2)
![w^2-3,\quad w=4](https://img.qammunity.org/2023/formulas/mathematics/high-school/n1bzfmuey4vyyrxf8x0ksqsyoidpur1k4z.png)
When we say that w = 4, it means that we can rewrite the expression and instead of "w", we will put "4", so
![w^2-3\Rightarrow4^2-3](https://img.qammunity.org/2023/formulas/mathematics/high-school/sjt8f8mrx6iovduw2nt1evdcy4jdq299vp.png)
Now we have a numerical expression to solve, we can easily solve it!
![\begin{gathered} 4^2-3 \\ \\ 4\cdot4-3 \\ \\ 16-3 \\ \\ 13 \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/high-school/ydzr0jltfbto90u9ghtcmaacvg3nfujook.png)
Therefore, the final answer is
![4^2-3=13](https://img.qammunity.org/2023/formulas/mathematics/high-school/g3s7l1s0p55fk2fs9uibsskl1eh230z7ui.png)
5)
Here we will do the same thing, the "hard" part is solving the numeric expression, it will be a little bit harder than the 2).
![3(6m-17),\quad m=5](https://img.qammunity.org/2023/formulas/mathematics/high-school/y0ivanydt3fiimz852mywx14md3w4o8vn2.png)
Again, repeat the same process, rewrite the expression, and instead of "m" you put "5"
![3(6m-17)\Rightarrow3(6\cdot5-17)](https://img.qammunity.org/2023/formulas/mathematics/high-school/qqe5m1z4yovofngxxfz46kjohqdipbkmg3.png)
Again, another expression to simplify, remember that we always solve what is inside ( ) first, and we have a multiplication inside ( ) so we must solve it first
![3(6\cdot5-17)=3(30-17)](https://img.qammunity.org/2023/formulas/mathematics/high-school/asbitp17oozsh7i2j94fc1mji6mfctrgsc.png)
Now we solve the multiplication inside ( ) we can do the subctration
![3(30-17)=3\cdot(13)](https://img.qammunity.org/2023/formulas/mathematics/high-school/97wesdhd8m5q5o2249or3na486p9hngz70.png)
The last step is just to solve another multiplication
![3\cdot(13)=39](https://img.qammunity.org/2023/formulas/mathematics/high-school/dvs7whpl9daemoxfjhq5quxu89bhlcfwo5.png)
Now we simplified everything we can have the final answer:
![3(6\cdot5-17)=39](https://img.qammunity.org/2023/formulas/mathematics/high-school/u0ur5gnkce8v1bg4wm4w78ext16pz6ue7s.png)
6)
Here we have a division, but it's similar with 5) and 2), we have
![(2a)/(3)+13,\quad a=15](https://img.qammunity.org/2023/formulas/mathematics/high-school/e1ae6kj2bua6dq6gstkes0cesqaua09pt1.png)
No secrets, repeat the process, but here, "a" will turn into "15", then
![(2a)/(3)+13\Rightarrow(2\cdot15)/(3)+13](https://img.qammunity.org/2023/formulas/mathematics/high-school/y1heus9aczpsekh6pxuv3xwqiuvhwhll58.png)
We can do the multiplication at the numerator of the fraction
![(2\cdot15)/(3)+13=(30)/(3)+13](https://img.qammunity.org/2023/formulas/mathematics/high-school/aw69xi0ubywlygaoz712je9uz40bfjrd9l.png)
Now we can simplify the fraction, 30 divided by 3 is 10, then
![(30)/(3)+13=10+13](https://img.qammunity.org/2023/formulas/mathematics/high-school/3749rmi68qaa5zkdzbh2qedgv19pw0xt7i.png)
Now just do the sum and it's done!
![10+13=23](https://img.qammunity.org/2023/formulas/mathematics/high-school/4r542l8vpa3iwfpi9ftz06iz3yqzvos03w.png)
Hence the final answer is
![(2\cdot15)/(3)+13=23](https://img.qammunity.org/2023/formulas/mathematics/high-school/7x6r7io31c92mfywxye1cc97i4kz2npxgo.png)
ANSWERS:
1) 43
2) 13
3) 67
4) 12
5) 39
6) 23