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1 year ago

7

The pizza shop offers a 15 percent discount for veterans and senior citizens. If the price of a pizza is $12, how would you find

the discounted price?
\

1 answer:

Zinaida [17]1 year ago

4 0

It would discount $1.80. the price would be 13.20 for them

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Find the point (x,y) of x2+14xy+49y2=100 that is closest to the origin and lies in the first quadrant.

Gala2k [10]

Notice that

$x^2+14xy+49y^2=(x+7y)^2$

so the constraint is a set of two lines,

$(x+7y)^2=100\implies\begin{cases}x+7y=10\\x+7y=10\end{cases}$

and only the first line passes through the first quadrant.

The distance between any point $(x,y)$ in the plane is $\sqrt{x^2+y^2}$ , but we know that $\sqrt{f(x,y)}$ and $f(x,y)$ share the same critical points, so we need only worry about minimizing $x^2+y^2$ . The Lagrangian for this problem is then

$L(x,y,\lambda)=x^2+y^2+\lambda(x+7y-10)$

with partial derivatives (set equal to 0)

$L_x=2x+\lambda=0$

$L_y=2y+7\lambda=0$

$L_\lambda=x+7y-10=0$

We have

$L_y-7L_x=2y-14x=0\implies y=7x$

which tells us that

$x+7y-10=0\iff x+49x=10\implies x=\dfrac15\implies y=\dfrac75$

so that $\left(\dfrac15,\dfrac75\right)$ is a critical point. The Hessian for the target function $x^2+y^2$ is

$H(x,y)=\begin{bmatrix}2&0\\0&2\end{bmatrix}$

which is positive definite for all $x,y$ , so the critical point is the site of a minimum. The minimum distance itself (which we don't seem to care about for this problem, but we might as well state it) is $\sqrt{\left(\dfrac15\right)^2+\left(\dfrac75\right)^2}=2$ .

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Let r= 12 be the reserve rate. Which of the following is the money multiplier?

Studentka2010 [4]

Answer:

B

Step-by-step explanation:

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Well first you got to add up of the sides

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2 years ago

Tulio Fernandez purchased a treadmill with an installment loan that has an APR of 12%. The treadmill sells for $1,672. The store

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1 year ago

Read 2 more answers

Which is a solution to the equation? (x −2)(x + 5) = 18 x = −10 x = −7 x = −4 x = −2

Leona [35]

Answer:

Solutions:

$x=-7$

$x=4$

Step-by-step explanation:

$(x-2)(x + 5) = 18$

Expanding the factored form:

$x^2+5x-2x-10=18$

$x^2+3x-28=0$

Factoring the second-degree polynomial:

$(x+7)(x-4)=0$

This is true for

$x=-7 \text{ or } x=4$

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1 year ago