A’Leila is building a pen for her pet donkey. The pen is a rectangle with one side
measuring b yards and the adjacent side measuring a yards. A’Leila knows that
a = 1/3b
Write two different expressions giving the perimeter of the donkey’s pen.
Expression 1: The perimeter can be expressed as P = 2(a + b). Since a = 1/3b, we can substitute this into the formula to get P = 2(1/3b + b) = (2/3 + 2)b = (8/3)b.
Expression 2: We can also express the perimeter as P = 2b + 2a. Substituting the value of a = 1/3b, we get P = 2b + 2(1/3b) = 2b + (2/3)b = (8/3)b.
Both expressions give the perimeter of the donkey's pen as (8/3)b.
Choose a value for a that is greater than 5 and less than 15. Evaluate the
perimeter of the pen for that value, using one of the expressions that you
wrote.
Let's choose a value of a = 8.
Using Expression 1: P = (8/3)b
To find the value of b, we can substitute the value of a into the equation a = 1/3b and solve for b:
8 = 1/3b
Multiplying both sides by 3:
24 = b
Now we can substitute the value of b back into the expression for P:
P = (8/3)(24) = 64 yards
Therefore, for a value of a = 8 yards, the perimeter of the pen is 64 yards using Expression 1.
Explain why you used that expression to evaluate the perimeter of the
donkey’s pen.
I used Expression 1, P = 2(a + b), to evaluate the perimeter of the donkey's pen because it directly reflects the definition of perimeter as the sum of the lengths of all sides. This expression adds the lengths of the two adjacent sides, a and b, and then multiplies the sum by 2 to account for the fact that there are two pairs of adjacent sides in a rectangle.
Using Expression 1 allowed me to substitute the given value of a into the equation and calculate the value of b. Once I found the value of b, I was able to substitute it back into the expression to find the perimeter of the pen.
As Kush and Egypt built their relationship, how did trade create interdependence between the two areas? (1 point) Responses Egypt depended on Kush for all trade items. Egypt depended on Kush for all trade items. Kush depended on Egypt for all trade items. Kush depended on Egypt for all trade items. Each one depended upon the other for trade items. Each one depended upon the other for trade items. none of the above
none of the above
As Kush and Egypt built their relationship, trade created interdependence between the two areas in a mutually beneficial way. The trade between Kush and Egypt allowed each civilization to obtain goods and resources that were not readily available in their own region. For example, Egypt had access to valuable resources such as gold, ivory, and incense that Kush desired. In return, Kush provided Egypt with resources such as ebony, silver, and slaves. Both regions depended on each other to acquire necessary goods and items that they did not possess themselves. This interdependence fostered economic growth and cultural exchange between Kush and Egypt.