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allsm [11]
3 years ago
8

Let f(x) = (x^2+3x-5)/(x^2-8x+15) What is the domain of f(x) ?

Mathematics
1 answer:
Lyrx [107]3 years ago
8 0

Answer:

So, Domain = {set of all the real numbers except 3, 5}

Interval notation = {x ∈ set of all real numbers/ x ≠3 and x ≠ 5}

Step-by-step explanation:

The given function is f(x) = \frac{x^2 + 3x - 5}{x^2 - 8x + 15}

Here we need to find the domain.

To find the domain, let's find the restricted domain.

If we set the denominator equal to zero and solve for x, we can find the restricted domain.

Here the denominator is x^2 -8x + 15 = 0

Now we can factorize and solve for x.

(x - 3)(x - 5) = 0

(x - 3) or (x - 5) = 0

x -3 = 0  and x - 5 = 0

Solving the above equations, we get

x = 3 and x = 5

The restricted domains are x = 3 and x = 5.

Now we can find the domain.

Except 3 and 5, all the real numbers can be domain of this function.

So, Domain = {set of all the real numbers except 3, 5}

= {x ∈ set of all real numbers/ x ≠3 and x ≠ 5}.

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Verizon [17]
Using equation of motion.

S = ut + (1/2)gt²

Where S = Height, t = time, g = acceleration due to gravity = 9.8 m/s²

time, t = 8 seconds 

Since it was dropped from height, initial velocity, u = 0

S = 0*t + (1/2)gt²

S = (1/2)gt²

S = (1/2)*9.8*8²  = 4.9 * 8 * 8 =  313.6

Therefore the ledge is 313.6 m tall.
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3 years ago
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mario62 [17]

Step-by-step explanation:

Since angles in the same segment are equal, Angle ABC (x) = Angle AOC.

Since Angles AOC and COD are supplementary, Angle AOC = 180° - 130° = 50°

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3 years ago
Add: (x2 + 5x + 2) + (x2 - 2x + 7).
Varvara68 [4.7K]
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3 years ago
Find the distance between the points (–8,10) and (4,10).
Semenov [28]

Answer:

12

Step-by-step explanation:

√(x2 - x1)² + (y2 - y1)²

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8 0
3 years ago
A newsletter publisher believes that below 68% of their readers own a Rolls Royce. Step 1 of 1 :State the null and alternative h
Vanyuwa [196]

The null hypothesis is p = 0.68 while the alternative hypothesis will be that it's below that is p < 0.68.

First, let us understand the Null and Alternative hypotheses:

The null hypothesis is simply to predict that there is no effect of the relationship between the variables.

The alternative hypothesis is to state the research prediction of a relationship or effect. In this case, the newsletter publisher believes that below 68% of their readers own a Rolls Royce.

The null hypothesis is that the proportion of readers who own a Rolls Royce is equal to 0.68.

Null hypotheses = H₀: p = 0.68

The alternate hypothesis is that the proportion of readers who own a Rolls Royce is below 0.68.

Alternate hypotheses = H₁: p < 0.68.

Thus, the null hypothesis is p = 0.68 while the alternative hypothesis will be that it's below that is p < 0.68.

To learn more about the Null and Alternative hypotheses visit:

brainly.com/question/25263462

#SPJ9

4 0
1 year ago
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