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Mashutka [201]
3 years ago
8

There were 9500 spectators at a football match. 6375 of them were men. Of the remaining spectators, there were 4 times as many c

hildren as women. How many children were there?
Mathematics
1 answer:
jek_recluse [69]3 years ago
3 0
X=# of women

9500=6375+w+4w
9500=6375+5w
3125=5w
625=w

625(4)=2500

There were 2500 kids at the game.
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The point (-3,3) lies on a circle. What is the length of the radius of this circle if the center is located at (10,6) ?
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The radius is from center to point on a circle. 
So your task is  count distance between two points: S(10,6) and A(-3,3). 
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|AB|=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\ \\ \hbox{So:} \\ \\ r=|SA|=\sqrt{(-3-10)^2+(3-6)^2}=\sqrt{(-13)^2+(-3)^2}=\sqrt{169+9}= \\ r= \sqrt{178}
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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

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Answer:

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