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RoseWind [281]
3 years ago
6

How much is 70% from 20

Mathematics
1 answer:
charle [14.2K]3 years ago
7 0

Answer:14

Step-by-step explanation:

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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
12 minutes to drive 30 laps; 48 minutes to drive 120 laps
myrzilka [38]
You can divide 12min.➗30lps. Then you divide 48➗120lps.
And the answer will be 12➗30=0.4 then 48➗120=0.4 and the answer is that the ratios or rates are equvalent by dividing.
7 0
3 years ago
Find the missing value: x2 (squared) = 625 5 10 25 50
Alona [7]

\bf x^2=625\implies x=\sqrt{625}\implies x=25

5 0
3 years ago
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You have six pizza toppings. How many different 3-topping pizzas can you make?
velikii [3]

Answer is to the question is  20

5 0
3 years ago
Eric buys two plants. One plant is 4 inches tall and grows 2 of an inch per week. Another plant is 3 inches tall and grows
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It’s Abe beacuse it grew 7 inch week and 4 tall 2 week.
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