Answer:
1. it is not a direct variation because the value k is not kept throughout the ordered pairs
2. -a^5 - 2a³ + 2a², leading coefficient is -1
Explanation:
1. to find the direct variation, we will use y/x = k with k representing our constant throughout the chart. if every value is equal to k, it is a direct variation
for this problem we will assume that the cup sizes are x and the cost is y
so the ordered pairs are (8, 0.90), (12, 1.35), (16, 1.80), and (24, 2.25)
.90/8 = 0.1125 <-- this is our k value for which every result has to be equal to
1.35/12 = 0.1125
1.80/12 = 0.1125
2.25/24 = 0.09375
since the value k was not kept throughout the ordered pairs, this is not a direct variation
2. the standard form of a polynomial is the exponents in descending order.
we have the following polynomial: 2a² - a^5 -2a³
to write it in standard form, we will go in descending order of the exponents. the largest exponent being first
-a^5 - 2a³ + 2a²
the leading coefficient of the polynomial is -1, as there is a negative sign in front of the newly formed polynomial