Answer:
<2, <3, <4
Step-by-step explanation:
You have parallel lines cut by a transversal, so alternate interior angles are congruent. Also, alternate exterior angles are congruent. Corresponding angles are congruent.
Vertical angles are always congruent.
I'll write each congruent angle and the reason.
<2, vertical
<3, corresponding
<4, alternate exterior angle
Answer:
0.96153846153
Step-by-step explanation:
creo que la respuesta es 0.96153846153
porque if you divide 50/52 if should give you the right respuesta!
let's call the children "c" and the adults "a"
the total # of people in the restaurant = c+a
so 2/9 of (c+a) = a
therefore 2/9c + 2/9a = a
and a + 95 = c since there are 95 MORE children.
Let's substitute a+95 for c in the equation 2/9(c+a) = a
this gives us 2/9(a+95 + a) = a
then 2/9 a + 2/9(95) + 2/9(a) = a
so 4/9a +190/9 = a
and 190/9 = 5/9 a
so 190 must = 5a
finally a = 38 so c must = 38 + 95 = 133 there are 133 children
9514 1404 393
Answer:
see attached
Step-by-step explanation:
I started with triangle GHJ on the right. It is isosceles, so ...
g = 48°
h = 2(90 -g) = 84°
k = 180° -h = 96°
Then, on the lower right, we have ...
a = 180° -143° = 37°
b = 143°
c = e = a = 37°
f = 90° -e = 53°
At vertex D, we also have ...
85° +d = b ⇒ d = 143° -85° = 58°
In triangle DGH, we have ...
m + d = h ⇒ m = h -d = 84° -58° = 26°
The sum of angles in triangle DGP is 180°, so ...
p = 180° -85° -26° = 69°
Finally, ...
s = p = 69°
r = 180° -p = 111°
_____
The relationships we used are ...
- corresponding angles are congruent (at a transversal of parallel lines)
- alternate interior angles are congruent
- an exterior angle equals the sum of remote interior angles
- acute angles in a right triangle are complementary
- angles in a triangle sum to 180°
- linear pair angles are supplementary
- angle sum theorem
The north displacement and the east displacement can be viewed as simply the legs of a right triangle and the distance between them is just the magnitude of the hypotenuse so:
h^2=x^2+y^2, where h is the distance between the two points, x is the easterly distance and y is the northerly distance....
h^2=.8^2+.6^2
h^2=.64+.36
h^2=1
h=1
So they are one mile apart from each other.
