5x + 20 = 90 - a = 90 - (3x + 40)
5x + 20 = 90 - 3x - 40 = 50 - 3x
5x + 3x = 50 - 20
8x = 30
x = 30/8 = 15/4
b = 3(15/4) + 40 = 45/4 + 40 = 51.25
The measure of a supplementary angle is 180 - 51.25 = 128.75
Answer: The required derivative is 
Step-by-step explanation:
Since we have given that
![y=\ln[x(2x+3)^2]](https://tex.z-dn.net/?f=y%3D%5Cln%5Bx%282x%2B3%29%5E2%5D)
Differentiating log function w.r.t. x, we get that
![\dfrac{dy}{dx}=\dfrac{1}{[x(2x+3)^2]}\times [x'(2x+3)^2+(2x+3)^2'x]\\\\\dfrac{dy}{dx}=\dfrac{1}{[x(2x+3)^2]}\times [(2x+3)^2+2x(2x+3)]\\\\\dfrac{dy}{dx}=\dfrac{4x^2+9+12x+4x^2+6x}{x(2x+3)^2}\\\\\dfrac{dy}{dx}=\dfrac{8x^2+18x+9}{x(2x+3)^2}](https://tex.z-dn.net/?f=%5Cdfrac%7Bdy%7D%7Bdx%7D%3D%5Cdfrac%7B1%7D%7B%5Bx%282x%2B3%29%5E2%5D%7D%5Ctimes%20%5Bx%27%282x%2B3%29%5E2%2B%282x%2B3%29%5E2%27x%5D%5C%5C%5C%5C%5Cdfrac%7Bdy%7D%7Bdx%7D%3D%5Cdfrac%7B1%7D%7B%5Bx%282x%2B3%29%5E2%5D%7D%5Ctimes%20%5B%282x%2B3%29%5E2%2B2x%282x%2B3%29%5D%5C%5C%5C%5C%5Cdfrac%7Bdy%7D%7Bdx%7D%3D%5Cdfrac%7B4x%5E2%2B9%2B12x%2B4x%5E2%2B6x%7D%7Bx%282x%2B3%29%5E2%7D%5C%5C%5C%5C%5Cdfrac%7Bdy%7D%7Bdx%7D%3D%5Cdfrac%7B8x%5E2%2B18x%2B9%7D%7Bx%282x%2B3%29%5E2%7D)
Hence, the required derivative is
Answer:
4.16
Step-by-step explanation:
4.16
because thousanth is 5
1. 4(x + 3) = 4x + 12
2. -7(4 - y) = -28 + 7y
3. 6(3x + 5y - 4) = 18x + 30y - 24
4. (9a - 3) / 3 = 3a - 1
5. (0.4(0.3m + 0.6n) / 1.2) = (0.12m + 0.24n) / 1.2 = 0.1m + 0.2n
6. -9 2/3(-2 1/4a + b + 8 1/4) = 21 3/4a - 9 2/3b - 79 3/4)
7. 64x + 24.....GCF = 8.......8(8x + 3)
8. -5y - 35......GCF = -5.....-5(y + 7)
9. 36 - 8z.......GCF = 4.......4(9 - 2z)
10. 54n - 81...GCF = 27......27(2n - 3)
11. -2x + 5......-2(x - 5/2)
12. 3x - 8 .......3(x - 8/3)
13. -1/2x + 6....-1/2(x - 12)
14. -x - 10.......-x(1 + 10)
Answer:
Step-by-step explanation:
48k+48=-3k-3
48k+45=-3k
-51k=-3
solving for k
.0588 or .059
