Are there instances that rational algebraic equation can be transformed into quadratic equation

yes you can

Step-by-step explanation:

for example you have a second order algebraic equation, which have the general form ax^2 + bx + c = 0, for any constants a, b, and c, you can use the quadratic equation to find the values of x. However, sometimes it is easier to simply factor the expression into (fx+g)(hx+i) = 0, for any constants f, g, h, and i, and then solve the two resulting equations fx+g = 0 and hx+i=0 for the values of x.

i hope this helps

the revenue of the fitness center, y, is the product of two factors: the number of members and the fee paid by each member. there are 320 members now, but number of members goes down by 10 for each $5 increase in fees, so if x is the number of $5 price increases then members is equal to (320 - 10x). since the fee is currently $45, and the fee increases by $5 for every price bump x, the fee is given by (45 + 5x). so, revenue y is given by y = (320 - 10x)(45 + 5x).

45.36 feet per second

step-by-step explanation:

tyrone travels 30 miles in 58.2 minutes.  

1 mile = 5280 feet; this means he travels

30(5280) = 158400 feet in 58.2 minutes.

1 minute = 60 seconds; this means he travels 158400 feet in

58.2(60) = 3492 seconds.

this gives us the unit rate of

158400/3492 = 45.36 feet per second.