9514 1404 393
Answer:
I, III
Step-by-step explanation:
You know from your study of the Pythagorean theorem that a triangle with sides 3, 4, and 5 will be a right triangle. Any scaled version of this triangle will also be a right triangle, so it is helpful to learn to recognize when scaled values of these numbers are used.
I -- the scale factor for a 3-4-5 right triangle is 2/10
II -- no isosceles right triangle has integer side lengths. (not a right triangle)
III -- the scale factor for a 3-4-5 right triangle is 1/13
IV -- the lengths do not form a triangle
Triangles I and III are right triangles.
_____
<em>Additional comment</em>
The sides of an isosceles right triangle have the ratios 1 : 1 : √2. The square root of 2 is irrational. No scaled version of this triangle can have rational side lengths.
Answer:
18+0.08B≥75
carolina needs to buy at least 713 paintballs
Step-by-step explanation:
18+0.08≥75 subtract 18
0.08B≥57 divide by 0.08
B≥712.5
Two immediate observations:
(1) Clearly, we can't have
, since that would make both the rational and the square root terms undefined.
(2) If
is real, then
only exists if
. This means that for
to exist, we require
.
If
, then we don't have to worry about
ever taking on a value of -2.
Answer:
64,000
Step-by-step explanation:
Multiply the numbers together:
-160 x -400 = 64,000
Answer:
does not exist
Step-by-step explanation:
The numerator has no real zeros. The denominator factors as ...
(x +4.7)(x -4.9)
so the expression has a vertical asymptote at x=4.9. It changes sign there, so the left limit is -∞ and the right limit is ∞. The limit does not exist.
