Question 1:
For this case we must find the value of the following expression:
![4 ^ 3-3 ^ 3](https://img.qammunity.org/2020/formulas/mathematics/middle-school/7cemo7nrfaopao4tdrmvjavq24ocl8oyn6.png)
So we have to:
![4 ^ 3 = 4 * 4 * 4 = 4 ^ 2 * 4 = 16 * 4 = 64\\3 ^ 3 = 3 * 3 * 3 = 3 ^ 2 * 3 = 9 * 3 = 27](https://img.qammunity.org/2020/formulas/mathematics/middle-school/w1vqhrvdh4l1ua9v210y044puanb6ce2wj.png)
Substituting we have:
![64-27 =\\37](https://img.qammunity.org/2020/formulas/mathematics/middle-school/zlwmihibr7d4ij8g7gphlvvvv4ad9y97wb.png)
Thus, the value of the expression is 37.
Answer:
![4 ^ 3-3 ^ 3 = 37](https://img.qammunity.org/2020/formulas/mathematics/middle-school/cbvmpi27d0ulf9h2gtu9u1nzeoa98kmdf5.png)
Option C
Question 2:
For this case we have the following expression:
![2 * 3 ^ 2](https://img.qammunity.org/2020/formulas/mathematics/middle-school/fluvih7mf9f2k1yb17pq5z0t8edyddtrnw.png)
We must simplify it!
We have to:
![3 ^ 2 = 3 * 3 = 9](https://img.qammunity.org/2020/formulas/mathematics/middle-school/irv4nxuw7a1plo0y896mc839nalwadvv7q.png)
Rewriting the expression we have
![2 * 9 =](https://img.qammunity.org/2020/formulas/mathematics/middle-school/ki8t89zvlgzwqgzu8wl9fua4yimehl2ept.png)
2 times 9 is 18.
Finally we have to:
![2 * 3 ^ 2 = 18](https://img.qammunity.org/2020/formulas/mathematics/middle-school/xsz9hhclohgde2jcl30kulasqrqw9l6iea.png)
Answer:
![2 * 3 ^ 2 = 18](https://img.qammunity.org/2020/formulas/mathematics/middle-school/xsz9hhclohgde2jcl30kulasqrqw9l6iea.png)
Option B
Question 3:
For this case we have that by definition, the perimeter of a square is given by:
![P = 4l](https://img.qammunity.org/2020/formulas/mathematics/middle-school/5ezut5lync25ohnpn5xlz1x5rn4w5fb7p0.png)
Where:
l: It's the side of the square
In this case they tell us that:
![l = 50 \ in](https://img.qammunity.org/2020/formulas/mathematics/middle-school/e5yg8e0161h6emipk8zgq8w5375ij27tqm.png)
Thus:
![P = 4 * 50\\P = 200 \ in](https://img.qammunity.org/2020/formulas/mathematics/middle-school/mjri441xqd7exoaotqmkp239053vi99iu1.png)
Now we must do a conversion. By definition we have to:
1 foot equals 12 inches. So:
![200 \ in * \frac {1} {12} * \frac {ft} {in} = \frac {50} {3} ft = 16.67ft\\](https://img.qammunity.org/2020/formulas/mathematics/middle-school/7449wgav7yzw044my8oi37vpmnct47pnbf.png)
Answer:
The perimeter of the garden is
![16.67 \ ft](https://img.qammunity.org/2020/formulas/mathematics/middle-school/oq8060598fj79cqku76m12x8mqq6dmvm23.png)
Question 4:
For this case we have to:
Let "p" be the variable that represents the number of pages Nora read yesterday.
If today I read 6 more than yesterday, then we can write the following expression:
![p + 6](https://img.qammunity.org/2020/formulas/mathematics/middle-school/4fxz8dixenmiwt3u2rdr4mmotu3ijh9sio.png)
So, the number of pages that Nora read today is
![p + 6](https://img.qammunity.org/2020/formulas/mathematics/middle-school/4fxz8dixenmiwt3u2rdr4mmotu3ijh9sio.png)
ANswer:
The number of pages that Nora read today is
![p + 6](https://img.qammunity.org/2020/formulas/mathematics/middle-school/4fxz8dixenmiwt3u2rdr4mmotu3ijh9sio.png)
Question 5:
For this case we have that by definition, the area of a triangle is given by:
![A = \frac {b * h} {2}](https://img.qammunity.org/2020/formulas/mathematics/middle-school/nskfgyvd43h5b9dznhzd5k5qm38omkmn00.png)
Where:
b: It is the base of the triangle
h: It is the height
We have as data that:
![b = 5 \ cm\\h = 8 \ cm](https://img.qammunity.org/2020/formulas/mathematics/middle-school/24rm0tfqh28t5mvhrznxl78vdlsvt7rnyp.png)
Substituting we have:
![A = \frac {5 * 8} {2} = \frac {40} {2} = 20 \ cm ^ 2](https://img.qammunity.org/2020/formulas/mathematics/middle-school/2x0g0ufvnhms5dbztfkp8lj6g3frs6abym.png)
The area of the triangle is
![20 \ cm ^ 2](https://img.qammunity.org/2020/formulas/mathematics/middle-school/hbtkh5d6ctma0w4eu1o03lkqz23arqgzkw.png)
Answer:
Option B