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3 years ago

Which of these expressions is equivalent to m^2 - n^2 - 14n - 49?

Mathematics

1 answer:

polet [3.4K]3 years ago

6 0

Answer:

n = m - 7 or n = -m - 7

Step-by-step explanation:

Solve for n:

m^2 - (n + 7)^2 = 0

The left hand side factors into a product with two terms:

(-7 + m - n) (7 + m + n) = 0

Split into two equations:

-7 + m - n = 0 or 7 + m + n = 0

Subtract m - 7 from both sides:

-n = 7 - m or 7 + m + n = 0

Multiply both sides by -1:

n = m - 7 or 7 + m + n = 0

Subtract m + 7 from both sides:

Answer: n = m - 7 or n = -m - 7

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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

Angelica earns d dollars for babysitting each week. She also receives an allowance of $10 per week. The expression (10+d)∙5 can

Katyanochek1 [597]

Answer:

The amount of money Angelica will have at the end of five weeks if d = $25 is $175.

Step-by-step explanation:

The given information are;

The allowance Angelica earns for baby sitting = d dollars per week

The amount she receives as allowance = $10 per week

The amount she will have at the end of 5 weeks = (10 + d)·5

The amount, A, of money Angelica will have at the end of five weeks if d = $25 is given as follows;

A = (10 + 25) × 5 = $175

The amount of money Angelica will have at the end of five weeks if d = $25 is $175.

7 0

3 years ago

Cara has 25$ to buy dry pet food and treats for the animal shelter. A pound of dog food cost $2 and treats are $1 apiece. If she

alina1380 [7]

Let x be the number of treats bought
Let y be the pounds of food bought

25= 2y+x

Given that she has buys 9 pounds of dog food:

25= 2(9)+x
25=18 +x
25-18 =x
7=x

With the money she has left over, she can buy 7 treats.

Hope I helped :)

5 0

3 years ago

in the diagram below P(x:y)is a point in the third quadrant. ROP=B and 17 cos B is equal to -15 calculate the values of x and y

Ipatiy [6.2K]

you showed no diagram or any picture / screenshot

4 0

2 years ago

10-d = -34-5d solve this equation

algol13

<h3><u>Explanation</u></h3>

Given the equation.

$10 - d = - 34 - 5d$

Solve the equation for d-term.

Because we cannot subtract or add up constants and variables, we simply move the same variable term to the same side and constant term to the same constant side.

$10 + 34 = - 5d + d \\ 44 = - 4d \\ \frac{44}{ - 4} = d \\ - 11 = d$

Answer Check

Substitute d = -11 in the equation.

$10 - ( - 11) = - 34 - 5( - 11) \\ 10 + 11 = - 34 + 55 \\ 21 = 21$

The equation is true for d = -11.

<h3><u>Answer</u></h3>

<u> $\large \boxed{d = - 11}$ </u>

7 0

3 years ago

Read 2 more answers