1. The argument is valid by the Law of Detachment.
2. Determine the contrapositive statement of the conditional, so we have...
If you live in Idaho, then you do not live in New York City.
3. If ticket prices are low and the line to purchase them is short, then I will go to the show.
4. If Satish takes the Tuesday 8:00am Chemistry class or the Tuesday 8:00am Physics class, then he will finish the program.
Solution:
<u>Note that:</u>
- Triangle ABC ≅ Triangle FGH
- AC = 30 units
- CB = 10 units
- BA = 35 units
- FH = 18 units
- HG = 6 units
<u>Looking at both the triangles, we can say that:</u>
- FH = 3AC/5 = 3(30)/5 = 90/5 = 18 units
- HG = 3BC/5 = 3(10)/5 = 30/5 = 6 units
<u>We can do the same with AB and FG.</u>
- FG = 3AB/5 = 3(35)/5 = 3(7) = 21 units
Find the amount of beads per inch:
12/5 = 2.4 (this doesn't make sense, but it will)
Now find the total beads on one foot, or 12 inches
2.4 x 12 = 28.8
Since 29 wont fit, 28 will be the largest whole number of beads that can fit on the string
The trick here is to notice that all 3 terms can be div. by 2:
2(x^2 + x - 12)
Note that -12 factors into -3 * 4 or -4 * 3. Thus,
x^2 + x - 12 = (x-4)(x+3), and so <span>2x2 + 2x − 24 = 2(x-4)(x+3).</span>
