Answer:
- -32x² +8x -8
- See below about the process
Step-by-step explanation:
The simplified expression is ...
3x(x -12x) +3x² -2(x -2)²
= 3x(-11x) +3x² -2(x² -4x +4) . . . . . simplify contents of parentheses
= -33x² +3x² -2x² +8x -8 . . . . . . . .eliminate parentheses
= (-33 +3 -2)x² +8x -8 . . . . . . . . . . group the coefficients of like terms
= -32x² +8x -8
Step-by-step explanation:
16. Length of a line = sqaureroot of ((x1-x0)^2 - (y1- y0)^2)
C (2,-3) D (6,3)
CD = sqaureroot of ((6-2)^2 + (3-(-3))^2)
CD = sqaureroot of ( 16 + 36)
CD = sqaureroot of 52 = 2 root 13 = length
17. E (5, - 1) because the point is under the x axis.
Midpoint = ((x1+ x0)/2 , (y1 +y0) /2)
B (8,1) C (2, - 3)
Midpoint of BC = ((2+8)/2 , (-3+1)/2)
= (10/2 , - 2/2)
= (5, - 1)
18. Length of AE
A (4,5) E(5,-1)
Square root of ((5-4)^2 + (-1-5)^2)
Square root of (1^2 + - 6^2)
Square root of ( 1 + 36)
Square root of 37 = root 37
Please gimme brainliest
Use the change-of-basis identity,
![\log_x(y) = \dfrac{\ln(y)}{\ln(x)}](https://tex.z-dn.net/?f=%5Clog_x%28y%29%20%3D%20%5Cdfrac%7B%5Cln%28y%29%7D%7B%5Cln%28x%29%7D)
to write
![xyz = \log_a(bc) \log_b(ac) \log_c(ab) = \dfrac{\ln(bc) \ln(ac) \ln(ab)}{\ln(a) \ln(b) \ln(c)}](https://tex.z-dn.net/?f=xyz%20%3D%20%5Clog_a%28bc%29%20%5Clog_b%28ac%29%20%5Clog_c%28ab%29%20%3D%20%5Cdfrac%7B%5Cln%28bc%29%20%5Cln%28ac%29%20%5Cln%28ab%29%7D%7B%5Cln%28a%29%20%5Cln%28b%29%20%5Cln%28c%29%7D)
Use the product-to-sum identity,
![\log_x(yz) = \log_x(y) + \log_x(z)](https://tex.z-dn.net/?f=%5Clog_x%28yz%29%20%3D%20%5Clog_x%28y%29%20%2B%20%5Clog_x%28z%29)
to write
![xyz = \dfrac{(\ln(b) + \ln(c)) (\ln(a) + \ln(c)) (\ln(a) + \ln(b))}{\ln(a) \ln(b) \ln(c)}](https://tex.z-dn.net/?f=xyz%20%3D%20%5Cdfrac%7B%28%5Cln%28b%29%20%2B%20%5Cln%28c%29%29%20%28%5Cln%28a%29%20%2B%20%5Cln%28c%29%29%20%28%5Cln%28a%29%20%2B%20%5Cln%28b%29%29%7D%7B%5Cln%28a%29%20%5Cln%28b%29%20%5Cln%28c%29%7D)
Redistribute the factors on the left side as
![xyz = \dfrac{\ln(b) + \ln(c)}{\ln(b)} \times \dfrac{\ln(a) + \ln(c)}{\ln(c)} \times \dfrac{\ln(a) + \ln(b)}{\ln(a)}](https://tex.z-dn.net/?f=xyz%20%3D%20%5Cdfrac%7B%5Cln%28b%29%20%2B%20%5Cln%28c%29%7D%7B%5Cln%28b%29%7D%20%5Ctimes%20%5Cdfrac%7B%5Cln%28a%29%20%2B%20%5Cln%28c%29%7D%7B%5Cln%28c%29%7D%20%5Ctimes%20%5Cdfrac%7B%5Cln%28a%29%20%2B%20%5Cln%28b%29%7D%7B%5Cln%28a%29%7D)
and simplify to
![xyz = \left(1 + \dfrac{\ln(c)}{\ln(b)}\right) \left(1 + \dfrac{\ln(a)}{\ln(c)}\right) \left(1 + \dfrac{\ln(b)}{\ln(a)}\right)](https://tex.z-dn.net/?f=xyz%20%3D%20%5Cleft%281%20%2B%20%5Cdfrac%7B%5Cln%28c%29%7D%7B%5Cln%28b%29%7D%5Cright%29%20%5Cleft%281%20%2B%20%5Cdfrac%7B%5Cln%28a%29%7D%7B%5Cln%28c%29%7D%5Cright%29%20%5Cleft%281%20%2B%20%5Cdfrac%7B%5Cln%28b%29%7D%7B%5Cln%28a%29%7D%5Cright%29)
