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suter [353]
3 years ago
12

Evaluate the expression -4x+5y-14 when x=0 and y= 3/5​

Mathematics
1 answer:
emmainna [20.7K]3 years ago
5 0

Answer:

-11

Step-by-step explanation:

Plug in 0 for x and 3/5 for y into the expression

-4(0) + 5(3/5) - 14

Multiply the numbers inside the parentheses

0 + 3 - 14

3 - 14 = -11, which is your 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 a movie starts at 10:40am and lasts for 1h and 59min, then what time should the movie end.
OverLord2011 [107]

Answer:

12:39

Step-by-step explanation:

First, to make it easier, round the amount of time the movie lasts to the nearest hour. In this case, the movie "lasts" for 2 hours.

Add 2 hours to 10:40am. Note that when it hits 12, the am becomes pm.

10:40 + 2:00 = 12:40

Now, subtract 1 minute from the amount (1 hr 60 min - 1 hr 59 min = 1 min)

12:40 - 0:01 = 12:39

12:39 pm should be the time the movie ends.

~

7 0
3 years ago
Read 2 more answers
100 is divisible by which of the following numbers 2,3,4,5,6,9 or 10?
pochemuha
The correct answer is B: 2,4,5, 10

We know that 100 is not divisible by 3 because 100/3 is 33.33 repeating, which is an irrational number.

We also know that 100 is not divisible by 6 because 100/6 is 16.66 repeating which is also an irrational number.

100/2=50 (rational)
100/4=25 (rational)
100/5=20 (rational)
100/10=20 (rational)

Hope this helps!
6 0
3 years ago
A store is selling 5 cans of tomato sauce for 4.50 what is the unit price
andrew-mc [135]
The unit price is 90 cents per can of tomato sauce.
6 0
2 years ago
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Jimmy is going scuba diving. He started at 10 ft below sea level. He then dove 15 ft further, then he got nervous and came up 5
ad-work [718]

Answer:

it is 55

Step-by-step explanation:

8 0
3 years ago
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