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2 years ago

10

Two sides and an angle are given. determine whether the given information results in one triangle, no triangle, three triangles,

two riangles c=35 a=18.7 c=16.1

1 answer:

Crazy boy [7]2 years ago

3 0

We are given 2 sides 18.7, 16.1 and a NON-included angle.
We have to calculate the altitude of the triangle.
altitude = 18.7 * sine (35)
altitude = 18.7 * 0.57358
altitude = <span> <span> <span> 10.725946 </span> </span> </span>
In this case, side c is greater than the altitude and is less than side a so 2 two triangles will be formed.

Source:
http://www.1728.org/trigssa.htm

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Step-by-step explanation:

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Since i² = -1, this becomes ...

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3 years ago

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>

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3 years ago

Select the statement that describes this expression: 1/2 x (734 − 246).

Furkat [3]

Answer:

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Step-by-step explanation:

The given expression is $\dfrac{1}{2}\times (734 - 246)$ .

We need to simply the above expression.

First of all, we will subtract 246 from 734. By doing so, we get 488.

Now, we can divide 488 by 2.

As a result we get 244.

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3 years ago

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Answer:

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Solving the equation using quadratic equation then as attached

x=14.25 units

To prove

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3 years ago

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mariarad [96]

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3 years ago