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klasskru [66]
3 years ago
9

How can I find x? Click for picture.

Mathematics
1 answer:
romanna [79]3 years ago
6 0
Answer:   You add up all the terms given of EACH angle, and make this an addition problem that is "equal to 180" ; since all triangles have three angles that add up to 180 degrees.  Then you solve for "x".
__________________________________________________
(as follows) ;  to get:    " x = 29 ⅔ ° " .
_______________________________________

         3x + 4 + 2x + x + 8 = 180  ;
_______________________________________
Combine the "like terms" ;

         3x + 2x + x = 6x ;

                 4 + 8 = 12

So, we have:  6x + 12 = 180 ;

Now, subtract "12" from each side of the equation:
__________________________________________
  6x + 12 − 12 = 180 <span>− 12 ;
</span>__________________________________________
 to get: 

      6x = 178 ;

Now, divide EACH SIDE of the equation by "6" ; to isolate "x" on one side of the equation; and to solve for "x" ;
______________________________________
    6x / 6 = 178 / 6 ;

to get:  x = 178/6 = 29 ⅔ ° .
______________________________________
             x = 29 ⅔ ° .
______________________________________
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What is the factorization of 729^15+1000?
igomit [66]

Answer:

The factorization of 729x^{15} +1000 is (9x^{5} +10)(81x^{10} -90x^{5} +100)

Step-by-step explanation:

This is a case of factorization by <em>sum and difference of cubes</em>, this type of factorization applies only in binomials of the form (a^{3} +b^{3} ) or (a^{3} -b^{3}). It is easy to recognize because the coefficients of the terms are <u><em>perfect cube numbers</em></u> (which means numbers that have exact cubic root, such as 1, 8, 27, 64, 125, 216, 343, 512, 729, 1000, etc.) and the exponents of the letters a and b are multiples of three (such as 3, 6, 9, 12, 15, 18, etc.).

Let's solve the factorization of 729x^{15} +1000 by using the <em>sum and difference of cubes </em>factorization.

1.) We calculate the cubic root of each term in the equation 729x^{15} +1000, and the exponent of the letter x is divided by 3.

\sqrt[3]{729x^{15}} =9x^{5}

1000=10^{3} then \sqrt[3]{10^{3}} =10

So, we got that

729x^{15} +1000=(9x^{5})^{3} + (10)^{3} which has the form of (a^{3} +b^{3} ) which means is a <em>sum of cubes.</em>

<em>Sum of cubes</em>

(a^{3} +b^{3} )=(a+b)(a^{2} -ab+b^{2})

with a= 9x^{5} y b=10

2.) Solving the sum of cubes.

(9x^{5})^{3} + (10)^{3}=(9x^{5} +10)((9x^{5})^{2}-(9x^{5})(10)+10^{2} )

(9x^{5})^{3} + (10)^{3}=(9x^{5} +10)(81x^{10}-90x^{5}+100)

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3 years ago
Line MN passes through points M(4, 3) and N(7, 12). If the equation of the line is written in slope-intercept form, y = mx + b,
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For finding the value of b, we must consider that Line MN passes through points M(4, 3) and N(7, 12). With this condition y = mx + b, can be written 3=4m+ b (because line passes through M(4,3) ) and 12=7m+b, b ( because line passes through M(7,12)). We have a system of equation 4m+ b=3 7m+b=12 For solving this, 4m+b- (7m+b)= 3-12, it is equivalent to -3m= -9 and then m=3, if m=3 so 4x3 +b =3 implies b= 3 -12= -9, so the value of b= -9 <span>
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