9514 1404 393
Answer:
A. no
B. no
C. obtuse
Step-by-step explanation:
For side lengths to form a triangle, the sum of the shorter two must exceed the longest.
A. 5 + 8 = 13 . . . . a line segment, not a triangle
B. 7 + 12 < 26 . . . . no closure, not a triangle
C. 11 + 15 > 20 . . . . a triangle. A picture shows it to be obtuse
You can also compare 11² +15² vs 20² ⇒ 346 vs 400. The long side is too long for a right triangle, so the triangle must be obtuse. (The Pythagorean theorem tells you a right triangle with those legs would have a long side of √346 = 18.6.)
Answer:
120
Step-by-step explanation:
3/8 3*8=24, 24+3 = 27
5/12 5*12 =60 60÷5= 65
27 + 65 = 92
212-212- 92=120
Answer:
(x, y) = (4, 9)
Step-by-step explanation:
You can use the second equation to write an expression for y.
y = 10 - 1/4x . . . . subtract 1/4x from the given 2nd equation
Now, substitute that for y in the first equation:
1/2x + 1/3(10 -1/4x) = 5
1/2x + 10/3 -1/12x = 5 . . . . eliminate parentheses
You can work this a couple of ways from here. One is to multiply by 12 to eliminate fractions. Another is to work with the numbers as they are. We'll do that, because we don't get enough practice doing arithmetic with fractions.
5/12x = 5/3 . . . . . subtract 10/3
x = (5/3)/(5/12) = 12/3 = 4
From above, we can use our expression for y:
y = 10 - 1/4·4 = 9
The solution is (x, y) = (4, 9).
Make the fractions have common denominators.
rings 5 / 9 * 5/5 = 25/45
earrings 5/15 * 3/3 = 15/45
So, now we can compare 25 to 15. 25 is 5/3 bigger than 15.
or the ring inventory is 1.666666666... times greater than the earring inventory.
N is greater than or equal to 30 would be the condition that must be met in order to make a statistical inference about a population based on a sample if the sample does not come from a normally distributed population.
