Q21. Find the real solutions of the equation (2x - 1)2 - 10(2x - 1) + 24 = 0. a.

Question

Q21. Find the real solutions of the equation (2x - 1)2 - 10(2x - 1) + 24 = 0.
   a. {5/2, -3/2}
   b. {-5/1, 3/2}
   c. {-7/2, -5/2}
   d. {7/2, 5/2}

Q22. Solve the rational equation (4x-1)/(2x+3)=(6x+8)/(3x-4)
   a. {28/15}
   b. {-28/53}
   c. {-20/53}
   d. {4/3}

Q23. Find the center (h, k) and radius r of the circle with the equation x2 - 16x + 64 + (y + 9)2 = 36.
   a. (h, k) = (8, -9); r = 6
   b. (h, k) = (9, -8); r = 36
   c. (h, k) = (-9, 8); r = 6
   d. (h, k) = (-8, 9); r = 36

Q24. Find the midpoint of the line segment joining the points P1 and P2.
P1 = (-1, 6); P2 = (-5, 3)
   a. (-6, 9)
   b. (2, 3/2)
   c. (4, 3)
   d. (-3, 9/2)

Q25. Find an equation for the line in general form Containing the points (-5, -7) and (0, 4).
   a. 11x - 5y = -20
   b. -2x + 4y = -16
   c. -11x - 5y = -20
   d. 2x - 4y = -16

Explanation / Answer

21.

(2x - 1)^2 - 10(2x - 1) + 24 = 0

simplifying the above equation :

4x^2 - 24x + 35 = 0

(2x-7)(2x-5) = 0

=> x = 7/2 and x = 5/2

option D is correct

22. (4x-1)/(2x+3)=(6x+8)/(3x-4)

simplifying :

(4x-1)(3x-4)=(6x+8)(2x+3)

12x^2-16x-3x+4 = 12x^2+18x+16x+24

-19x + 4 = 34x + 24

-53x = 20

x = -20/53

option C is correct

23.x^2 - 16x + 64 + (y + 9)^2 = 36

x^2 - 2*8*x + 8^2 + (y+9)^2 = 36

we know that (a-b)^2 = a^2 + 2*a*b + b^2

=> (x-8)^2 + (y+9)^2 = 6^2

general equation of a circle is:

(x-h)^2 + (y-k)^2 = r^2

=> (h,k) = (8 , -9) and r = 6

option A is correct

24. P1 = (-1, 6); P2 = (-5, 3)

x coordinate of the mid point is = (x1+x2)/2 = [-1+(-5)]/2 = -3

y coordinate of the mid point is = (y1+y2)/2 = [6+3]/2 = 9/2

=> the mid point is : (-3 , 9/2)

option D is correct

25. (-5, -7) and (0, 4)

first find the slope , m = (y2-y1)/(x2-x1) = (4+7)/(0+5) = 11/5

using the point slope form and using any of the to given points

lets take (0,4) and the slope m = 11/5

point slope form is : y-y1 = m(x-x1)

=> y - 4 = 11/5(x)

or 5y - 20 = 11x

11x - 5y = - 20

option A is correct

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