9514 1404 393
Answer:
1. B, E
2. A, E
16. B'(1, 5)
Step-by-step explanation:
Lines p and r are parallel, as are lines a and b. Either of the lines in one parallel pair is perpendicular to the lines in the other parallel pair. Line q has no necessary relation to anything, so can be ignored. (No answer containing q can be correct.)
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1. p ⊥ b
r ⊥ a
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2. r║p
a║b
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16. Point B(3, 2) translated (right, up) = (-2, 3) will be ...
B' = B + (-2, 3) = (3, 2) +(-2, 3) = (3 -2, 2 +3)
B' = (1, 5)
Note: (x, y) coordinates are (<em>right</em>, <em>up</em>). So, in translation problems it is important to <em>pay attention.</em> Often, the up/down translation is listed before the left/right translation. If you're not paying attention, you may inadvertently reverse the numbers that need to be added to the coordinates to do the translation.
The length of OM is 4/3 the length of OJ, and the length of ON is 4/3 the length of OK. Thus, two pairs of sides from the triangles are proportional to each other.
Also, angle O from one of the triangles is equal to angle O of the other triangle because they are the same angle.
Thus, the two triangles are similar by SAS (side-angle-side) similarity theorem. This theorem is quite similar to the SAS congruence theorem.
To make a similarity statement, we just have to match corresponding parts when naming the triangle.
Similarity statement: ΔOJK~ΔOMN
Answer:
a. 208.5 ft.
b. 144.9 ft.
Both correct to the nearest tenth.
Step-by-step explanation:
(a) sin 46 = 150 / h where h is the length of the wire.
h = 150/ sin 46
= 208.5 ft.
(b) tan 46 = 150 / x where x is the distance required.
x = 150 / tan 46
x = 144.9 ft.
The first thing to do is to calculate how many ways you can choose 3 people from a set of eight. In order to do this, we need to use the attached formula.
(The letter 'n' stands for the entire set and 'r' stands for the number of objects we wish to choose.)
So we wish to choose 3 people ('r') form a set of 8 ('n')
combinations = n! / r! * (n - r)!
combinations = 8 ! / (3! * 5!)
combinations = 8 * 7 * 6 * 5! / (3!) * (5!)
combinations = 8 * 7 * 6 / 3 * 2
combinations = 56
Now of those 56 combinations, the 3 people can finish in 6 different ways.
For example, persons A, B and C could finish
ABC or ACB or BAC or BCA or CAB or CBA
So to get the TOTAL combinations we multiply 56 * 6 which equals
336 so the answer is (a)
