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Alenkinab [10]
3 years ago
12

Determine the domain of the function, and choose the correct interval and inequality notations,

Mathematics
1 answer:
pickupchik [31]3 years ago
8 0

Answer:

<u></u>

  • <u>See below</u>

Explanation:

Determining the <em>domain</em> of the function P(x) = 2x + 8 is very trivial and does not require the uses of separate intervals.

The domain of a function is the set of input values (x) for which the function is defined. Thus, the domain of P(x) = 2x + 8 is all the real number, which in interval notaion is:

  • (- ∞, ∞)

The symbol ∞ is used to indicate that there is not limit for the value of x: it can goe from any negative number to any positive number).

For didactic purposes let's determine the domain of the function

P(x) = 2/(x+8).

In this case, the function is not defined when the denominator equals 0.

Then, the domain excludes the values for which x + 8 = 0.

  • x + 8 = 0 ⇒ x = - 8.

Then, the solution is all the real numbers different to - 8.

In <em>interval notation</em> it is:

  • (- ∞, -8) ∪ (-8, ∞)

In form of <em>inequaliy</em> that is:

  • x < - 8 ∪ x > - 8

That means, all the real numbers less than - 8 and all the real numbers greater than 8.

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You roll a dice three times what is the probability that you roll an even number on the first roll, and odd on the second roll a
Dafna1 [17]
<h3>Answer:</h3>

D. 1/24

<h3>Step-by-step explanation:</h3>

Assuming the die is fair and the events are independent, the probability of the series of events is the product of the probabilities of the individual events.

p(even) = 3/6 = 1/2

p(odd) = 3/6 = 1/2

p(5) = 1/6

Then the joint probability is ...

.. (1/2)·(1/2)·(1/6) = 1/24

7 0
3 years ago
Which verbal expression represents the algebraic expression 3y?
AlexFokin [52]
The algebraic expression 3y would be represented verbally by 3 multiplied by y!

5 0
3 years ago
Read 2 more answers
How many meters tall is the statue of liberty if it is thirty times the height of a 154 centimeter person?
Reptile [31]
The question states that the Statue of Liberty is 30 times the height of a 154 centimeter person and asks how many meters tall the <span>the Statue of Liberty is.
This is basically asking us to find 30 times 154 centimeters and convert it to meters.

30 • 154 = 4620
This tells us that the </span>Statue of Liberty is 4,620 centimeters (cm) tall.

Now we must convert 4,620 cm to meters (m).
There are 100 cm in 1 m.
This means 100 cm = 1 m.
That means that meters are 100 times larger than centimeters.
With this in mind, we can divide the number of cm by 100 to convert it to m.

4,620 ÷ 100 = 46.2
That means that 4,620 cm is equal to 46.2 m.

The final answer:
If the Statue of Liberty is 30 times taller than 154 centimeters, then the Statue of Liberty is 46.2 meters tall.
So the answer is 46.2 meters.

Hope this helps!
8 0
3 years ago
Read 2 more answers
Pls help! will mark branliest!!! :)
Ket [755]

The area of the house is the amount of space on the house.

  • The length of the addition is x + 20
  • The area of the original house is x^2 + 30x + 200

<h3>The length of the addition</h3>

The area of the addition is given as:

Area = x^2 + 10x - 200

Expand

Area = x^2 + 20x - 10x - 200

Factorize

Area = x(x + 20) - 10(x + 20)

Factor out x + 20

Area = (x -10)(x + 20)

The width of the addition is x - 10.

Hence, the length of the addition is x + 20

<h3>The area of the original house</h3>

The dimension of the original house is

x + 20 by x + 10

So, the area is:

Area =(x + 20)(x + 10)

Expand

Area =x^2 + 20x + 10x + 200

This gives

Area =x^2 + 30x + 200

Hence, the area of the original house is x^2 + 30x + 200

Read more about areas at:

brainly.com/question/24487155

8 0
2 years ago
***BRAINLIEST IF ANSWERED*******
Lisa [10]

Answer:

First find line DE using Pythagoras theorem

That's

DE² = 7² + 24²

DE = √ 49 + 576

DE = 25

The correct trigonometric ratio for triangle DEF is

Cos(E) = 24/25

Hope this helps

8 0
3 years ago
Read 2 more answers
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