Answer:
c
Step-by-step explanation:
Here's how this works:
Get everything together into one fraction by finding the LCD and doing the math. The LCD is sin(x) cos(x). Multiplying that in to each term looks like this:
![[sin(x)cos(x)]\frac{sin(x)}{cos(x)}+[sin(x)cos(x)]\frac{cos(x)}{sin(x)} =?](https://tex.z-dn.net/?f=%5Bsin%28x%29cos%28x%29%5D%5Cfrac%7Bsin%28x%29%7D%7Bcos%28x%29%7D%2B%5Bsin%28x%29cos%28x%29%5D%5Cfrac%7Bcos%28x%29%7D%7Bsin%28x%29%7D%20%3D%3F)
In the first term, the cos(x)'s cancel out, and in the second term the sin(x)'s cancel out, leaving:

Put everything over the common denominator now:

Since
, we will make that substitution:

We could separate that fraction into 2:
×
and 
Therefore, the simplification is
sec(x)csc(x)
Answer:
Part A:
( 1.8333, -0.08333)
Part B:
x = 2 or x = 5/3
Step-by-step explanation:
The quadratic equation
has been given.
Part A:
We are required to determine the vertex. The vertex is simply the turning point of the quadratic function. We shall differentiate the given quadratic function and set the result to 0 in order to obtain the co-ordinates of its vertex.

Setting the derivative to 0;
6x - 11 = 0
6x = 11
x = 11/6
The corresponding y value is determined by substituting x = 11/6 into the original equation;
y = 3(11/6)^2 - 11(11/6) + 10
y = -0.08333
The vertex is thus located at the point;
( 1.8333, -0.08333)
Find the attached
Part B:
We can use the quadratic formula to solve for x as follows;
The quadratic formula is given as,

From the quadratic equation given;
a = 3, b = -11, c = 10
We substitute these values into the above formula and simplify to determine the value of x;

Answer:
20 years
Step-by-step explanation:
9000/ 100= 900 = 10%
900/2= 450
450 x 2= 900
900 x 10= 9000
Now we multiply 10 by 2 because we doubled the value of our 450 into a 900 and now we get 20.
Answer:
Step-by-step explanation:
(3x -2) - (4x +1)
= 3x - 2 - 4x - 1
= - x - 3