Which phrase does not describe a rational number? Select one:

repeating decimal

integer number

terminating decimal

О

non-repeating, non-terminating decimal

Explanation:

Any rational number is of the form p/q, where p and q are integers and q is nonzero. So basically it's any fraction you can think of.

If a decimal terminates (ie stops) then it is a rational number.

For instance, 0.9 = 9/10 is rational

If a decimal repeats in some way, then it is rational

Eg: 0.0833333 = 1/12

The dots after the 3 indicate the 3's go on forever.

So far, the facts mentioned allow us to rule out choices A and C. Choice B can be ruled out as well because any integer is always rational. We can easily prove it as such by writing the integer x as x/1.

A more concrete example could be writing the integer 7 as 7/1. So this shows 7 is rational and any integer is rational. Simply stick the integer over 1.

The only thing left at this point is choice D. Any non-repeating non-terminating decimal will be irrational. An example would be pi = 3.14159... which goes on forever without a pattern that repeats. Effectively the decimal digits of pi are more or less random. An irrational number is one that is not rational, and therefore cannot be written as a ratio of two integers.

answer: solve 5\cdot 2^x=2405⋅2  

x

=2405, dot, 2, start superscript, x, end superscript, equals, 240.

solution

to solve for xxx, we must first isolate the exponential part. to do this, divide both sides by 555 as shown below. we do not multiply the 555 and the 222 as this goes against the order of operations!

\begin{aligned} 5\cdot 2^x& =240 2^x& =48 \\ \end{aligned}  

5⋅2  

x

2  

x

​    

=240

=48

​

step-by-step explanation:

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).