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2 years ago

Can someone please solve 2/7y + 5 = -9

Mathematics

1 answer:

drek231 [11]2 years ago

4 0

Answer:

y = -49

Step-by-step explanation:

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How do I solve this?

Yuki888 [10]

The answer is B. The values of y must only be positive because it is equal to
$| - x|$
The other options states that the values of y could be negative which is why it is wrong.

3 0

3 years ago

Peter works as a delivery person for a bike shipping company. The graph shows a linear model for his delivery times on different

aev [14]

Answer/Step-by-step explanation:

✍️The equation of the line in point-slope form:

The equation is given as $y - b = m(x - a)$ , where,

(a, b) = a point on the line.

$slope (m) = \frac{y_2 - y_1}{x_2 - x_1}$

Let's find the slope (m) of the line, housing (3, 21) and (6, 12):

$slope (m) = \frac{y_2 - y_1}{x_2 - x_1} = \frac{12 - 21}{6 - 3} = \frac{-9}{3} = -3$

Substitute a = 3 and b = 21, m = -3 into $y - b = m(x - a)$ .

Thus, the point-slope equation would be:

✅ $y - 21 = -3(x - 3)$

✍️The equation of the line in slope-intercept form:

Rewrite $y - 21 = -3(x - 3)$ , so that y is made the subject of the formula.

$y - 21 = -3x + 9$

Add 21 to both sides

$y = -3x + 9 + 21$

$y = -3x + 30$

✅The slope-intercept equation of the line is $y = -3x + 30$

Where,

-3 = how much did his delivery time decrease per day (slope)

30 = how long it initially took Peter to deliver his packages (y-intercept)

5 0

2 years ago

A company wishes to manufacture some boxes out of card. The boxes will have 6 sides (i.e. they covered at the top). They wish th

Serhud [2]

Answer:

The dimensions are, base $b=\sqrt[3]{200}$ , depth $d=\sqrt[3]{200}$ and height $h=\sqrt[3]{200}$ .

Step-by-step explanation:

First we have to understand the problem, we have a box of unknown dimensions (base $b$ , depth $d$ and height $h$ ), and we want to optimize the used material in the box. We know the volume $V$ we want, how we want to optimize the card used in the box we need to minimize the Area $A$ of the box.

The equations are then, for Volume

$V=200cm^3 = b.h.d$

For Area

$A=2.b.h+2.d.h+2.b.d$

From the Volume equation we clear the variable $b$ to get,

$b=\frac{200}{d.h}$

And we replace this value into the Area equation to get,

$A=2.(\frac{200}{d.h} ).h+2.d.h+2.(\frac{200}{d.h} ).d$

$A=2.(\frac{200}{d} )+2.d.h+2.(\frac{200}{h} )$

So, we have our function $f(x,y)=A(d,h)$ , which we have to minimize. We apply the first partial derivative and equalize to zero to know the optimum point of the function, getting

$\frac{\partial A}{\partial d} =-\frac{400}{d^2}+2h=0$

$\frac{\partial A}{\partial h} =-\frac{400}{h^2}+2d=0$

After solving the system of equations, we get that the optimum point value is $d=\sqrt[3]{200}$ and $h=\sqrt[3]{200}$ , replacing this values into the equation of variable $b$ we get $b=\sqrt[3]{200}$ .

Now, we have to check with the hessian matrix if the value is a minimum,

The hessian matrix is defined as,

$H=\left[\begin{array}{ccc}\frac{\partial^2 A}{\partial d^2} &\frac{\partial^2 A}{\partial d \partial h}\\\frac{\partial^2 A}{\partial h \partial d}&\frac{\partial^2 A}{\partial p^2}\end{array}\right]$

we know that,

$\frac{\partial^2 A}{\partial d^2}=\frac{\partial}{\partial d}(-\frac{400}{d^2}+2h )=\frac{800}{d^3}$

$\frac{\partial^2 A}{\partial h^2}=\frac{\partial}{\partial h}(-\frac{400}{h^2}+2d )=\frac{800}{h^3}$

$\frac{\partial^2 A}{\partial d \partial h}=\frac{\partial^2 A}{\partial h \partial d}=\frac{\partial}{\partial h}(-\frac{400}{d^2}+2h )=2$

Then, our matrix is

$H=\left[\begin{array}{ccc}4&2\\2&4\end{array}\right]$

Now, we found the eigenvalues of the matrix as follow

$det(H-\lambda I)=det(\left[\begin{array}{ccc}4-\lambda&2\\2&4-\lambda\end{array}\right] )=(4-\lambda)^2-4=0$

Solving for $\lambda$ , we get that the eigenvalues are: $\lambda_1=2$ and $\lambda_2=6$ , how both are positive the Hessian matrix is positive definite which means that the function $A(d,h)$ is minimum at that point.