Question

Help on 3,4,5 please!

Answer 1

Answer:

  3.  DF = 15

  4.  (x +y +2)(x +y +3)

  5. Tuesday

Step-by-step 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.