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Nadusha1986 [10]
3 years ago
12

Would be highly appreciated if u can show work that would be great :)

Mathematics
1 answer:
Gemiola [76]3 years ago
7 0

Answer:

Solving for X in a Right Triangle

Add 90 degrees for the right angle to the degree measurement of the other marked angle. This measurement will be found inside the triangle at the angle that is not denoted by the X variable.

Subtract the sum of the two angles from 180 degrees. The sum of all the angles of a triangle always equals 180 degrees.

Write down the difference you found when subtracting the sum of the two angles from 180 degrees. This is the value of X.

Solving for X in an Isosceles Triangle

Locate the two base angles that are marked with half-circles with lines through them. These two angles are the same size.

Multiply the measurement given for one of the angles by two, if these angles have a measurement given. In this case you are solving for X at the vertex. Subtract the doubled measurement of the angles from 180. This is the value of the X angle at the vertex.

Subtract the measurement of the vertex angle from 180, if you are only given the measurement of the vertex angle. Divide the difference of the subtraction by two. This will give you the value of X at either of the base angles.

Solving for X in Other Triangles

Add the given degrees of the two angles provided and subtract that from 180 to solve for X in obtuse and acute triangles.

Compare the result with the visual representation of the triangle. With obtuse triangles, one angle will be larger than 90 degrees. If you are solving for this angle, be sure the figure you obtain for X is larger than 90 degrees. Acute triangles all have angles smaller than 90 degrees. Be sure that X is smaller than 90 degrees when solving for an acute triangle.

Determine if the triangle is equilateral by observing the half-circles drawn around all three of the angles with single lines drawn through all of them. If you are dealing with an equilateral triangle, all the angles equal 60 degrees and no additional mathematics is needed to determine the measurements.

Step-by-step explanation:

You might be interested in
Solve 3k^2=8k+8,using completing the square method ​
GenaCL600 [577]

Answer:

3k2=8k+8 

Two solutions were found :

 k =(8-√160)/6=(4-2√ 10 )/3= -0.775

 k =(8+√160)/6=(4+2√ 10 )/3= 3.442

Reformatting the input :

Changes made to your input should not affect the solution:

 (1): "k2"   was replaced by   "k^2". 

Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation : 

                     3*k^2-(8*k+8)=0 

Step by step solution :

Step  1  :

Equation at the end of step  1  :

3k2 - (8k + 8) = 0

Step  2  :

Trying to factor by splitting the middle term

 2.1     Factoring  3k2-8k-8 

The first term is,  3k2  its coefficient is  3 .

The middle term is,  -8k  its coefficient is  -8 .

The last term, "the constant", is  -8 

Step-1 : Multiply the coefficient of the first term by the constant   3 • -8 = -24 

Step-2 : Find two factors of  -24  whose sum equals the coefficient of the middle term, which is   -8 .

     -24   +   1   =   -23     -12   +   2   =   -10     -8   +   3   =   -5     -6   +   4   =   -2     -4   +   6   =   2     -3   +   8   =   5     -2   +   12   =   10     -1   +   24   =   23

Observation : No two such factors can be found !! 

Conclusion : Trinomial can not be factored

Equation at the end of step  2  :

3k2 - 8k - 8 = 0

Step  3  :

Parabola, Finding the Vertex :

 3.1      Find the Vertex of   y = 3k2-8k-8

Parabolas have a highest or a lowest point called the Vertex .   Our parabola opens up and accordingly has a lowest point (AKA absolute minimum) .   We know this even before plotting  "y"  because the coefficient of the first term, 3 , is positive (greater than zero). 

 Each parabola has a vertical line of symmetry that passes through its vertex. Because of this symmetry, the line of symmetry would, for example, pass through the midpoint of the two  x -intercepts (roots or solutions) of the parabola. That is, if the parabola has indeed two real solutions. 

 Parabolas can model many real life situations, such as the height above ground, of an object thrown upward, after some period of time. The vertex of the parabola can provide us with information, such as the maximum height that object, thrown upwards, can reach. For this reason we want to be able to find the coordinates of the vertex. 

 For any parabola,Ak2+Bk+C,the  k -coordinate of the vertex is given by  -B/(2A) . In our case the  k  coordinate is   1.3333  

 Plugging into the parabola formula   1.3333  for  k  we can calculate the  y -coordinate : 

  y = 3.0 * 1.33 * 1.33 - 8.0 * 1.33 - 8.0 

or   y = -13.333

Parabola, Graphing Vertex and X-Intercepts :

Root plot for :  y = 3k2-8k-8

Axis of Symmetry (dashed)  {k}={ 1.33} 

Vertex at  {k,y} = { 1.33,-13.33}  

 k -Intercepts (Roots) :

Root 1 at  {k,y} = {-0.77, 0.00} 

Root 2 at  {k,y} = { 3.44, 0.00} 

Solve Quadratic Equation by Completing The Square

 3.2     Solving   3k2-8k-8 = 0 by Completing The Square .

 Divide both sides of the equation by  3  to have 1 as the coefficient of the first term :

   k2-(8/3)k-(8/3) = 0

Add  8/3  to both side of the equation : 

   k2-(8/3)k = 8/3

Now the clever bit: Take the coefficient of  k , which is  8/3 , divide by two, giving  4/3 , and finally square it giving  16/9 

Add  16/9  to both sides of the equation :

  On the right hand side we have :

   8/3  +  16/9   The common denominator of the two fractions is  9   Adding  (24/9)+(16/9)  gives  40/9 

  So adding to both sides we finally get :

   k2-(8/3)k+(16/9) = 40/9

Adding  16/9  has completed the left hand side into a perfect square :

   k2-(8/3)k+(16/9)  =

   (k-(4/3)) • (k-(4/3))  =

  (k-(4/3))2 

Things which are equal to the same thing are also equal to one another. Since

   k2-(8/3)k+(16/9) = 40/9 and

   k2-(8/3)k+(16/9) = (k-(4/3))2 

then, according to the law of transitivity,

   (k-(4/3))2 = 40/9

We'll refer to this Equation as  Eq. #3.2.1  

The Square Root Principle says that When two things are equal, their square roots are equal.

