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Serggg [28]
2 years ago
8

Solve the following

Mathematics
1 answer:
sesenic [268]2 years ago
4 0

Step-by-step explanation:

derivative:zero becouse ever number has daritive is zero

6:

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Suppose the roots of the polynomial $x^2 - mx + n$ are positive prime integers (not necessarily distinct). Given that $m < 20
Vsevolod [243]

Answer:

<em>18</em> values for n are possible.

Step-by-step explanation:

Given the quadratic polynomial:

$x^2 - mx + n$

such that:

Roots are positive prime integers and

$m < 20$

To find:

How many possible values of n are there ?

Solution:

First of all, let us have a look at the sum and product of a quadratic equation.

If the quadratic equation is:

Ax^{2} +Bx+C

and the roots are: \alpha and \beta

Then sum of roots, \alpha+\beta = -\frac{B}{A}

Product of roots, \alpha \beta = \frac{C}{A}

Comparing the given equation with standard equation, we get:

A = 1, B = -m and C = n

Sum of roots,  \alpha+\beta = -\frac{-m}{1} = m

Product of roots, \alpha \beta = \frac{n}{1} = n

We are given that m  

\alpha and \beta are positive prime integers such that their sum is less than 20.

Let us have a look at some of the positive prime integers:

2, 3, 5, 7, 11, 13, 17, 23, 29, .....

Now, we have to choose two such prime integers from above list such that their sum is less than 20 and the roots can be repetitive as well.

So, possible combinations and possible value of n (= \alpha \times \beta) are:

1.\ 2,  2\Rightarrow  n = 2\times 2 = 4\\2.\ 2, 3 \Rightarrow  n = 6\\3.\ 2, 5 \Rightarrow  n = 10\\4.\ 2,  7\Rightarrow  n = 14\\5.\ 2, 11 \Rightarrow  n = 22\\6.\ 2, 13 \Rightarrow  n = 26\\7.\ 2, 17 \Rightarrow  n = 34\\8.\ 3,  3\Rightarrow  n = 3\times 3 = 9\\9.\ 3, 5 \Rightarrow  n = 15\\10.\ 3, 7 \Rightarrow  n = 21\\

11.\ 3,  11\Rightarrow  n = 33\\12.\ 3, 13 \Rightarrow  n = 39\\13.\ 5, 5 \Rightarrow  n = 25\\14.\ 5, 7 \Rightarrow  n = 35\\15.\ 5, 11 \Rightarrow  n = 55\\16.\ 5, 13 \Rightarrow  n = 65\\17.\ 7, 7 \Rightarrow  n = 49\\18.\ 7, 11 \Rightarrow  n = 77

So,as shown above <em>18 values for n are possible.</em>

3 0
3 years ago
Solve the one step equations- 3.7+w=9.24
mariarad [96]
<span>Simplifying -3.7 + w = 9.24 Solving -3.7 + w = 9.24 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '3.7' to each side of the equation. -3.7 + 3.7 + w = 9.24 + 3.7 Combine like terms: -3.7 + 3.7 = 0.0 0.0 + w = 9.24 + 3.7 w = 9.24 + 3.7 Combine like terms: 9.24 + 3.7 = 12.94 w = 12.94 Simplifying w = 12.94</span>
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3 years ago
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Please help me with this it might look easy to you but not to me :
Rasek [7]

Answer:

10

Step-by-step explanation:

5/6 =0.8333

12x0.8333 = 10

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Which point is a reflection of Q(-4, -6) across the x-axis and the y-axis?
e-lub [12.9K]

Answer: Provide an image please?

Step-by-step explanation:

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Answer:

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Step-by-step explanation:

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