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Anika [276]
2 years ago
15

What are the zeros of the polynomial function f(x)=x^3-x^2-6x

Mathematics
1 answer:
aalyn [17]2 years ago
6 0

Answer:

(

x

)

=

x

(

x

2

−

x

−

6

)

=

x

(

x

−

3

)

(

x

+

2

)

=

0

 

x

=

0

,

x

=

3

,

x

=

−

2

Explanation:

To find the zeros of the polynomial above first factor out the common factor then factor the remaining polynomial and set it equal to zero. Finally solve for x.

Step-by-step explanation:

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A collection of 20 coins made up of only nickels, dimes, and quarters has a total value of $3.35. If the dimes were nickels, the
Kay [80]

Answer:  The required number of quarters in the collection is 11.

Step-by-step explanation:  Given that a collection of 20 coins made up of only nickels, dimes and quarters has a total value of $3.35.

If the dimes were nickels, the nickels were quarters and the quarters were dimes, the collection of coins would have a total value of $2.75.

We are to find the number of quarters in the collection.

Let x, y and z represents the number of nickels, dimes and quarters respectively in the collection.

We will be using the following values of nickels, dimes and quarters in form of dollar :

1 nickel = $ 0.05,   1 dime = $ 0.10   and    1 quarter = $0.25.

Then, according to the given information, we have

x+y+z=20\\\\\Rightarrow x=20-y-z~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\0.05x+0.10y+0.25z=3.35\\\\\Rightarrow 5x+10y+25z=335\\\\\Rightarrow x+2y+5z=67~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)\\\\0.05y+0.25x+0.10z=2.75\\\\\Rightarrow 5y+25x+10z=275\\\\\Rightarrow y+2z+5x=55~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(iii)

Substituting the value of x from equation (i) in equations (ii) and (iii), we have

(20-y-z)+2y+5z=67\\\\\Rightarrow y+4z=47\\\\\Rightarrow y=47-4z~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(iv)

and

y+2z+5(20-y-z)=55\\\\\Rightarrow -4y-3z=-45\\\\\Rightarrow y=\dfrac{45-3z}{4}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(v)

Comparing the values of y from equations (iv) and (v), we get

47-4z=\dfrac{45-3z}{4}\\\\\Rightarrow 188-16z=45-3z\\\\\Rightarrow 16z-3z=188-45\\\\\Rightarrow 13z=143\\\\\Rightarrow z=\dfrac{143}{13}\\\\\Rightarrow z=11.

Thus, the required number of quarters in the collection is 11.

7 0
2 years ago
Choose the correct simplification of (9xy^5)^2.
Grace [21]

Answer:

D) 81x²y¹⁰

Step-by-step explanation:

(9xy⁵)²

Because all of 9xy⁵ are in the parentheses, each component is raised to the 2nd degree.

(9)² = 81

(x)² = x²

(y⁵)² = y¹⁰ -- When you raise an exponent to another exponent, you multiply the exponents.

Now combine the components.

D) 81x²y¹⁰

5 0
2 years ago
Solve for x xx: 7 x + 4 9 ∘ 7x+49 ​∘ ​​ 2 x + 9 4 ∘ 2x+94 ​∘ ​​
Murrr4er [49]
The value for x is 9 because:

7x +49 = 2x + 94
7x-2x=45
5x=45
x=45/5
x=9
6 0
3 years ago
ASAP! GIVING BRAINLIEST! Please read the question THEN answer correctly! No guessing. Show your work or give an explaination.
iogann1982 [59]

Answer:

A

Step-by-step explanation:

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-If it moves to the right, you SUBTRACT the amount of units

-It it moves to the left, you ADD the amount of units.

So in this case, it is moving to the right 12 units so it is (x-12)^{2}

6 0
3 years ago
Read 2 more answers
Can someone please explain this Trig question, Find sec(x) in terms of sin(x)
Scilla [17]

The explanation is:

 The definition of "secant of (x)" is:  1 / (sine of x) .

5 0
3 years ago
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