25 (a square) - 4 (b square) + 28bc - 49 (c square)

Mathematics

1 answer:

LUCKY_DIMON [66]3 years ago

8 0

Answer:

(5a - [2b - 7c]) and (5a + [2b + 7c])

Step-by-step explanation:

Factor 25a^2 - 4b^2 + 28bc - 49c^2.

Note that - 4b^2 + 28bc - 49c^2 involves the variables b and c, whereas 25a^2 has only one variable. Thus, try to rewrite - 4b^2 + 28bc - 49c^2 as the square of a binomial:

- 4b^2 + 28bc - 49c^2 = -(4b^2 - 28bc + 49c^2), or

-(2b - 7c)^2.

Thus, the original 25a^2 - 4b^2 + 28bc - 49c^2 looks like:

[5a]^2 - [2b - 7c]^2

Recall that a^2 - b^2 is a special product, the product of (a + b) and (a - b). Applying this pattern to the problem at hand, we conclude:

Thus, [5a]^2 - [2b - 7c]^2 has the factors (5a - [2b - 7c]) and (5a + [2b + 7c])

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Suppose that the populations of the United States and China both increase by 12 million people in one year. What would be the re

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Question:

Suppose that the populations of the United States and China both increase by 12 million people in one year. What would be the relative change for each country? Answer to the nearest tenth of a percent (1 decimal place). Make sure that you fill in each answer area before checking "How Did I Do?".

If you assume that the U.S. population is about 300 million, an increase of 12 million would result in a relative change of Number %.

If you assume that China has about 1 billion people, an increase of 12 million would result in a relative change of Number %.

Answer:

The relative change of the United States and China is 4% and 1.2%, respectively.

Step-by-step explanation:

Given

Represent population with p. So, we have:

United States

$\triangle p = 12\ million$