Answer:
x = -1 and x = 5
Step-by-step explanation:
<em>What are the solutions of the equation (x – 3)² + 2(x – 3) -8 = 0? Use u substitution to solve.</em>
<em />
(x – 3)² + 2(x – 3) -8 = 0 -------------------------------------------------------(1)
To solve this problem, we will follow the steps below;
let u = x-3
we will replace x-3 by u in the given equation:
(x – 3)² + 2(x – 3) -8 = 0
u² + 2u -8 = 0 ----------------------------------------------------------- --------------(2)
We will now solve the above quadratic equation
find two numbers such that its product gives -8 and its sum gives 2
The two numbers are 4 and -2
That is; 4×-2 = -8 and 4+(-2) = 2
we will replace 2u by (4u -2u) in equation (2)
u² + 2u -8 = 0
u² + 4u - 2u -8 = 0
u(u+4) -2(u+4) = 0
(u+4)(u-2) = 0
Either u + 4 = 0
u = -4
or
u-2 = 0
u = 2
Either u = -4 or u = 2
But u = x-3
x = u +3
when u = -4
x = u + 3
x = -4 + 3
x=-1
when u = 2
x = u + 3
x = 2 + 3
x=5
Therefore, x = -1 and x =5
x
A solution with a pH of 11 has a [H+] of 
Option B is correct option.
Step-by-step explanation:
A solution with a pH of 11 has a [H+] of= ?
pH=?
Concentration of H+ [H+]= ?
Formula used: ![pH=-log[H+]](https://tex.z-dn.net/?f=pH%3D-log%5BH%2B%5D)
Putting values and finding [H+]
![pH=-log[H+]\\\,[H+]\,=10^{-pH}\\\,[H+]\,=10^{-11}\\\,[H+]\,=1.0\times 10^{-11}](https://tex.z-dn.net/?f=pH%3D-log%5BH%2B%5D%5C%5C%5C%2C%5BH%2B%5D%5C%2C%3D10%5E%7B-pH%7D%5C%5C%5C%2C%5BH%2B%5D%5C%2C%3D10%5E%7B-11%7D%5C%5C%5C%2C%5BH%2B%5D%5C%2C%3D1.0%5Ctimes%2010%5E%7B-11%7D)
So, A solution with a pH of 11 has a [H+] of
Option B is correct option.
Answer:
Step-by-step explanation:
-5x + 5
Answer:
139 ft
Step-by-step explanation:
So the zip line forms a right triangle. The height of the triangle is 150 ft, and the opposite angle is 40°. The horizontal distance covered by the zip liner can be found with trigonometry, specifically with tangent.
tan 40° = 150 / x
x = 150 / tan 40°
x ≈ 179 feet
But this includes the 40 ft long body of water, so the amount of ground covered is:
179 ft - 40 ft = 139 ft
