(x²-x)²-14(x²-x)+24=0
seven years ago John was eleven time as old as his doughter . now he is four time as old as she . How old is he now ???

 

 

1. Express the decimal number 5:78 as a fraction.
2. Use scientic notation to calculate
(0:00000112)(0:00023)
(23400000000)(0:00000000000067)
3. Factor the expression completely. (a) ��1 + 1
x
2
�� ��1 �� 1
x
2
(b) x��
1
2 (x + 1)
1
2 + x
1
2 (x + 1)
��1
2
4. Simplify the expression
1
x2 + 3x + 2 ��
1
x2 �� 2x �� 3
5. Find all real solution for the equation:
(a)
x + 5
x �� 2
=
5
x + 2
+
28
x2 �� 4
(b) 2x + px + 1 = 8
(c) (x2 �� x)2 �� 14(x2 �� x) + 24 = 0 (d) x �� 2px �� 1 = 0
6. Solve the inequality, and write your answer in interval format:
(a) x2(x + 2) > 2x(x + 2) (b) 1 +
2
x + 1 
2
x
(c) j2x �� 1j  jx + 2j (d) ��x + 2  2x �� 1 < x + 4
7. The sh population in a certain lake rises and falls according the formula F(t) = 1000(30��13t��t2). Here
F is the number of sh at the time t, where t measured in years, starting 1992. By what year will all the
sh population have died?
8. Seven years ago John was eleven time as old as his daughter. Now John is four time as old as she is. How
old is John now?
9. Stan and Hilda can mow the lawn in 40 min if they work together. If Hilda works twice as fast as Stan,
how long would it take Stan to mow the lawn alone?
10. Sketch the region:
(a) D = f(x; y)j1 < x < 4 and y  2g (b) K = f(x; y)j y > jx �� 2j and (x �� 2)2 + y2  22g
11. Test the graph of the equation x2y2 + xy = 1 for symmetry.
12. Find the center and the radius of the circle x2 + y2 �� 2x + 6y = 6.
13. Find the equation of the perpendicular bisector of the line segment joining the points A(3; 4), and B(7; 2).
14. Let A be the set of all Human beings. Dene f : A ��! A and g : A ��! A, by f(x) = the father of x,
and g(x) = the sister of x. Determine if f or g is a function.
15. Find the domain of the function f(x) = r x + 3
4 �� x2
16. Sketch the graph of the function f(x) =  x + 1; if x > 1
x2 �� 1; if x  1
17. Use the graph of the function f(x) = px to sketch the graph of the function g(x) = 2(p3 �� x)+1. Show
all the steps.
18. If f(x) = px and g(x) =
1
x2 . Find (g  f)(x) and its domain.
19. Determine if the function g : R ��! R, dened by g(x) = 3x + 5 is one to one.
20. Find f��1, its domain and its range: (a) f(x) = px �� 3 (b) f(x) =
3x + 2
x �� 1

أسفه بس الجذر ما نزل معي و المربع معناه الجذر انا حليت اغلب الأسئلة ولكن البعض لا اللي يقدر يعطيني الاجابة بس بالتفاصيل عشان افهمهن زين


مشكوووورررريييييين

 

 

بسم الله الرحمن الرحيم
اخي العزيز لحل المعادلة : x²-x)²-14(x²-x)+24=0)
ضع y=x²-x
y^2-14y+24=0
y=12 , y=2
x²-x=y=2 ---> (x-2)(x+1)=0 ----> x=2 or x=-1
if y= 12 then x²-x=12 ----> x =4 or x=-3

 

 

مشكور الله يعطيك العافية ...سلمت

 

 

وبعد هذه السؤال اذا ممكن
|x+2|≥|2x-1|

 

 

انا عندي أقتراح للحل بس نا أدري إذا يعتبر صحيح وهو
نربع الطرفين وبكذا راح نشيل المطلق . ونحلها بطريقة العادية

 

 

اقتراحك صحيح لان : ب^2 = مقياس ( ب ) ^2