Now expand the right side:
![xyz = 1 + \dfrac{\ln(c)}{\ln(b)} + \dfrac{\ln(a)}{\ln(c)} + \dfrac{\ln(b)}{\ln(a)} \\\\ ~~~~~~~~~~~~+ \dfrac{\ln(c)\ln(a)}{\ln(b)\ln(c)} + \dfrac{\ln(c)\ln(b)}{\ln(b)\ln(a)} + \dfrac{\ln(a)\ln(b)}{\ln(c)\ln(a)} \\\\ ~~~~~~~~~~~~ + \dfrac{\ln(c)\ln(a)\ln(b)}{\ln(b)\ln(c)\ln(a)}](https://tex.z-dn.net/?f=xyz%20%3D%201%20%2B%20%5Cdfrac%7B%5Cln%28c%29%7D%7B%5Cln%28b%29%7D%20%2B%20%5Cdfrac%7B%5Cln%28a%29%7D%7B%5Cln%28c%29%7D%20%2B%20%5Cdfrac%7B%5Cln%28b%29%7D%7B%5Cln%28a%29%7D%20%5C%5C%5C%5C%20~~~~~~~~~~~~%2B%20%5Cdfrac%7B%5Cln%28c%29%5Cln%28a%29%7D%7B%5Cln%28b%29%5Cln%28c%29%7D%20%2B%20%5Cdfrac%7B%5Cln%28c%29%5Cln%28b%29%7D%7B%5Cln%28b%29%5Cln%28a%29%7D%20%2B%20%5Cdfrac%7B%5Cln%28a%29%5Cln%28b%29%7D%7B%5Cln%28c%29%5Cln%28a%29%7D%20%5C%5C%5C%5C%20~~~~~~~~~~~~%20%2B%20%5Cdfrac%7B%5Cln%28c%29%5Cln%28a%29%5Cln%28b%29%7D%7B%5Cln%28b%29%5Cln%28c%29%5Cln%28a%29%7D)
Simplify and rewrite using the logarithm properties mentioned earlier.
![xyz = 1 + \dfrac{\ln(c)}{\ln(b)} + \dfrac{\ln(a)}{\ln(c)} + \dfrac{\ln(b)}{\ln(a)} + \dfrac{\ln(a)}{\ln(b)} + \dfrac{\ln(c)}{\ln(a)} + \dfrac{\ln(b)}{\ln(c)} + 1](https://tex.z-dn.net/?f=xyz%20%3D%201%20%2B%20%5Cdfrac%7B%5Cln%28c%29%7D%7B%5Cln%28b%29%7D%20%2B%20%5Cdfrac%7B%5Cln%28a%29%7D%7B%5Cln%28c%29%7D%20%2B%20%5Cdfrac%7B%5Cln%28b%29%7D%7B%5Cln%28a%29%7D%20%2B%20%5Cdfrac%7B%5Cln%28a%29%7D%7B%5Cln%28b%29%7D%20%2B%20%5Cdfrac%7B%5Cln%28c%29%7D%7B%5Cln%28a%29%7D%20%2B%20%5Cdfrac%7B%5Cln%28b%29%7D%7B%5Cln%28c%29%7D%20%2B%201)
![xyz = 2 + \dfrac{\ln(c)+\ln(a)}{\ln(b)} + \dfrac{\ln(a)+\ln(b)}{\ln(c)} + \dfrac{\ln(b)+\ln(c)}{\ln(a)}](https://tex.z-dn.net/?f=xyz%20%3D%202%20%2B%20%5Cdfrac%7B%5Cln%28c%29%2B%5Cln%28a%29%7D%7B%5Cln%28b%29%7D%20%2B%20%5Cdfrac%7B%5Cln%28a%29%2B%5Cln%28b%29%7D%7B%5Cln%28c%29%7D%20%2B%20%5Cdfrac%7B%5Cln%28b%29%2B%5Cln%28c%29%7D%7B%5Cln%28a%29%7D)
![xyz = 2 + \dfrac{\ln(ac)}{\ln(b)} + \dfrac{\ln(ab)}{\ln(c)} + \dfrac{\ln(bc)}{\ln(a)}](https://tex.z-dn.net/?f=xyz%20%3D%202%20%2B%20%5Cdfrac%7B%5Cln%28ac%29%7D%7B%5Cln%28b%29%7D%20%2B%20%5Cdfrac%7B%5Cln%28ab%29%7D%7B%5Cln%28c%29%7D%20%2B%20%5Cdfrac%7B%5Cln%28bc%29%7D%7B%5Cln%28a%29%7D)
![xyz = 2 + \log_b(ac) + \log_c(ab) + \log_a(bc)](https://tex.z-dn.net/?f=xyz%20%3D%202%20%2B%20%5Clog_b%28ac%29%20%2B%20%5Clog_c%28ab%29%20%2B%20%5Clog_a%28bc%29)
![\implies \boxed{xyz = x + y + z + 2}](https://tex.z-dn.net/?f=%5Cimplies%20%5Cboxed%7Bxyz%20%3D%20x%20%2B%20y%20%2B%20z%20%2B%202%7D)
(C)
Answer:
24 will be your answer.
Step-by-step explanation:
1500 x 60 = the number of cans made in one hour (90,000)
90,000 x 8 = the number of cans made in 8 hours (720,000)
720,000 x 300 = 216,000,000 ml of cola
Hope this helps you out!