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solniwko [45]
3 years ago
12

H(x)= 9/x( x^2-49) Determine the domain of the function

Mathematics
1 answer:
Norma-Jean [14]3 years ago
8 0

Answer: The domain of the function h(x) = \frac{9}{x(x^2-49)} is:

Interval Notation: (-∞ , -7) ∪ (-7 , 0) ∪ (0 , 7) ∪ (7, ∞)

Set-Builder Notation: { x | x ≠ 0 , 7 , -7 }

All real numbers besides 0, 7, and -7.

Step-by-step explanation:

In order to find the domain of your rational function, we need to simplify it:

h(x) = \frac{9}{x(x^2-49)} = \frac{9}{(x)(x+7)(x-7)}

Remember, most of the time, the domain of a rational function consists of all real numbers besides zero.

To find the domain, we equal the equations in the denominator to zero.

x=0

x+7=0 --> x=-7

x-7=0 --> x=7

So all real numbers except for 0, -7, and 7 are in the domain of this rational function.

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Help please inequalities are kicking my butt any help is greatly appreciated thank you in advance
Hitman42 [59]

Answer:

Correct option is (C)

Step-by-step explanation:

we are given that -Tim design a pair of shorts,S, and T-shirts,t.

Tim sell Sorts for $12 and T-shirts for $8 each.

Tim can work atmost 18 hours a day so we can write time\leq 18

Time taken to design a T-shirt is 30 minutes and for Shorts, it is 45 minutes.

\frac{30}{60}t+\frac{45}{60}s\leq   18\\\text{Multiply both the sides by 60}\\30t+45s\leq 1080\\\text{Divide both the sides by 45}\\s+0.66t\leq 24\\\text{Subtract 0.66t from both the sides}\\s\leq 24-0.66t

He must design 12 itesm each day, so we can write t+s\geq 12

Further it can be written as

t+s\geq 12\\\text{Subtract t from both the sides}\\s\geq 12-t

Also Tim can not design more than 30 items in one day, so we can write

t+s\leq 30\\\text{Subtsract t from both the sides}\\s\leq 30-t

Hence from the above equations , its claer that

s\geq 12-t,s\leq 30-t,s\leq 24-0.66t,s\geq 0,t\geq 0

7 0
3 years ago
the water slides have 20 temporary employees and 5 permanent employees. what percentage of the employees at the water slides are
Kobotan [32]
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Paul jogged 3.25 miles, rick jogged 3 1/3 miles and sean jogged 3 1/8 miles. list the boys from least to greatest distance jogge
Novosadov [1.4K]

Answer:

Sean jogged 3.125, Paul jogged a distance of 3.25, Rick jogged 3.33

Step-by-step explanation:

make the fractions into decimals once they are in decimal form you cna then go and place them into the correct order.

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