Answer:
f(g(x)) = 7x + 27
Step-by-step explanation:
We have, f(x) = 7x+13 and g(x) = x+2.
So, the function f(g(x)) is obtained by substituting the function g(x) = x+2 in f(x) = 7x+13,
i.e. f(g(x)) = f(x+2)
i.e. f(g(x)) = 7 × (x+2) + 13
i.e. f(g(x)) = 7x + 14 + 13
i.e. f(g(x)) = 7x + 27
Thus, f(g(x)) = 7x + 27
Your answer would be 9/27 but can be converted to 1/3. Hope this helps
Answer:
Part a)
of fabric
Part b)
of thread
Step-by-step explanation:
we know that
A seamstress uses
centimeters of thread for every
centimeters of fabric
Part a)
by proportion
Find how much fabric is involved if the seamstress uses
centimeters of thread
![\frac{7.6}{5.7}\frac{cm\ fabric}{cm\ thread} =\frac{x}{4.2}\frac{cm\ fabric}{cm\ thread} \\ \\x=4.2*7.6/5.7\\ \\x=5.6\ cm\ fabric](https://tex.z-dn.net/?f=%5Cfrac%7B7.6%7D%7B5.7%7D%5Cfrac%7Bcm%5C%20fabric%7D%7Bcm%5C%20thread%7D%20%3D%5Cfrac%7Bx%7D%7B4.2%7D%5Cfrac%7Bcm%5C%20fabric%7D%7Bcm%5C%20thread%7D%20%5C%5C%20%5C%5Cx%3D4.2%2A7.6%2F5.7%5C%5C%20%5C%5Cx%3D5.6%5C%20cm%5C%20fabric)
Part b)
by proportion
Find how many centimeters of thread is needed if the seamstress is working with
centimeters of fabric
![\frac{7.6}{5.7}\frac{cm\ fabric}{cm\ thread} =\frac{21.2}{x}\frac{cm\ fabric}{cm\ thread} \\ \\x=5.7*21.2/7.6\\ \\x=15.9\ cm\ thread](https://tex.z-dn.net/?f=%5Cfrac%7B7.6%7D%7B5.7%7D%5Cfrac%7Bcm%5C%20fabric%7D%7Bcm%5C%20thread%7D%20%3D%5Cfrac%7B21.2%7D%7Bx%7D%5Cfrac%7Bcm%5C%20fabric%7D%7Bcm%5C%20thread%7D%20%5C%5C%20%5C%5Cx%3D5.7%2A21.2%2F7.6%5C%5C%20%5C%5Cx%3D15.9%5C%20cm%5C%20thread)
Each batch has 18 cookies
7*18+252= 378
So 378 cookies