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sesenic [268]
3 years ago
6

Factor the expression using the GCF. The expression 21m−49n factored using the GCF is...

Mathematics
2 answers:
Roman55 [17]3 years ago
6 0

Answer:  7(3m - 7n)

<u>Step-by-step explanation:</u>

Factor each term then see what value(s) they have in common:

          21m         -          49n

            ∧                        ∧

          3 · 7 · m              7 · 7 · n

Both terms have a 7 in common.  What is left over after removing the 7?

21m: 7(3m)

49n: 7(7n)

GCF: 7           Leftovers: 3m <em>and</em>  7n

Factored form of expression is: 7(3m - 7n)

a_sh-v [17]3 years ago
3 0
As 7 is a factor of both 21 and 49, you can take out 7 from both numbers.

7(3m-7n)
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Find f(-5) and f(12) for each piecewise function f(x){-4x+3 if x&lt;3
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<h3>Answers:</h3>
  • f(-5) = 23
  • f(12) = 433

==================================================

Explanation:

The given piecewise function is

f(x) = \begin{cases}-4x+3 \ \text{ if } \ x < 3\\-x^3 \ \text{ if } \ 3 \le x \le 8\\3x^2+1 \ \text{ if } \ x > 8\end{cases}

At first piecewise functions may be strange confusing things, but they aren't so bad. I like to think of it like this: f(x) is a function that changes its identity based on what the input x is. We have three situations

  • f(x) = -4x+3 when x < 3
  • f(x) = -x^3 when 3 \le x \le 8
  • f(x) = 3x^2+1 when x > 8

In a sense, we have three different functions but they are combined somehow.

If x is smaller than 3, then we go for the first definition. Or if x is between 3 and 8, then we go for the second definition. Or if x is larger than 8, then we go for the third definition.

-----------------------

f(-5) means f(x) when x = -5. We see that -5 is smaller than 3, so x = -5 makes x < 3 true. We'll use the first definition

f(x) = -4x+3

f(-5) = -4(-5)+3

f(-5) = 20+3

f(-5) = 23

------------------------

Now the input is x = 12. This is larger than 8. In other words, x = 12 makes x > 8 true. We'll use the third definition

f(x) = 3x^2+1

f(12) = 3(12)^2+1

f(12) = 3(144)+1

f(12) = 432+1

f(12) = 433

------------------------

Side notes:

  • We won't use the second definition since we don't have any x inputs between 3 and 8
  • To say "less than or equal to" on a keyboard, you can write "<=" without quotes. For example, x \le 5 is the same as x<=5
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7. The area of a square piece of cardboard is 70 cm2. What is the
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Answer:

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