Answer:
3. DF = 15
4. (x +y +2)(x +y +3)
5. Tuesday
Explanation:
3. The angle congruence tells you the triangles are similar. Corresponding sides have a ratio of 5/4:
DE/AB = 10/8 = 5/4
EF/BC = 12.5/10 = 5/4
DF/AC = ?/12 = 5/4
Multiplying by 12, we find ...
DF = 12(5/4) = 15
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4. The first three terms look like (x+y)². The next two look like 5(x+y). So we can group terms to make the expression look like ...
(x+y)² + 5(x+y) +6
We recognize factors of 6 that sum to give 5 as being 2 and 3, so we can factor this as ...
(x+y +2)(x+y +3)
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5. Jan 1 falls on a day of the week that is the first of 3 days of which there are 5 in the month.
There are 3 days between Monday and Friday, but only 2 days between Friday and Monday. Hence the 1st of January must fall on Tuesday that year.
There will be 4 of Fri, Sat, Sun, Mon, and 5 of Tue, Wed, Thu in the month.