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3 years ago

Bernard is two years older than his sister Therese and four years younger than his sister

Mathematics

1 answer:

hjlf3 years ago

6 0

Firstly Bernard = x

A) lets focus on Therese first. Bernard id two years older than her so for Therese’s equation in terms of x it would be x+2. Now for Josephine Bernard is 4 years younger than HER so it would be 4-x.

B) The mother is the PRODUCT of the sisters’ ages so (multiplication)

It would be like this: (x+2)(4-x)= 40 This is all in terms of x.

Solving for the equation (using distributive property) we get:

4x-x+8-2x=40

(Reorganize to group like terms, remember to go in order from the numeral numbers with variables, to variables only then numbers only): 4x-2x-x+8=40 (now combine like terms and simplify): x+8=40 this is his mom’s age in terms of x

C) HERE we can solve for x:

Isolating x to get the answer we move the 8 to the other side of the equation and it becomes a negative 8 so:

x=40-8

x=32

Therefore Bernard is 32 years old.

Hope this helps!

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A square is inscribed in a circle with an area of 10 pi square inches. what is the area of the square

Naddik [55]

We need to determine the radius and diameter of the circle. If the area of the circle is 10 pi in^2, then, according to the formula for the area of a circle,

A = 10 pi in^2 = pi*r^2. Thus, 10 in^2 = r^2, and r = radius of circle = sqrt(10) in.

Thus, the diam. of the circle is 2sqrt(10) in. This diam. has the same length as does the hypotenuse of one of the triangles making up the square.

Thus, [ 2*sqrt(10) ]^2 = x^2 + x^2, where x represents the length of one side of the square. So, 4(10) in^2 = 2x^2. Then:
40 in^2 = 2x^2, or 20 in^2 = x^2, and so the length x of one side of the square is sqrt(20). The area of the square is the square of this result:

Area of the square = x^2 = [ sqrt(20) ]^2 = 20 in^2 (answer). Compare that to the 10 pi sq in area of the circle (31.42 in^2).

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3 years ago

13. En un pueblo, 5 personas escucharon una noticia. En una hora, cada una de ellas

Vera_Pavlovna [14]

Answer:

En 5 horas se habrá enterado todo el pueblo.

Step-by-step explanation:

Sabemos que en un pueblo 5 personas escucharon una noticia.

Una hora más tarde, cada una de ellas le contó la noticia a otras 5.

Luego, éstas contaron la noticia a otras 5 y así sucesivamente.

Nadie cuenta ni escucha la noticia más de una vez y en ese pueblo hay un poco más de 19000 habitantes.

La ecuación a desarrollar para resolver el problema es la siguiente :

Comenzamos con 5 personas que escucharon la noticia a la ''hora 0''.

Una hora más tarde, cada una de ellas le contó a 5 personas, es decir , pasada la primera hora tendremos :

$5+5^{2}=30$ (I)

Las 5 personas originales de la ''hora 0'' más 25 personas que se enteraron pasada la primera hora. La ecuación que planteamos es la siguiente :

$5^{1}+5^{2}+5^{3}+...+5^{x}>19000$ (II)

Buscamos el valor de $x$ que satisface la ecuación (II).

Probando y realizando las sumas encontramos que :

$5^{1}+5^{2}+5^{3}+5^{4}+5^{5}+5^{6}>19000$

$19530>19000$

El valor de $x$ que satisface (II) es $x=6$ .

Para hallar el número de horas nos fijamos que en (I) el valor del mayor exponente del 5 es el número 2. Para ese valor 2, el tiempo que pasó es una hora.

Entonces para nuestro $x=6$ , el número de horas que pasaron son 5 horas (1 menos que el valor de $x$ )

Todo el pueblo se habrá enterado en 5 horas de la noticia.

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4 years ago

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3 years ago

Read 2 more answers

Plz help right now illl give brainlist 5.0 and say thanks

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