After the fraction x plus 2 all over 2 minus the fraction x plus 1 all over 3 x have been combined using the least common denominator of 6x, what is the numerator? a. 3x2 + 4x + 1 b. 3x2 + 4x − 2 c. −3x2 − x + 4 d. −x2 + 3x + 4

(B) 3x² + 4x - 2 will be numerator of the required fraction.

Explanation: According to the question,

Given expression: (x+2)/2 - (x+1)/3x   (1)            

Since, the least common factor of 2 and 3x= 6x

So, from equation (1),  3x(x+2)/6x - 2(x+1)/6x

=(3x² + 6x - 2x - 2)/6x

= (3x² + 4x  - 2)/6x, here, 3x² + 4x  - 2 is numerator and 6x is denominator.

Thus, required answer is 3x² + 4x  - 2.

when rotating a figure 180 degrees, imagine that you are able to take the figure and turn it clockwise or counterclockwise around a center point. to rotate a figure 180 degrees, you will need to apply the rule (x, y) → (-x, -y). start by using a coordinate grid with coordinates for each vertex of the figure. the center point of the coordinate grid is located at (0, 0), which is what you will rotate the figure around. write down the original coordinates of the shape you are going to rotate. then, apply the rule. for example, coordinate (1, 2) becomes (-1, -2). another example would be, coordinate (-4, -2) becoming (4, 2). after you change each original coordinate to the rotated coordinate, you will draw your new figure.

step-by-step explanation:

yx = 36

step-by-step explanation:

cos f = opposite side/ hypotenuse

cos f = yw / yx

we know cos f = 4/9 and yw =16

4/9 = 16/yx

multiply each side by yx

4/9 yx = 16/ yx * yx

4/9 yx = 16

multiply each side by 9/4

9/4 * 4/9 yx = 16 *9/4

yx = 36