from the Bank to the library = 4 miles.
Distance from the library back to supermarket =
![\sqrt{3^2 + 4^2} = 5](https://tex.z-dn.net/?f=%20%5Csqrt%7B3%5E2%20%2B%204%5E2%7D%20%20%3D%205)
Total Distance = 3 + 4 + 5 = 12 miles.
Answer: 12 miles