Answer:The correct answer is 4 packages of hot dogs and 5 packages of hot dog buns
Explanation:
To find the least number of packages of each item the team has to buy, it is necessary to find the Least Common Multiple of the two numbers (10 and 8), which is the lowest integer that is multiple of both 10 and 8, and therefore represents the least number of hot dogs and hot dog buns the team has to buy to get the same number of the two items. Now, to find the LCM follow this process:
1. List the two numbers
10
8
2. Now, find the multiplies of each number
10 x 1 = 10 / 10 x 2= 20/ 10 x 3= 30 / 10 x 4 = 40...
8 x 1= 8/ 8 x 2 = 16 / 8 x 3 = 24 / 8 x 4 = 32 / 8 x5 = 40...
3. Notice the first common number in both, in this case, 40 because 10 x 4 = 40 and 8 x 5= 40.
This means the Least Common Multiple is 40, and therefore the team should buy 40 of each item. Additionally, this means they need to buy 4 packages of hot dogs (each package contains 10 units) and 5 packages of hot dog buns (each package contains 8 units).
It would be an acute isosceles triangle
Shawn can expect to make 12 free throw in his next game
Step-by-step explanation:
(1 + ax)⁴(2 - x)³ = (1 + 2ax + a²x²)²(8 - 12x + 6x² - x³) =
(1 + 4a²x² + a⁴x⁴ + 4ax + 2a²x² + 4a³x³)(8 - 12x + 6x² - x³) = ... 6x² + 32a²x² - 48ax² + 16ax² ...
= ... x²(6 + 32a² - 32a) ...
32a² - 32a + 6 = 6
32a(a - 1) = 0 → 32a = 0 → a = 0 OR a - 1 = 0 → a = 1