Note that the square root of

   (k-(4/3))2   is

   (k-(4/3))2/2 =

  (k-(4/3))1 =

   k-(4/3)

Now, applying the Square Root Principle to  Eq. #3.2.1  we get:

   k-(4/3) = √ 40/9 

Add  4/3  to both sides to obtain:

   k = 4/3 + √ 40/9 

Since a square root has two values, one positive and the other negative

   k2 - (8/3)k - (8/3) = 0

   has two solutions:

  k = 4/3 + √ 40/9 

   or

  k = 4/3 - √ 40/9 

Note that  √ 40/9 can be written as

  √ 40  / √ 9   which is √ 40  / 3 

Solve Quadratic Equation using the Quadratic Formula

 3.3     Solving    3k2-8k-8 = 0 by the Quadratic Formula .

 According to the Quadratic Formula,  k  , the solution for   Ak2+Bk+C  = 0  , where  A, B  and  C  are numbers, often called coefficients, is given by :

                                     

            - B  ±  √ B2-4AC

  k =   ————————

                      2A 

  In our case,  A   =     3

                      B   =    -8

                      C   =   -8 

Accordingly,  B2  -  4AC   =

                     64 - (-96) =

                     160

Applying the quadratic formula :

               8 ± √ 160 

   k  =    —————

                    6

Can  √ 160 be simplified ?

Yes!   The prime factorization of  160   is

   2•2•2•2•2•5  

To be able to remove something from under the radical, there have to be  2  instances of it (because we are taking a squarei.e. second root).

√ 160   =  √ 2•2•2•2•2•5   =2•2•√ 10   =

                ±  4 • √ 10 

  √ 10   , rounded to 4 decimal digits, is   3.1623

 So now we are looking at:

           k  =  ( 8 ± 4 •  3.162 ) / 6

Two real solutions:

 k =(8+√160)/6=(4+2√ 10 )/3= 3.442 

or:

 k =(8-√160)/6=(4-2√ 10 )/3= -0.775 

Two solutions were found :

 k =(8-√160)/6=(4-2√ 10 )/3= -0.775

 k =(8+√160)/6=(4+2√ 10 )/3= 3.442

5 0
3 years ago
Read 2 more answers
ZABD and ZDBC are supplementary angles.
IRINA_888 [86]

Answer:

the answer is 50

Step-by-step explanation:

180-130=50

4 0
2 years ago
Read 2 more answers
Graph the line with slope <br> 3/4<br><br><br> passing through the point (1,4)<br><br><br> .
Valentin [98]

To graph the line, we must first find out the equation for the line in slope-intercept form (y = mx + b). So far, we only have the slope, so the line's equation is y = 3/4x + b. But, by inserting the values of x and y in the point we know, we can find the y - intercept.


4 = 3/4 + b


b = 13/4


That means that the equation of our line is y = 3/4x + 13/4. Now we can graph. But, there is another way to go about (slightly faster too). Since we know the coordinates of 1 point, we can put that line down. Then, since we know that slope is rise over run, we can say, that with a slope of 3/4, one would go 3 points up for every 4 to the right. Now we can go 3 points up and 4 points to the right of point (1,4). That would be (5, 7). Now we can graph (since we have 2 points, or an equation).


The graph looks like this:



3 0
3 years ago
Can someone please help me
Marrrta [24]

Based on the knowledge of <em>trigonometric</em> expressions and properties of <em>trigonometric</em> functions, the value of the <em>sine</em> function is equal to - √731 / 30.

<h3>How to find the value of a trigonometric function</h3>

Herein we must make use of <em>trigonometric</em> expressions and properties of <em>trigonometric</em> functions to find the right value. According to trigonometry, both cosine and sine are <em>negative</em> in the <em>third</em> quadrant. Thus, by using the <em>fundamental trigonometric</em> expression (sin² α + cos² α = 1) and substituting all known terms we find that:

\sin \theta = -\sqrt{1 - \cos^{2}\theta}

\sin \theta = - \sqrt{1 - \left(-\frac{13}{30} \right)^{2}}

sin θ ≈ - √731 / 30

Based on the knowledge of <em>trigonometric</em> expressions and properties of <em>trigonometric</em> functions, the value of the <em>sine</em> function is equal to - √731 / 30.

To learn more on trigonometric functions: brainly.com/question/6904750

#SPJ1

7 0
2 years ago
Solve the inequality.<br> 5x - 7 &lt; 8x + 8<br> The solution set is x |
timofeeve [1]

Answer:

- 5 < x

Step-by-step explanation:

To solve, we need to isolate the variable: x

5x - 7 < 8x + 8

Subtract 5x from both sides

5x -  5x -7 < 8x -5x + 8

- 7 < 3x + 8

Subtract 8 from both sides

- 7 -8 < 3x + 8 -8

-15< 3x

Divide both sides by 3

- 15/3< 3x/3

- 5 < x

5 0
3 years ago
Read 2 more answers
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