Answer:
length is 17 in, width is 20
Step-by-step explanation:
let's shape this as an algebraic equation, where x= the length of one side.
since the width is 3 inches longer than the length, x will be the length and x+3 will be the width.
the perimeter is 74 in, and the perimeter is the added length of all sides. in a rectangle, 2 sides are the length and 2 sides are the width, so:
74 = 2x + 2(x + 3)
let's distribute the 2.
74 = 2x + 2x + 6
now, we combine the x's.
74 = 4x + 6
after this step, subtract 6 from the right to add it to the left side.
68 = 4x
finally, divide both sides by 4.
17 = x
perfect! now that we know the length, we just have to add 3 to find the width.
17 + 3 = 20
So, we are given 5^8. It was happy and content. But then... we had to write it as a quotient of two exponential terms with the same base in four different ways and use negative or zero exponents and ahhhhhh!!!
... anyways...
We'll build a quotient of two exponential terms with the same base 5. Something like this:
5^a / 5^b
We need them to make 5^8 when we are done. I'll first use a zero exponent.
[1] Now, zero exponents are nice since they make things equal 1. Like 5^0 = 1. Well, obviously, 5^8 / 1 = 5^8. So, our first quotient can be:
5^8 / 5^0
Done.
[2] Let's try this on its head. This one's a little weird. Remember that negative exponents flip things upside down. So 5^-8 = 1/5^8 and 1/5^-8 = 5^8 for example. In fact... that's the answer!
5^0 / 5^-8 = 5^8
Done.
[3] Let's try to not use 0s or 8s. We can be clever and do something like this:
5^-1 / 5^-9
What the heck is that? Well, we just flip them and get:
5^-1 / 5^-9 = 5^9 / 5^1 = 5^8
Done.
[4] Can you come up with one last trick on your own? Try it!
~In a total of 30 minutes Ashley has read 40 pages (20 the first 10 minutes and 20 more pages after her break)
~y=1.2x
~y is the total amount of pages Adam read
~x is the amount of time he read
~The function for Ashley should look like this y=2x
~The functions are similar because they both read at a constant rate for a constant amount of time
~The functions are different because Ashley reads 2 pages a minute where as Adam reads more or less (depending on if Adam took a break or not)
~I figure this because even though Adam's pages per minute is less, assuming he doesn't take a break his function (if graphed) could eventually exceed Ashley's.
For Example:
let's say Ashley reads for 10 minutes (2 pages per minute) she takes a 5 minute break and reads for another 10 minutes (also 2 pages a minute)
That would look like this:
Answer:
33%
Step-by-step explanation:
350 * 100 = 35,000
35,000 / 550 = 63.4
100 - 63 = 37
If I did this wrong I am very sorry. 37 is close to 33. The closest answer would be the first choice (approximately 33%).