Rewrite the following linear equaton in slope intercept form Y-5=3(x+1)

Find the LCM of this set of numbers. 5 and 25

Andrej [43]

Answer:

25

Step-by-step explanation:

LCM = Least Common Multiple

To find the LCM, start by listing multiples, or the product of any two numbers.

5: 5, 10, 15, 20, 25, 30, 35...

25: 25, 50, 75, 100, 125, 150, 175...

Now, let's find the LCM by selecting the smallest shared multiple out of the lists we made.

5: 5, 10, 15, 20, 25, 30, 35...

25: 25, 50, 75, 100, 125, 150, 175...

Therefore, 25 is the LCM of 5 and 25.

4 0

4 years ago

Use the Chain Rule to find the indicated partial derivatives. z = x^4 + xy^3, x = uv^4 + w^3, y = u + ve^w Find : ∂z/∂u , ∂z/∂v

k0ka [10]

I'll use subscript notation for brevity, i.e. $\frac{\partial f}{\partial x}=f_x$ .

By the chain rule,

$z_u=z_xx_u+z_yy_u$

$z_v=z_xx_v+z_yy_v$

$z_w=z_xx_w+z_yy_w$

We have

$z=x^4+xy^3\implies\begin{cases}z_x=4x^3+y^3\\z_y=3xy^2\end{cases}$

and

$\begin{cases}x=uv^4+w^3\\y=u+ve^w\end{cases}\implies\begin{cases}x_u=v^4\\x_v=4uv^3\\x_w=3w^2\\y_u=1\\y_v=e^w\\y_w=ve^w\end{cases}$

When $u=1,v=1,w=0$ , we have

$\begin{cases}x(1,1,0)=1\\y(1,1,0)=2\end{cases}\implies\begin{cases}z_x(1,2)=12\\z_y(1,2)=12\end{cases}$

and the partial derivatives take on values of

$\begin{cases}x_u(1,1,0)=1\\x_v(1,1,0)=4\\x_w(1,1,0)=0\\y_u(1,1,0)=1\\y_v(1,1,0)=1\\y_w(1,1,0)=1\end{cases}$

So we end up with

$\boxed{\begin{cases}z_u(1,1,0)=24\\z_v(1,1,0)=60\\z_w(1,1,0)=12\end{cases}}$

3 0

3 years ago

Kylie installed a fence along the 500-foot perimeter of her rectangular backyard. She left an opening for a gate. In the diagram

pentagon [3]

The correct answer is B.

8 0

3 years ago

Read 2 more answers

Ava bought 2 sandwiches for a total of $5.25, a bowl of soup for $3.00, and a bag of chips for $1.25. How much change did she ge

Alborosie

Answer:

Step-by-step explanation:

5.25

3.00

1.25

_____

$ 9.50

- 20.00

_______

$10.5

6 0

3 years ago

A company's profit C (in thousands of dollars) can be modeled by the polynomial function C = - 5x ^ 3 + 6x ^ 2 + 15x , where x i

steposvetlana [31]

Answer:

849 items.

Step-by-step explanation:

Given that the profit C (in thousands of dollars) for x thousands of items related as

$C = - 5x ^ 3 + 6x ^ 2 + 15x \\\\\Rightarrow -5x^3+6x^2+15x -C=0\cdots(i)$

As the profit is $14,000 for producing 2000 items, so

C= 14 thousand dollars and

x= 2 thousand items.

Putting C= 14 in the equation ( we have),

$-5x^3+6x^2+15x -14=0\cdots(ii)$

Now, x=2 is one of the solutions to the equation (ii), so (x-2) is a factor of the equation (ii), we have

$(x-2)(-5x^2-4x+7)=0 \\\\\Rightarrow x-2=2 \; or \; -5x^2-4x+7=0$

We have the given solution for x-2=0, so sloving -5x^2-4x+7=0 for other solutions.

$-5x^2-4x+7=0 \\\\\Rightarrow x= \frac {-(-4)\pm \sqrt {(-4)^2-4\times (-5)7}}{2\times (-5)} \\\\\Rightarrow x= \frac {4\pm \sqrt {156}}{2\times (-5)} \\\\\Rightarrow x= \frac {4\pm 12.49}{2\times (-5)} \\\\\Rightarrow x = \frac {4+ 12.49}{2\times (-5)}, \frac {4- 12.49}{2\times (-5)} \\\\\Rightarrow x = -1.649, 0.849$

As the number of items cant be negative, so x= 0.849 thousand is the other number of items.

Hence, the other number of items for the same profit is 849 items.

4 0

3 years ago