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3 years ago

Solve the system of equations.

Mathematics

1 answer:

Ira Lisetskai [31]3 years ago

7 0

There are two possible answers:
(6, -12)
(8, 14)

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The profitability, P, of a popular restaurant franchise can be modeled by the function P (t) = t4 – 10t3 + 28t2 – 24t, where t i

vekshin1

In this question, the profit of the restaurant after t months is given by a polynomial function. To find when it begins to show a profit, we find the numerical values of the function for t, and it shows a profit when $t > 0$

Profit after t months:

$P(t) = t^4 - 10t^3 + 28t^2 - 24t$

0 months:

This is P(0). So

$P(0) = 0^4 - 10*0^3 + 28*0^2 - 24*0 = 0$

1 month:

This is P(1). So

$P(1) = 1^4 - 10*1^3 + 28*1^2 - 24*1 = -5$

2 months:

This is P(2). So

$P(2) = 2^4 - 10*2^3 + 28*2^2 - 24*2 = 0$

3 months:

This is P(3). So

$P(3) = 3^4 - 10*3^3 + 28*3^2 - 24*3 = -9$

4 months:

This is P(4). So

$P(4) = 4^4 - 10*4^3 + 28*4^2 - 24*4 = -32$

5 months:

This is P(5). So

$P(5) = 5^4 - 10*5^3 + 28*5^2 - 24*5 = -45$

6 months:

This is P(6). So

$P(6) = 6^4 - 10*6^3 + 28*6^2 - 24*6 = 0$

7 months:

This is `P(7). So

$P(7) = 7^4 - 10*7^3 + 28*7^2 - 24*7 = 175$

After 7 months it shows profit, so it starts showing profit on the 6th month, and thus, the correct answer is given by option D.

For another example of a function involving numeric value, you can check brainly.com/question/24231879

8 0

2 years ago

Use the given transformation to evaluate the integral.

GuDViN [60]

For the transformation

$\begin{cases}x=7u+v\\y=u+7v\end{cases}$

the Jacobian is

$\dfrac{\partial(x,y)}{\partial(u,v)}=\begin{bmatrix}7&1\\1&7\end{bmatrix}$

with determinant

$\det\left(\begin{bmatrix}7&1\\1&7\end{bmatrix}\right)=48$

The vertices of the triangle in the $u,v$ -plane are

$(x,y)=(0,0)\implies(u,v)=(0,0)$

$(x,y)=(7,1)\implies(u,v)=(1,0)$

$(x,y)=(1,7)\implies(u,v)=(0,1)$

Then the integral is

$\displaystyle\iint_R(x-8y)\,\mathrm dA=-48\int_0^1\int_0^{1-v}(u+55v)\,\mathrm du\,\mathrm dv=\boxed{-448}$

3 0

2 years ago

Kylie explained that (–4x + 9)2 will result in a difference of squares because (–4x + 9)2 = (–4x)2 + (9)2 = 16x2 + 81. Which sta

LUCKY_DIMON [66]

The expression (-4x + 9)^2 cannot be equal to (-4x)^2 + 9^2 because it is actually equal to the product of two factors (3 + 2sqrt x) (3- 2 sqrt x). One cannot use obviously distributive property. Hence the answer to this problem should be C. as she did not understand both perfect square trinomial and did not determine the product

4 0

2 years ago

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Write a real-world problem that could be solved using a proportion

sweet [91]

What proportion of the pie did my mom eat if 1/2 is left? - That's a question you could use. Hope I helped!!!!!

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2 years ago

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Which best illustrates the distinction between statistical significance and practical importance

ankoles [38]

Answer: