Suppose r(x) and t(x) are two functions with the same domain, and let h(x)=r(x)+t(x). Suppose also that each of the 3 functions r, t and h, has a maximum value in this domain (i. e. a value that is greater than or equal to all the other values of the function).

Let M = the maximum value of r(x),
N = the maximum value of t(x), and
P = the maximum value of h(x).
How might the following always be true that M+N=P?

Prove the relationship to be true, or state what relationship does exist between the numbers M+N and P.

If the maximum of function r(x) and t(x) occur at the same point c in domain P = max(r(x)+t(x)) = M+N

In general P  ≤  M+N

Step-by-step explanation:

If the maximum of function r(x) and t(x) occur at the same point c in domain then M=r(c) and N=t(c) So in this case P = max(r(x)+t(x)) = M+N

In general P  ≤  M+N

by definition of maximum  

r(x)≤M,t(x)≤N   for all x in domain

=>  r(x)+t(x)≤M+N   for all x in domain

=> max(r(x)+t(x)) <= M+N

=> P  ≤  M+N

Thus we get in general the relationship is P  ≤  M+N

can you rephrase the question ? it is unclear : -)

step-by-step explanation:

the final amount you will pay is $68.04.

the tip is determined by the pre-tax amount, so we calculate the tip based on the original bill, not after we've added sales tax.

to find the tip:

we can divide 54.00 by 100 to get 1% of 54. then we multiply that by 18.

54 / 100 = .54

.54 x 18 = 9.72

tip = 9.72$

to find the tax:

we can divide 54.00 by 100 to get 1% of 54. then we can multiply that by 8 to get 8%.

54 / 100 = .54

.54 x 8 = 4.32

tax= 4.32

now we can add the tip and tax to the bill to get our total.

54 + 9.72 + 4.32 = 68.04

total: $68.04

step-by-step explanation: