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ikadub [295]
3 years ago
12

The average weight of David, Esther, and Henry is 42.6 kg. Esther is twice as heavy as Henry. David is 5.2 kilograms lighter tha

n Esther, what is Esther's weight?
Mathematics
1 answer:
kari74 [83]3 years ago
7 0

Answer:

  53.2 kg

Step-by-step explanation:

Let E represent Esther's weight. Then Henry's weight is E/2, and David's weight is E-5.2. Their average weight is ...

  ((E-5.2) + E + (E/2))/3 = 42.6

  2.5E -5.2 = 127.8 . . . . . . . . . . multiply by 3, simplify

  2.5E = 133 . . . . . . . . . . . . . . . . add 5.2

  E = 133/2.5 = 53.2 . . . . kg

Esther's weight is 53.2 kg.

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Factor -3/4 out of 3/2x - 9/4y
Vikki [24]

Answer:

-\frac{3}{4} \times (-2x +3y)

Step-by-step explanation:

To factor out -3/4 out of that equation, multiply and divide by -3/4.

Say ;

=\frac{3}{2}x -\frac{9}{4}y

=(\frac{3}{2}x -\frac{9}{4}y) \times \frac{-\frac{3}{4} }{-\frac{3}{4}}

Now, rearranging and making necessary commutations.

=-\frac{3}{4} \times (\frac{3}{2}x -\frac{9}{4}y) \times \frac{1 }{-\frac{3}{4}}

=-\frac{3}{4} \times (-2x +3y)

Factoring -3/4 we get an equation without any fractions

= -2x + 3y

3 0
3 years ago
Problema de capacidades Una empresa aceitera ha envasado 3000 litros de aceite en 1200 botellas de dos y de cinco litros. ¿Cuánt
mariarad [96]

Answer:

Hay 200 botellas de 5 litros y 1000 botellas de 2 litros.

Step-by-step explanation:

Un sistema de ecuaciones lineales es un conjunto de dos o más ecuaciones de primer grado, en el cual se relacionan dos o más incógnitas.

Resolver un sistema de ecuaciones consiste en encontrar el valor de cada incógnita para que se cumplan todas las ecuaciones del sistema.

En este caso, las variables a calcular son:

  • x= cantidad de botellas de 2 litros.
  • y= cantidad de botellas de 5 litros.

Una empresa aceitera ha envasado 3000 litros de aceite en 1200 botellas de dos y de cinco litros. Entonces es posible plantear el siguiente sistema de ecuaciones:

\left \{ {{2*x+5*y=3000} \atop {x+y=1200}} \right.

Existen varios métodos para resolver un sistema de ecuaciones. Resolviendo por el método de sustitución, que consiste en despejar o aislar una de las incógnitas y sustituir su expresión en la otra ecuación, despejas x de la segunda ecuación:

x= 1200 - y

Sustituyendo la expresión en la primer ecuación:

2*(1200 - y) + 5*y=3000

Resolviendo se obtiene:

2*1200 - 2*y + 5*y= 3000

2400 +3*y= 3000

3*y= 3000 - 2400

3*y= 600

y= 600÷3

y= 200

Reemplazando en la expresión x= 1200 - y:

x= 1200 - y

x=1200 -200

x= 1000

<u><em>Hay 200 botellas de 5 litros y 1000 botellas de 2 litros.</em></u>

7 0
2 years ago
A pound of chocolate costs 7 dollars. Joe buys p pounds. Write an equation to represent the total cost c that Joe pays.
pickupchik [31]

Answer:

Total cost, c = 7p

Step-by-step explanation:

1pound =$7

Joe buys p pounds,

p pounds = $7 * p

p pounds = 7p

3 0
3 years ago
Given f(x)=2x+1 and g(x)=7-x. Find g(f(x)).
Darina [25.2K]

Answer:

f(g(x)) = 2(7 - x) + 1

Step-by-step explanation:

f(x) = 2x + 1

g(x) = 7 - x

The question in the picture itself says to find f(g(x)) so i'll find that instead

f(g(x)) = 2(7 - x) + 1

f(g(x)) = 14 - 2x + 1

f(g(x)) = -2x + 15

6 0
2 years ago
Daniel drew a toy from a treasure chest containing 30 different toys. He selected a bouncy ball without replacement and then sel
borishaifa [10]

Answer:

Pr = \frac{1}{870}

Step-by-step explanation:

Given

n =30

Required

Probability of selecting 2 toys of different types

From the question, we understand that all toys are different i.e. 1 of each type.

And the selection is without replacement;

So, after the first toy is selected; there are n - 1 toys left.

So, the probability is:

Pr = \frac{1}{n} * \frac{1}{n - 1}

Substitute n =30

Pr = \frac{1}{30} * \frac{1}{30- 1}

Pr = \frac{1}{30} * \frac{1}{29}

Pr = \frac{1}{30*29}

Pr = \frac{1}{870}

5 0
2 years ago
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