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3 years ago

The piecewise function f(x) has opposite expressions. f(x) = Which is the graph of f(x)?

Mathematics

2 answers:

agasfer [191]3 years ago

8 0

its the third graph or answer c

Anarel [89]3 years ago

6 0

Answer:

4) is the opposite function of 3), and vice versa. Because f(x) =2x-1 and its opposite f(x)=-2x+1. And we can see them both in pictures 3 and 4.

Step-by-step explanation:

A piecewise function is a function defined in a sequence of intervals. The most known piecewise function is the modular function. (1st picture)

An opposite function is given by f(x)=-x of f(x)=x

The following pictures describe the following functions:

1) f(x)=-|2x|+2

2) f(x)= 2.34x-2.34 and f(x)= -2.34x-2.34

Notice how the second function express the opposite line, by the opposite angular coefficient.

3) f(x) =2x-1 and f(x)=-2x+1

4) f(x) = -2x+1 and f(x)=2x-1

Different intervals but the same functions are graphed in 3 and 4. So the graph of f(x)=2x-1 and its opposite f(x)=-2x-1

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Two containers hold several balls. Once a second, one of the balls is chosen at random and switched to the other container. Afte

natka813 [3]

Answer:

(a) 8 balls

(b) 4 balls

Step-by-step explanation:

Let

$N \to$ Number of balls

For a box, the probability that there are N balls in it is:

$Pr = 0.5^N$

For 2 boxes, it is:

$Pr = 2 * 0.5^N$

From the question, we have:

$\frac{80}{10000} \to$ Favorable outcome

To solve for N, we have:

$2 * 0.5^N = \frac{80}{10000}$

$2 * 0.5^N = 0.008$

Divide both sides by 2

$0.5^N = 0.004$

Take log of both sides

$\log(0.5^N) = \log(0.004)$

Apply law of logarithm

$N\log(0.5) = \log(0.004)$

Make N the subject

$N = \frac{\log(0.004)}{\log(0.5)}$

$N =7.966$

Approximate

$N = 8$

Solving (b): Balls in one of the two boxes.

Here, we assume that each ball will have almost the same number of balls at a given instance;

Hence, we have:

$Balls \approx \frac{N}{2}$

$Balls \approx \frac{8}{2}$

$Balls \approx 4$

<em>4 balls in each box</em>

6 0

3 years ago

How to understand piecewise functions

Nataly [62]

Each piece is defined over some (limited) domain. When you are evaluating or graphing a piecewise function, you only evaluate or graph the function whose domain includes the variable value of interest.

6 0

3 years ago

What is the length and the width of a rectangle with perimeter of 48 inches if its length is 7 inches longer than its width.

sattari [20]

Answer:

Length and the width of the rectangle is 15.5 inches and 8.5 inches respectively.

Step-by-step explanation:

Given:

Length = 7 inches + Width

=> P = 48 inches

=> L = (7 + W) inches............. (1)

Perimeter 'P' is the sum of all sides of the rectangle 2 (L + W)

∴ 48 inches = 2 (L + W) .................(2)

Substitute for L in equation (2)

∴ 48 inches = 2 [(7 + W) + W]

48 = 2[7 + 2W]

48 = 14 +4W

48 - 14 = 4W

34 = 4W

W = 8.5 inches

Recall that: Length, L = (7 + W)

∴ L = (7 + 8.5)

L = 15.5 inches

4 0

3 years ago

Read 2 more answers

Use the method of Gauss to find the sum.1+2+3+.....+400

nikklg [1K]

Gauss' method for addition relies on the fact that you can 'pair' certain numbers together. Look at the example:

1+2+3+4+5+6+7+8+9+10

We could manually add all these together from left to right but a clever way to think about this is if we add together the ends of the sum (10+1) we get 11. If we then move one in from the ends and add these (2+9) we also get 11. This means that 1+2+...+9+10 is the same as 11+11+...+11+11.

Because each 2 numbers adds to 11 we know the total number of 11's we have to add together is the length of the sum divided by 2. In our case 5 (10 ÷ 2). We need to add 5 lots of 11 to get our answer. This is the same as 11 × 5 which is easily seen to be 55.

(If you add the 10 numbers together on a calculator you'll see 1+2+3+4+5+6+7+8+9+10 = 55) so this method really makes it a lot quicker.

Looking at your sequence, if we pair the ends together we get 401 (400+1) and we multiply this by the length of the sequence divided by 2. In your case, 200 (400 ÷ 2).

So the sum of all the numbers from 1 to 400 must be 401 × 200 = 80,200.

Remember the steps:
1. Pair the ends together and add them
2. Times this number by the length of the sequence halved

Hope this helps.

6 0

3 years ago

hiker is climbing down a valley. He stops for a water break 4 times. Between each break, he descends 15 meters. How many meters

sergij07 [2.7K]

The word in the problem that indicates is a negative number is “descend”

8 0

3 years ago

Read 2 more answers