A chef uses 4.5

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

Vsevolod [243]

Answer:

18 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 18 values for n are possible.

3 0

3 years ago

Does anyone know how to do these maths question???

Dmitry_Shevchenko [17]

Answer:

Part 1) $f(g(x))=3(x^2)+2$

Part 2) $g(f(5))=289$

Step-by-step explanation:

we know that

A composite function is a function that depends on another function. A composite function is created when one function is substituted into another function

we have

$f(x)=3x+2$

$g(x)=x^{2}$

Part 1) Determine f(g(x))

To find f(g(x)) substitute the function g(x) as the variable in function f(x)

so

$f(g(x))=3(x^2)+2$

Part 2) Determine g(f(x))

To find g(f(x)) substitute the function f(x) as the variable in function g(x)

so

$g(f(x))=(3x+2)^2$

For x=5

$g(f(5))=(3(5)+2)^2$

$g(f(5))=289$

3 0

3 years ago

A bicycle store costs $3300 per month to operate. The store pays an average of $75 per bike. The average selling price of each

Klio2033 [76]

S=Selling price 135
V=Variable cost 75
F=Fixed cost 3300
Let quantity be Q
The formula to break even is
135Q-75Q-3300=0
Solve for Q
60Q-3300=0
60Q=3300
Q=3300/60
Q=50
So the store must sell 50 bicycles to break even

Hope it helps!

6 0

3 years ago

Read 2 more answers

The Osiris Diamond Company sold two

PSYCHO15rus [73]

Answer:

4

Step-by-step explanation a dog poops 5 kg a day

4 0

2 years ago

Graph the function. y=1+0.5x

Contact [7]