15÷1/3= 45 so the students made 45 clay plates
Answer:
![[ln \frac{x(x^2 + 1)}{(x + 1)}]^\frac{3}{2}](https://tex.z-dn.net/?f=%5Bln%20%5Cfrac%7Bx%28x%5E2%20%2B%201%29%7D%7B%28x%20%2B%201%29%7D%5D%5E%5Cfrac%7B3%7D%7B2%7D)
Step-by-step explanation:
![\frac{3}{2} [ln x(x^2 + 1) - ln(x + 1)]](https://tex.z-dn.net/?f=%5Cfrac%7B3%7D%7B2%7D%20%5Bln%20x%28x%5E2%20%2B%201%29%20-%20ln%28x%20%2B%201%29%5D)
ln(m/n)= lnm - ln(n)
![\frac{3}{2}[ln x(x^2 + 1) - ln(x + 1)]](https://tex.z-dn.net/?f=%5Cfrac%7B3%7D%7B2%7D%5Bln%20x%28x%5E2%20%2B%201%29%20-%20ln%28x%20%2B%201%29%5D)
![\frac{3}{2}[ln \frac{x(x^2 + 1)}{(x + 1)}]](https://tex.z-dn.net/?f=%5Cfrac%7B3%7D%7B2%7D%5Bln%20%5Cfrac%7Bx%28x%5E2%20%2B%201%29%7D%7B%28x%20%2B%201%29%7D%5D)
3/2 is before ln. so we move the fraction 3/2 to the exponent
as per log property we move the fraction to the exponent
They are equivalent because they have the same numbers and when you do the math it give 96 for both of them
Step-by-step explanation:
Given AB = CD
<em>ADDING</em><em> </em><em>BC</em><em> </em><em>ON</em><em> </em><em>BOTH</em><em> </em><em>SIDES</em><em> </em>
<em>WE</em><em> </em><em>GET</em>
<em>AB</em><em>+</em><em>BC</em><em>=</em><em>CD</em><em>+</em><em>BC</em>
<em>THEREFORE</em><em> </em><em> </em><em>AC</em><em> </em><em>=</em><em>BD</em>
<em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em> </em><em>HAVE</em><em> </em><em>A NICE DAY</em><em>!</em>
(Note: this is hard to explain without graphing. You might want to graph both of these lines just to make sure I did this correctly. :))
Y = -4(x) is the y = mx + b where m = slope and b = the y intercept.
So the slope of line A is -4 / 1 and the y intercept is 0. (If it's 0 there is no point in writing it down, so it was left out of the equation.)
The slope of line B with be equal to the slope of line A, so we can fill that in our equation. y = -4 x + ??
We know that y increases as x decreases.
Now we just need to scale 8, -3 down until x = 0.
(8 - 4, -3 + 1) = (4, -2)
(4 - 4, -2 + 1) = (0, -1)
y = -4x -1 is your final answer. Hope that helps! :)
