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Rufina [12.5K]
2 years ago
6

-3+>24 ,slove for x​

Mathematics
1 answer:
jenyasd209 [6]2 years ago
8 0
What In the world that is not a problem
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Dado dos ángulos complementarios, uno mide (2x + 10) y el otro (x + 20),
rusak2 [61]

Answer:

El valor de <em>x</em> es igual a 20 o <em>x</em> = 20.

Step-by-step explanation:

Lo primero que se debe saber es que <em>dos ángulos complementarios suman un ángulo recto o 90º</em>.

Supongamos que el valor de un ángulo \\ \alpha y un ángulo \\ \beta valen:

\\ \alpha = 2x + 10 [1]

\\ \beta = x + 20 [2]

Como la suma de  \\ \alpha + \beta = 90 [3]

Entonces

\\ \alpha + \beta = (2x + 10) + (x + 20) = 90

Sumamos los factores comunes entre si:

\\ (2x + x) + (10 + 20) = 90

Para la primera expresión debemos recordar que se suman sólo los coeficientes. Así:

\\ (2 + 1)x + (10 + 20) = 90

\\ 3x + 30 = 90

Para despejar la incógnita <em>x</em>, debemos tener en cuenta que <em>una igualdad no se altera si se suma, se resta, se multiplica o divide un mismo valor a cada lado de ella</em>. Por esta razón, para despejar 3x, lo primero que podemos hacer es sumar -30 a cada lado de la expresión (lo que es igual a restar 30 a cada lado de la misma). Así tenemos:

\\ 3x + 30 - 30 = 90 - 30

\\ 3x + 0 = 90 - 30

\\ 3x = 60

Ahora dividimos cada miembro de la igualdad entre 3 (o multiplicamos cada lado de la igualdad por \\ \frac{1}{3} ):

\\ \frac{3}{3}x = \frac{60}{3}

Como sabemos que:

\\ \frac{3}{3} = 1

Entonces:

\\ 1*x = \frac{60}{3}

\\ x = \frac{60}{3}

\\ x = 20

De esta manera, el valor de <em>x</em> es igual a 20 o x = 20.

Lo anterior lo podemos comprobar considerando las ecuaciones [1], [2] y [3]. Así tenemos que:

\\ \alpha = 2x + 10 [1]

Sustituimos x por el valor de 20:

\\ \alpha = 2*20 + 10 = 40 + 10 = 50

\\ \beta = x + 20 [2]

Hacemos lo mismo para [2]:

\\ \beta = 20 + 20

\\ \beta = 40

De esta manera:

\\ \alpha + \beta = 90 [3]

\\ 50 + 40 = 90

4 0
3 years ago
What is the answer to 85% of 62
Stella [2.4K]

Answer:

52.7

Step-by-step explanation:

Of means multiply

85% * 62

.85 * 62

52.7

6 0
2 years ago
Read 2 more answers
En un triangulo ABC, el angulo B mide 64° y el angulo C mide 72°. La bisectriz interior CD corta a la altura BH y a la bisectriz
nadezda [96]

Answer:

The difference between the greatest and the smallest angle of the triangle PBQ is 98°.

Step-by-step explanation:

The question is:

In a triangle ABC, angle B measures 64 ° and angle C measures 72°. The inner bisector CD intersects the height BH and the bisector BM at P and Q respectively. Find the difference between the greatest and the smallest angle of the triangle PBQ.

Solution:

Consider the triangle ABC.

The measure of angle A is:

angle A + angle B + angle C = 180°

angle A = 180° - angle B - angle C

             = 180° - 72° - 64°

             = 44°  

It is provided that CD and BM are bisectors.

That:

angle BCP = angle PCH = 36°

angle CBQ = angle QBD = 32°

angle BHC = 90°

Compute the measure of angle HBC as follows:

angle HBC = 180° - angle BHC + angle BCH

                  = 180° - 90° - 72°

                  = 18°

Compute the measure of angle BPC as follows:

angle BPC = 180° - angle PCB + angle CBP

                  = 180° - 18° - 36°

                  = 126°

Then the measure of angle BPQ will be:

angle BPQ = 180° - angle BPC

                  = 180° - 126°

angle BPQ = 54°

Compute the measure of angle PBQ as follows:

angle PBQ = angle B - angle QBD - angle HBC

                  = 64° - 32° - 18°

angle PBQ = 14°

Compute the measure of angle BQP as follows:

angle BQP = 180° - angle PBQ - angle BPQ

                  = 180° - 14° - 54°  

angle BQP = 112°

So, the greatest and the smallest angle of the triangle PBQ are:

angle BQP = 112°

angle PBQ = 14°

Compute the difference:

<em>d</em> = angle BQP - angle PBQ

  = 112° - 14°

  = 98°

Thus, the difference between the greatest and the smallest angle of the triangle PBQ is 98°.

4 0
3 years ago
I really need help- eeeeeeeeeeeeeeeeeeeeeeeeeeeee
Juliette [100K]

Answer:

-2, -5, 2, then 5

Step-by-step explanation:

3 0
2 years ago
Read 2 more answers
19 is 25% of what number?
zepelin [54]

Answer:

19/25 * 100 = 76%

Step-by-step explanation:

3 0
3 years ago
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