What does that mean I don't get it I will randomly guess 500000000
Answer:
Step-by-step explanation:
The standard way of writing equation of a line in a point-slope form is as given;
y - y0 = m(x-x0)
m is the slope of the line
(x0,y0) is a point on the line.
Given the point (-2,-6), in order to determine with of the equation that correctly uses the point, we will substitute the point into the formula and get the necessary equation.
y - y0 = m(x-x0)
y - (-6) = m(x-(-2))
y+6 = m(x+2)
Since we are not given the slope, let's assume the slope is 5/2
The equation becomes y+6 =5/2(x+2). Option D is correct
Answer:
![\sqrt[3]{2y^3} * 7\sqrt{18y} = 21(y^{\frac{3}{2}})(2^{\frac{5}{6}})](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B2y%5E3%7D%20%2A%207%5Csqrt%7B18y%7D%20%3D%2021%28y%5E%7B%5Cfrac%7B3%7D%7B2%7D%7D%29%282%5E%7B%5Cfrac%7B5%7D%7B6%7D%7D%29)
Step-by-step explanation:
The question is poorly formatted.
Given
![\sqrt[3]{2y^3} * 7\sqrt{18y}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B2y%5E3%7D%20%2A%207%5Csqrt%7B18y%7D)
Required
Derive an equivalent expression
Express 18 as 9 * 2
![\sqrt[3]{2y^3} * 7\sqrt{9 * 2y}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B2y%5E3%7D%20%2A%207%5Csqrt%7B9%20%2A%202y%7D)
Split the expression as follows:
![\sqrt[3]{2y^3} * 7\sqrt{9} * \sqrt{2y}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B2y%5E3%7D%20%2A%207%5Csqrt%7B9%7D%20%2A%20%5Csqrt%7B2y%7D)
Take positive square root of 9
![\sqrt[3]{2y^3} * 7*3 * \sqrt{2y}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B2y%5E3%7D%20%2A%207%2A3%20%2A%20%5Csqrt%7B2y%7D)
![\sqrt[3]{2y^3} * 21 * \sqrt{2y}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B2y%5E3%7D%20%2A%2021%20%2A%20%5Csqrt%7B2y%7D)
![21*\sqrt[3]{2y^3} * \sqrt{2y}](https://tex.z-dn.net/?f=21%2A%5Csqrt%5B3%5D%7B2y%5E3%7D%20%2A%20%20%5Csqrt%7B2y%7D)
The cube root can be rewritten to give:
![21*\sqrt[3]{2}*\sqrt[3]{y^3} * \sqrt{2y}](https://tex.z-dn.net/?f=21%2A%5Csqrt%5B3%5D%7B2%7D%2A%5Csqrt%5B3%5D%7By%5E3%7D%20%2A%20%20%5Csqrt%7B2y%7D)
![\sqrt[3]{y^3} = y^{3*\frac{1}{3}} = y](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7By%5E3%7D%20%3D%20y%5E%7B3%2A%5Cfrac%7B1%7D%7B3%7D%7D%20%3D%20y)
So, we have:
![21*\sqrt[3]{2} * y * \sqrt{2y}](https://tex.z-dn.net/?f=21%2A%5Csqrt%5B3%5D%7B2%7D%20%2A%20y%20%2A%20%20%5Csqrt%7B2y%7D)
Rewrite as:
![21y *\sqrt[3]{2} * \sqrt{2y}](https://tex.z-dn.net/?f=21y%20%2A%5Csqrt%5B3%5D%7B2%7D%20%20%2A%20%20%5Csqrt%7B2y%7D)
Split 
![21y *\sqrt[3]{2} * \sqrt{2} * \sqrt{y}](https://tex.z-dn.net/?f=21y%20%2A%5Csqrt%5B3%5D%7B2%7D%20%20%2A%20%20%5Csqrt%7B2%7D%20%2A%20%5Csqrt%7By%7D)
Collect Like Terms
![21y*\sqrt{y} *\sqrt[3]{2} * \sqrt{2}](https://tex.z-dn.net/?f=21y%2A%5Csqrt%7By%7D%20%2A%5Csqrt%5B3%5D%7B2%7D%20%20%2A%20%20%5Csqrt%7B2%7D)
Represent in index form
Apply law of indices
Hence:
Let's convert the problem into Arithmetic progression:
It would be: 5, 9, 13, ....
Here, a = 5, d = 9 - 5 = 4
We know, S(n) = n/2 [ 2a + (n-1)d ]
Substitute the known values,
434 = n/2 [ 2(5) + (n - 1)4 ]
434 * 2 = n [ 10 + 4n - 4 ]
868 = 10n + 4n² - 4n
= 4n² + 6n - 868 = 0
d = b² - 4ac
d = 6² - 4(4)(-868)
d = 36+13888
d = 13924
Now, roots = -b +- √d / 2a
= (-6 + √13924) / 2(4) OR (-6 - √13924) / 2(4)
= (-6 + 118) / 8 OR (-6 - 118) / 8
= 112/8 OR -124/8
= 14 OR -15.5
As number of sticks can't be in negative/decimal or fraction form, -15.5 would be fully rejected.
In short, Your Answer would be 14 [ Remaining root ]
Hope this helps!
