Micah is buying items for a party. There are 6 cups in a package and 8 plates in a package. If he wants to have the same amount of each item, what is the least number of packages of cups he needs to buy

24

Step-by-step explanation:

From the question, we are informed that Micah is buying items for a party and that there are 6 cups in a package and 8 plates in a package.

We are further told that he wants to have the same amount of each item. The least number of packages of cups he needs to buy would be calculated by finding the least common multiple of 6 and 8.

Multiples of 6 = 6, 12 18, 24, 30

Multiples of 8 = 8, 16, 24, 32, 40

The answer is 24 cups

a4 - 3a2 - 1

step-by-step explanation:

step   1   :

equation at the end of step   1   :

  ((a4) -   3a2) -   1

step   2   :

trying to factor by splitting the middle term

2.1     factoring   a4-3a2-1  

the first term is,   a4   its coefficient is   1 .

the middle term is,   -3a2   its coefficient is   -3 .

the last term, "the constant", is   -1  

b. an equilateral triangle inscribed in a circle

step-by-step explanation:

we are given the figure of two circles having a triangle inside.

now, we know that,

"when a figure is lying inside an another figure, then the outside figure is known as circumscribed figure and the figure lying inside is referred to as the inscribed figure".

as we see that, the circles are containing the triangle completely.

thus, the circles are the circumscribed figures and the triangle is the inscribed figure.

hence, we get, 'an equilateral triangle is inscribed in a circle'.