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2 years ago

How do I work it out ?

Mathematics

1 answer:

algol [13]2 years ago

4 0

Answer:

x - y = 5

Explanation:

As you can see in the first problem the ration is x to y = 8 to 3. This means for every 8 x values, there are 3 y values. Therefore, x - y should be the same as 8 - 3, which is 5.

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Simplify: 3(2x-y)-(5x+4y-2) <br>Please show steps

il63 [147K]

Answer:

6 x ^2 − 5 x y − 4 y ^2

Step-by-step explanation:

Expand

( 2 x + y ) (3 x − 4 y )

using the FOIL Method.

Apply the distributive property.

2 x ( 3 x − 4 y ) + y ( 3 x − 4 y )

Apply the distributive property.

2 x ( 3 x )+ 2 x (− 4 y ) + y ( 3x − 4 y )

Apply the distributive property.

2 x ( 3 x ) + 2 x( − 4 y ) + y ( 3 x) + y ( −4 y )

Simplify and combine like terms.

6 x ^2 − 5 x y − 4^ 2

7 0

2 years ago

Read 2 more answers

Una heladeria dispone de 20 frutas distintas para elaborar sus malteadas. Si los clientes pueden elegir tres sabores para mezcla

Dahasolnce [82]

Answer:

Existen 6840 permitaciones de malteadas de tres sabores distintos que la heladería puede ofrecer.

Step-by-step explanation:

En este caso, el cliente que adquiere una malteada de tres sabores distintos sigue el siguiente procedimiento:

1) El primer sabor sale de cualquiera de las 20 frutas disponibles.

2) El segundo sabor es distinto al primer sabor, es decir, que sale de las 19 frutas restantes.

3) El tercer sabor es distinto al primer sabor y al segundo sabor, es decir, que sale de las 18 frutas restantes.

Puesto que existe una doble conjunción y que puede importar el orden según la preferencia del cliente, se habla matemáticamente de una permutación, definida como:

$n\mathbb{P}k = \frac{n!}{(n-k)!}$ (1)

Donde:

$n$ - Número de sabores disponibles, adimensional.

$k$ - Número de sabores escogidos, adimensional.

Si tenemos que $n = 20$ y $k = 3$ , entonces la cantidad de malteadas de tres sabores distintos es:

$n\mathbb{P}k = \frac{20!}{(20-3)!}$

$n\mathbb{P}k = \frac{20!}{17!}$

$n\mathbb{P}k = 20\cdot 19\cdot 18$

$n\mathbb{P}k = 6840$

Existen 6840 permitaciones de malteadas de tres sabores distintos que la heladería puede ofrecer.

5 0

3 years ago

Simplify: − 7( 21 − 16) + 3(9) (24 − 18)

Mekhanik [1.2K]

The answer to the problem is 127

6 0

3 years ago

Read 2 more answers

[10] In the following given system, determine a matrix A and vector b so that the system can be represented as a matrix equation

irina1246 [14]

Answer:

$y=-\frac{158}{579}$

Step-by-step explanation:

To find the matrix A, took all the numeric coefficient of the variables, the first column is for x, the second column for y, the third column for z and the last column for w:

$A=\left[\begin{array}{cccc}1&1&2&2\\-7&-3&5&-8\\4&1&1&1\\3&7&-1&1\end{array}\right]$

And the vector B is formed with the solution of each equation of the system: $b=\left[\begin{array}{c}3\\-3\\6\\1\end{array}\right]$

To apply the Cramer's rule, take the matrix A and replace the column assigned to the variable that you need to solve with the vector b, in this case, that would be the second column. This new matrix is going to be called $A_{2}$ .

$A_{2}=\left[\begin{array}{cccc}1&3&2&2\\-7&-3&5&-8\\4&6&1&1\\3&1&-1&1\end{array}\right]$

The value of y using Cramer's rule is:

$y=\frac{det(A_{2}) }{det(A)}$

Find the value of the determinant of each matrix, and divide:

$y==\frac{\left|\begin{array}{cccc}1&3&2&2\\-7&-3&5&-8\\4&6&1&1\\3&1&-1&1\end{array}\right|}{\left|\begin{array}{cccc}1&1&2&2\\-7&-3&5&-8\\4&1&1&1\\3&7&-1&1\end{array}\right|} =\frac{158}{-579}$

$y=-\frac{158}{579}$

7 0

3 years ago

Nina has some nickels and 9 pennies in her pocket. Her friend, Maurice has twice as many nickels as Nina. Together these coins a

algol13

So Maurice would have 2N nickels

Total number of coins is N + 2N + 9 = 3N + 9

Each nickel is 5 pennies

3N of nickels = 15N pennies

-----------

Their worth is 84 cents

15N + 9 = 84

15N = 75

N = 75/15 = 5

N = 5

This means Nina has 5 nickels.

4 0

3 years ago