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Likurg_2 [28]
2 years ago
9

An angle measures 77° what is the measure of its supplement

Mathematics
2 answers:
gregori [183]2 years ago
6 0

Since a supplementary angle is 180 degrees do:

180 - 77

= 103 degrees

Pavel [41]2 years ago
6 0
The answer would be 103 because 180-77=103
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Simplify the radical expression.
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Step-by-step explanation:

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9√3

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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
Helppppp pleaseeeee fasttttt thankkkkk youuuuu
Digiron [165]
Pretty sure it is nine. I hope I helped
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3 years ago
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