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alina1380 [7]
2 years ago
6

The room can hold a maximum of 400 people. If there are already 134 people

Mathematics
1 answer:
Olegator [25]2 years ago
6 0

Answer:

x+ 134 is less than or equal to 400 is the answer

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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
If Jamie has five dollars and purchases a soda for one dollar and fifteen cents, how much change does Jamie get back
nika2105 [10]
5.00
-
1.15
--------
3.85
3 0
3 years ago
Read 2 more answers
What is the range of this data set? {43, 17, 12, 17, 19, 11, 17, 20, 30} 13 17 32 I don't know.
nekit [7.7K]

Answer:

Range is 32

Step-by-step explanation:

11,12,13,17,17,17,17,19,20,32,43

43-11 = 32

8 0
2 years ago
Read 2 more answers
Your Local grocery store is having a special on soda. They're selling a 12-pack of 12-oz cans for $4.75. The 20-oz bottles are a
sasho [114]

Answer:

12 pack

Step-by-step explanation:

5 0
3 years ago
PLEASE HELP!!!!!!! A family has two cars. The first car has a fuel efficiency of 35 miles per gallon of gas and the second has a
Marianna [84]

Answer:

The answer to your question is car 1 = 30 gal and car 1 = 20 gal

Step-by-step explanation:

car 1 = a

car 2 = b

Efficiency of car 1 = 35 mi/gal

Efficiency for car 2 = 20 mi/gal

Total distance = 1450

Total gas consumption = 50 gal

Equations

                          35a + 20b = 1450            ------- (I)

                             a   +     b =  50               ------- (II)

Solve by elimination

Multiply equation II by -35

                          35a  + 20b  = 1450

                         -35a  - 35b   = -1750

Simplify

                            0    - 15b    =  -300

Solve for b

                                        b =  -300/-15

Result

                                        b = 20

Substitute b in equation II to find a

                               a +  20  = 50

Solve for a

                               a  = 50 -20

Result

                               a  = 30

4 0
3 years ago
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