<span>For a system of equations to have infinitely many solutions, the equations have to be lineary dependent, (i.e. one of the equations is a multiple of the other equation). For the given equation to have infinitely many solutions, the second equation have to be a multiple of the first equation.
The first equation can be rewritten as y - 2x = -5
The second equation is the first equation multiplied by 2, i.e. 2(y - 2x= -5) = 2y - 4x = -10
Therefore, the correct answer is -10 (option a).</span>
Part A
Represents 'Reflection'. This is so because the y-coordinates of P, Q and R remain the same in P' , Q' and R', and only the x-coordinate changes. Hence, it is reflection along the y-axis
Part B
Represents 'Rotation'. Here, the x-coordinates and y-coordinates of each of the points have changed, and the figure has been rotated clockwise around the point Q by 90°
Part C
Represents a combination of 'Translation' and 'Reflection'. Here either of the two has happened:
- First, all the points have been moved downwards by a fixed distance, thus changing the y-coordinate. Then, the resulting image has been reflected along the y-axis, thus changing the x-coordinate of all the points
- First, all the points have been moved to the right by a fixed distance, thus changing the x-coordinate. Then, the resulting image has been reflected along the x-axis, thus changing the y-coordinate of all the points
Part D
Represents 2 'Translations'. Here the image has been shifted by a fixed distance in both the downward direction and the right direction. Thus, it has resulted in change of both x and y coordinates.
Answer:
4.5 sq. units.
Step-by-step explanation:
The given curve is 
⇒ 
...... (1)
This curve passes through (0,0) point.
Now, the straight line is y = 3x - 6 ....... (2)
Now, solving (1) and (2) we get,
⇒ (y - 3)(y + 2) = 0
⇒ y = 3 or y = -2
We will consider y = 3.
Now, y = 3x - 6 has zero at x = 2.
Therefor, the required are = 
= ![\sqrt{3} [{\frac{x^{\frac{3}{2} } }{\frac{3}{2} } }]^{3} _{0} - [\frac{3x^{2} }{2} - 6x ]^{3} _{2}](https://tex.z-dn.net/?f=%5Csqrt%7B3%7D%20%5B%7B%5Cfrac%7Bx%5E%7B%5Cfrac%7B3%7D%7B2%7D%20%7D%20%7D%7B%5Cfrac%7B3%7D%7B2%7D%20%7D%20%7D%5D%5E%7B3%7D%20_%7B0%7D%20-%20%5B%5Cfrac%7B3x%5E%7B2%7D%20%7D%7B2%7D%20-%206x%20%5D%5E%7B3%7D%20_%7B2%7D)
= ![[\frac{\sqrt{3}\times 2 \times 3^{\frac{3}{2} } }{3}] - [13.5 - 18 - 6 + 12]](https://tex.z-dn.net/?f=%5B%5Cfrac%7B%5Csqrt%7B3%7D%5Ctimes%202%20%5Ctimes%203%5E%7B%5Cfrac%7B3%7D%7B2%7D%20%7D%20%20%7D%7B3%7D%5D%20-%20%5B13.5%20-%2018%20-%206%20%2B%2012%5D)
= 6 - 1.5
= 4.5 sq. units. (Answer)
Inscribed is a polygon inside a circle with all points on a given point in the circle. Circumscribed is a circle inside a polygon with any given point touching just one point on the polygon. Hope this helped.
