Answer:
- width: 18 in
- length: 27 in
Step-by-step explanation:
The relations between length (L) and width (W) are ...
W +9 = L
LW = 486
Substituting gives ...
(W+9)W = 486
W^2 +9W -486 = 0 . . . put in standard form
(W +27)(W -18) = 0 . . . . factor
W = 18 . . . . the positive solution
The width of the rectangle is 18 inches; the length is 27 inches.
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<em>Comment on factoring</em>
There are a number of ways to solve quadratics. Apart from using a graphing calculator, one of the easiest is factoring. Here, we're looking for factors of -486 that have a sum of 9.
486 = 2 × 3^5, so we might guess that the factors of interest are -2·3² = -18 and 3·3² = 27. These turn out to be correct: -18 +27 = 9; (-18)(27) = -486.
Part A: Shiloh would collect data on which student spends the most time at the beach
Part B: It is a statistical question
You leave at 1 P.M., the wedding ceremony starts at 5 P.M.
This gives you a 4 hour gap, the Wedding is 350 miles away, and you're traveling at 65 miles an hour.
Simply you can use two methods, (65 * 4) to verify if you'd make it or not or (350/65) to ensure how many hours it would take in total.
65 * 4 = 260 | Since this is not 350, we can verify that you'd be late.
350/65 = 5.4 (estimated) | Meaning it'd take about 5.4 hours.
To know how long that is we'd have to convert over.
5.4 = 5 2/5ths, 60 minutes are in an hour. Divide 60 by 5 to get 12, meaning:
1/5ths = 12/60ths, with that said multiply that by 2 to get your answer.
2/5ths = 24/60ths or 24 minutes.
This means you'd take 5 hours and 24 minutes to get there.
Originally we stated that the process would take 4 hours. Subtract:
(5 hours and 24 minutes) - (4 hours) = (1 hour and 24 minutes)
Concluding that you'd be late by an hour and 24 minutes.
I hope this helps, have a great rest of your day! ^ ^
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Answer:
AC is the longest side
AB is the shortest side
Step-by-step explanation:
We can find the third angle
A+B+C = 180
55+80+C = 180
135+C = 180
C = 180-135
C =45
The longest side is opposite the largest angle
B is the largest angle so AC is the longest side
C is the the smallest angle so AB is the shortest side
Answer: 16) 
(17) 
(18) 
(19) 3x - 18
<u>Step-by-step explanation:</u>
Inverse is when you swap the x's and y's and then solve for y
16) Given: y = x²
Swapped: x = y²
17) Given: y = 2x + 4
Swapped: x = 2y + 4
x - 4 = 2y
18) Given: y = (x + 2)²
Swapped: x = (y + 2)²
√x = y + 2
19) Given: 
Swapped: 
3(x - 6) = y
3x - 18 = y
