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Dahasolnce [82]
2 years ago
12

The counting numbers, together with 0, are called the _ _ _ _ _ numbers.

Mathematics
1 answer:
german2 years ago
4 0

Answer:

Whole numbers

hope this helps!

Step-by-step explanation:

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Find f(-5) and f(12) for each piecewise function f(x){-4x+3 if x<3
Law Incorporation [45]
<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
3 0
3 years ago
M 5x + 1 A 3x (4x + 2)9 N L If LA is an altitude of triangle LMN, find the following: MNE​
Darya [45]

I d k the answer but thanks for the points! LOL

3 0
3 years ago
Inez has 699 pennies and 198 nickels. Estimate how many more pennies than nickels she has.
HACTEHA [7]
There are five hundred and one more pennies than nickels
7 0
3 years ago
Read 2 more answers
Fully simplify ( 3 x + y 4 ) 2
Ainat [17]

Answer:

2/4-5

Step-by-step explanation:

5 0
2 years ago
Read 2 more answers
True or false? Jdkdjdjdjjddjds
Damm [24]

Answer:

True

Step-by-step explanation:

To divide fractions, flip one of the fractions then multiply them together.

-1/10 ÷ -3/5 =

-1/10 ÷ -5/3=

-1/10 x -5/3 = 5/30

Because a negative times a negative is a positive the product/quotient is positive.

3 0
3 years ago
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