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olga nikolaevna [1]
3 years ago
13

Third-degree, with zeros of −3 , − 2 , and 1 , and passes through the point ( 3 , 11 ) .

Mathematics
1 answer:
Masja [62]3 years ago
8 0

Answer:

y  =   ( x + 3 ) *  ( x +  2 ) * ( x - 1 )* 11/60

Step-by-step explanation:

Lets   y  =  f(x)   in a cartesian coordinates

Having three zeros:

x = -3       ⇒   x  = -2      ⇒   and   x = 1  

That meas that if   x  takes the above mentioned  values " y " must be zero

therefore  y  must be of the form

f (x)  =  y  =  ( x + 3 ) *  ( x +  2 ) * ( x - 1 )     (1)

In that case for y to be zero one of the factors should be zero or

y  =  0        x  + 3 = 0    and  x = - 3  is a zero of the function y .

The same reasoning applies for the other two roots

Now we have to evaluate the other condition.

According to problem statement the function passes through the point ( 3, 11 ) , that means that when x =  3 ,  y have to be 11, therefore we plug in equation (1)  that value to see what happens

y  =   ( x + 3 ) *  ( x +  2 ) * ( x - 1 )

11  =  ( 3 + 3 ) * ( 3 + 2 ) + ( 3 - 1)   =  6*5*2  = 60

Then we adjust the expression (1) to meet the condition of the function passing through point  ( 3 , 11) as:

y  =  ( 3 + 3 ) * ( 3 + 2 ) + ( 3 - 1) * 11/60    (2)

and check to see if we did right

for y to be zero      x   can be    x = - 3    x  =  -2   and  x = 1 in all these cases y = 0.  And if  x  =  3   in equation (2)  y = 11. And that what we want to shown. Then the solution is:

y  =   ( x + 3 ) *  ( x +  2 ) * ( x - 1 )* 11/60

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Step-by-step explanation:

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Answer:

y=-1/3x + 33

Step-by-step explanation:

You can start by writing this in point slope form and converting to slope intercept later. Since the slope of the perpendicular line is y=3x-30, this line must have a slope of -1/3. It's point slope form is therefore:

y-25=-1/3(x-24)

Now, you can convert to slope intercept by isolating y:

y=-1/3(x-24)+25

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Hope this helps!

4 0
3 years ago
The ratio of blue jays to Robin's was 6 to 7. If there were 84 Robins, how many blue jays were there?​
Paul [167]

Answer:

72

Step-by-step explanation:

<em>Since the ratio of blue jays to robin's was 6 to 7 then if there were 84 robins how many blue jays were there.</em>

<em>6 to 7 can also be express as 6/7</em>

<em>Thus, we can set up a proportion</em>

<em>6/7 = x/84</em>

<em>Now, we have to solve for x</em>

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3 0
2 years ago
Regina, Phil, and Joseph each wrote expressions to represent their hourly earnings for an after-school job where h represents th
Vladimir79 [104]

Answer:

Disagree

On weeks when Joseph works extra 2/3 hours more than Phil, Phil and Joseph can earn the same amount of money

Step-by-step explanation:

The given expression for the hourly earnings of Regina, Phil and Joseph are as follows;

Regina: 6.50·h + 16

Phil: 3·(2.5·H + 5)

Joseph: 7.50·h + 10

The number of hours worked = h

The hourly earnings for Phil equated to the hourly earnings of Joseph gives;

3·(2.5·H + 5) = 7.50·h + 10

Simplifying we get;

3 × 2.5·h + 3 × 5 = 7.50·h + 10

7.5·h + 15 = 7.50·h + 10

Which gives

15 =  10 + 5 = 10 which is not correct.

Therefore, when both Phil and Joseph works the same number of hours, in the week, Phil will earn 5 units more Joseph

However, we have that, where Joseph works extra 5/7.5 or 2/3 hours more than Phil, every week, they will earn the same amount of money every week.

Therefore, it is possible for Phil and Joseph to earn the same amount of money when Joseph works extra 2/3 hours more than Phil which gives;

On weeks when Joseph works extra 2/3 hours more than Phil, Phil and Joseph can earn the same amount of money.

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Answer:

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