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dybincka [34]
3 years ago
10

Which of the following represents the zeros of f(x) = x3 − 12x2 + 47x − 60?

Mathematics
2 answers:
topjm [15]3 years ago
6 0

Answer:

x=3, 4, or 5

Step-by-step explanation:

x^3 − 12x^2 + 47x − 60=0

First we have to determine one value of x by hit and trial method for which , the above polynomial becomes 0

on trying random values of x , we sees that for x = 3 , the polynomial becomes 0

Hence (x-3) is one of the factor

Hence now let us move with the factorization part

The above polynomial can be re written as

x^2(x-3)-9x(x-3)+20(x-3)

(x-3)(x^2-9x+20)

(x-3)(x^2-5x-4x+20)

(x-3)(x(x-5)-4(x-5))

(x-3)(x-5)(x-4)

hence we have our f(x) = (x-3)(x-5)(x-4)

In order to find the zeroes we put f(x) =0

Hence

[tex](x-3)(x-5)(x-4)=0

Therefore

if (x-3)=0 , x=3

if (x-5) , x= 5

if (x-4), x=4

Nutka1998 [239]3 years ago
4 0
This actually should be reported. There are no choices. However there are ways of finding out what the zeros are and I will do that first to begin with. 

The first is a bit of a cheat. My calculator will do it, so I'm just going to get the answer from it. 

x can equal 3
x can be 5
x can be 4

So f(x)= a (x - 3)(x-5 )(x -4) is the basic equation. You need another point other than the zeros to determine the value of a.

Method 2
Get the graph. 
I've done that below. Basically it agrees with what my calculator says.

Method 3
You could factor it, but simple factoring methods don't work with this question.

Method 4
You could do this in a method similar to a quadratic, but I can't do that. It is on my to do list to lean though.

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Read 2 more answers
Find the value of x that will make AB<br> А<br> 9x - 40<br> В.<br> 3x + 20<br> x = [?]
Charra [1.4K]

Answer:

x = 10

Step-by-step explanation:

∵ Both angle ∠A and are corresponding angles.

∠A = ∠B

9x - 40 = 3x + 20

9x = 3x + 20 + 40

9x - 3x = 20 + 40

6x = 60

x = 60/6

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∴ x = [10]

7 0
2 years ago
The diameters of bolts produced in a machine shop are normally distributed with a mean of 5.18 millimeters and a standard deviat
dimulka [17.4K]

As per the concept of normal distribution, the two diameters of the bolt that has separate the top 3% and the bottom 3% are 5.2836 mm and 5.0764 mm respectively .

Normal distribution:

Normal distribution means the probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean and it has the bell shaped curve.

Given,

The diameters of bolts produced in a machine shop are normally distributed with a mean of 5.18 millimeters and a standard deviation of 0.07 millimeters.

Here we need to find the two diameters that separate the top 3% and the bottom 3% and these diameters could serve as limits used to identify which bolts should be rejected. we have also round off the result into nearest hundredth.

Here we have the given question with the values of,

The value of Mean is 5.18 millimeters

The value of Standard deviation is 0.07 millimeters.

Here we have to consider the following two cases, they are.

Case 1

We need to find x₁ such that that is P(X > x₁) = 3% when we convert it into decimal then we get P (X > x₁) = 0.03

So, as per the probability,

P (X ≤ x₁) = 1 - 0.03 = 0.97

So, z corresponding to the value of p = 0.97 is 1.48

Apply the given values to the formula of normal distribution then we get,

=> 1.48 = (x₁ -  5.18) /0.07

=> 0.1036 = x₁ - 5.18

Therefore, the value of x₁ is  5.2836

So, the diameter of the both with separate top 3% is 5.2836.

Case 2:

Next we have to take P(X < x₂) = 3% when we convert it into decimal then we get P (X < x₂) = 0.03

So, as per the given probability, the value of

P (X ≤ x₂) = 1 - 0.03 = 0.97

So, z corresponding to but here we have to use the negative because of the less than concept p = 0.97 is -1.48

Apply the values on the formula of normal distribution then we get,

-1.48 = (x₂ -  5.18) /0.07

Move the value to the other side

-0.1036 = x₂ - 5.18

When we simplify it,

x₂ =  5.0764

So, the diameter of the both with separate bottom 3% is 5.0764

To know more about Normal distribution here.

brainly.com/question/12421652

#SPJ1

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Simplify this expression. Write your answer using positive exponents.<br>​
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What expression ? There isn’t one
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