Liquideet ?
These questions & answers don't format as easily here on Google
Answers, so I?ve loaded a Word document file here for you which can
handle the Microsoft Equation editor:
http://www.mooneyevents.com/algebra2005.doc
And the answers are posted below:
1. Perform the indicated operations and simplify:
(2x2 - 3x + 12) - (2x2 +2x -6) =
2x2 - 3x + 12 - 2x2 - 2x + 6 = 18 ? 5x
2. Multiply:
a^3*b^3(a^2*b^3c) =
Multiplication of exponentials results in addition of exponents:
a^5b^6c
3. Divide:
x^9/x^16
Division of exponential terms is done via subtraction (numerator ? denominator):
x^-7= 1/x^7
4. Multiply
(3x + 7)(x2 - 2x +3) =
3x3 ? 6x2 + 9x + 7x2 -14x +21 = 3x3 + x2 - 5x + 21
5. Word Problem:
The sum of 15 and twice a number is 41. What is the number?
15 + 2x = 41; 2x = 26; x = 13
6. Square:
(b - 12)^2 = (b-12) * (b-12) = b^2 -12b -12b +144 = b^2 - 24b +144
7. Divide:
(14x^4y^9)/(7x^3y^5) = 2xy^4
8. Plug In
P = 3100
r = .05
t = 5
A = P(1 + rt) = 3100(1 + 0.25) = 3,875
9. Solve for x:
3(x + 2) = 4x; 3x +6 = 4x;
6 = x
10. Solve for y:
3(by +c) = 9; by + c = 3; by = 3 ? c;
y = (3-c)/b
11. Function Problem:
Given that f(x) = 3x + 7, find f(7).
f(7) = 21 + 7 = 28
12. Slope Problem:
Given coordinates (x1 = 2, y1 = 4) and (x2 = 4, y2 = -1), find the
slope of the line.
Slope = (y2 ? y1)/(x2 ? x1) = (-5)/2 = - 2.5
13. Factor:
x2 - x - 90 = (x ? 10)(x+9)
14. Reduce to lowest terms:
(x-2)(x+2)/(x+5)(x-2) = (x+2)/(x+5)
15. Solve for x and y using the addition method:
2x + 3y = -6
x - 3y = 6
3x = 0; x = 0
16. Solve for x and y using the substitution method:
-2x + y = 3
- x + y = 2
y = 2 + x ; -2x + 2 + x = 2 ; -x = 0 ;
x = 0
17. Simplify:
(10^-9)^1/3 =
10^-9*1/3 = 10^-3 This can also be written as 1/10^3
18. Solve for x:
(7x + 1)^1/2 = 6; 7x + 1 = 6^2
7x = 35; x = 5
19. Solve for x:
x2 + 4x - 21 = 0
(x + 7)(x ? 3) = 0
x = 3, -7
20. Solve using the quadratic formula:
x2 + 12x - 45 = 0
In an equation with the form ax^2 + bx + c = 0, we add (b/2a)^2 to
each side: the ultimate solution being:
X = [-b +- (b2 ? 4ac)^1/2]/2a ; x = [-12 +- (144 ? 4*(-45))^1/2]/2 =
[-12 +- (324)^1/2]/2 = [-12 +- 18]/2;
x = 6/2 = 3;
x = -30/2 = -15
21. Solve for x:
x/90 = 2/30
x = (90 * 2)/30 = 6
22. Solve for x:
x^2 = 144
x^2 ? 144 = 0; (x ? 12) (x + 12) = 0
x = -12, 12
23. Change to logarithm form:
10^2 = 100
Google has a calculation function that aids this simply by entering
log 100 in the Google search window:
log 100 = 2
2 = log (base 10) 100, which is commonly written 2 = log10 100
24. Solve for x: e^x = 12
e = 12 1/x ; if we use e as the natural log, 2.7183 we can solve for x;
2.7183 = natural ln 12 = 2.4849
Again, you can use the Google to figure the natural ln of 12 by typing
?ln 12? into the search window.
25. Solve for x:
10^x = 10,000
10^1 = 10
10^2 = 100
10^3 = 1,000
10^4 = 10,000
10^100 = Googol
Obviously x = 4
Alternately you can take log (base10) of 10,000 = 4
If there are any questions or confusion over format, please let me know.
Google search strategy:
Natural logarithm e
Quadratic equation
Best regards,
Omnivorous-GA |