Linear… do not take my word for that
Answer:6 rows per minute
Step-by-step explanation:
keeping in mind that complex roots never come alone, their sister is always with them, the conjugate, so if we know that "i" or namely "0 + i" is there, her sister the conjugate "0 +i" must also be there too, so let's take a peek
![\begin{cases} x=-5\implies &x+5=0\\ x=0+i\implies &x-i=0\\ x=0-i\implies &x+i=0 \end{cases}\implies \underline{a(x+5)(x-i)(x+i)=\stackrel{0}{y}} \\\\[-0.35em] ~\dotfill](https://tex.z-dn.net/?f=%5Cbegin%7Bcases%7D%20x%3D-5%5Cimplies%20%26x%2B5%3D0%5C%5C%20x%3D0%2Bi%5Cimplies%20%26x-i%3D0%5C%5C%20x%3D0-i%5Cimplies%20%26x%2Bi%3D0%20%5Cend%7Bcases%7D%5Cimplies%20%5Cunderline%7Ba%28x%2B5%29%28x-i%29%28x%2Bi%29%3D%5Cstackrel%7B0%7D%7By%7D%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill)
![\underset{\textit{difference of squares}}{(x-i)(x+i)}\implies [x^2-i^2]\implies [x^2-(-1)]\implies (x^2+1) \\\\[-0.35em] ~\dotfill\\\\ \underline{a(x+5)(x^2+1)=y}~\hfill \stackrel{\textit{we also know that}}{f(\stackrel{x}{-3})=60}~\hfill a[(-3)+5][(-3)^2+1]=60 \\\\\\ a(2)(10)=60\implies 20a=60\implies a=\cfrac{60}{20}\implies a=3 \\\\[-0.35em] ~\dotfill\\\\ ~\hfill \underline{3(x+5)(x^2+1)=y}~\hfill](https://tex.z-dn.net/?f=%5Cunderset%7B%5Ctextit%7Bdifference%20of%20squares%7D%7D%7B%28x-i%29%28x%2Bi%29%7D%5Cimplies%20%5Bx%5E2-i%5E2%5D%5Cimplies%20%5Bx%5E2-%28-1%29%5D%5Cimplies%20%28x%5E2%2B1%29%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill%5C%5C%5C%5C%20%5Cunderline%7Ba%28x%2B5%29%28x%5E2%2B1%29%3Dy%7D~%5Chfill%20%5Cstackrel%7B%5Ctextit%7Bwe%20also%20know%20that%7D%7D%7Bf%28%5Cstackrel%7Bx%7D%7B-3%7D%29%3D60%7D~%5Chfill%20a%5B%28-3%29%2B5%5D%5B%28-3%29%5E2%2B1%5D%3D60%20%5C%5C%5C%5C%5C%5C%20a%282%29%2810%29%3D60%5Cimplies%2020a%3D60%5Cimplies%20a%3D%5Ccfrac%7B60%7D%7B20%7D%5Cimplies%20a%3D3%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill%5C%5C%5C%5C%20~%5Chfill%20%5Cunderline%7B3%28x%2B5%29%28x%5E2%2B1%29%3Dy%7D~%5Chfill)
Check the picture below.
Answer: A
Step-by-step explanation:
Tangent ∡Y = opposite/adjacent
Line XZ: Opposite
Line YX: Adjacent
Tangent ∡Y = 6/8 or 3/4
-14, -13, -12.
This is done by calling the first number x, the second x+1 and the third x+2. Then write the equation using the descriptions as...
x + 2(x+1) + 3(x+2) = -76
Distribute and solve.