1. Decide whether the pair of lines is parallel, perpendicular, or neither?
The lines are?
2x + 3y = 4
2x + 3y = 9
Slope of the first line is -2/3
Slope of the second line is -2/3
Since the slopes of the pair of lines is equal, they are parallel.
2. Solve. -10 ≤ 3x - 5 ≤ -4 What is the solution set is?
or
3. Evaluate. x + y divided by 9, for x = 60 and y = 12, x + y divided by 9 = ?
4. Find the indicated outputs for f(x)=3x squared - 3x, f(0) = ? f(-1) =? f(2) = ?
f(0) = 3(0)2 - 3(0) = 0
f(-1) = 3(-1)2 - 3(-1) = 6
f(2) = 3(2)2 - 3(2) = 6
5. Solve. 4 > 3x + 3 or 9 ≤ - 5x + 3 What's the solution to the einequality?
or So the combined solution is
6. Solve by the subsitiution method. 9x + 7y = -13 x = 9 - 6y What is the solution of the system?
9x + 7y = -13
x = 9 - 6y
Substitute x = 9 - 6y in the first equation,
9(9 - 6y) + 7y = -13
81 - 54y + 7y = -13
47y = 94
y = 2
Now plug y = 2 in the second equation to get x,
x = 9 - 6(2)
x = -3
So the solution is x = -3, and y = 2
Or in ordered pair notation, (-3, 2)
7. Solve. y - 9 > -12
y > -12 + 9
y > -3
Solution set can also be shown as (-3, +∞)
8. Translate to an algebraic expression. The product of 12% & some number. The translation is?
0.12y (the question was incomplete but I assumed the variable is "y")
9. Solve using the multiplication system. -5/8x = -9/10 The solution is?
x =
10. Simplify. 2[-50-(-74-16)] = ?
80
11. Find the slope & the y - intercept. f(x) = -5x - 9 The slope is ? The y - intercept is? (0, ?)
The slope is -5
The y-intercept is -9
12. Solve for the indicated letter. a = 2b, for b The solution set is b = ?
b =
13. Solve the following system of equations. x+ 9y = 5 x = 3 - 9y What is the solution set?
Substitute x = 3 - 9y in the first equation,
3 - 9y + 9y = 5
3 = 5
This can not be true, hence there is no solution to this system.
14. Solve. 0.9x + 6 ≤ 1.3x - 3 The solution set is?
9 ≤ 0.4x
x ≥ 22.5
15. Find the domain of the function. p(x) = x squared - 2x + 9 What is the domain of p?
Domain is all real numbers.
16. Multiple. 9/4 * [1/7]
Result is
17. Solve. 5/4x + 1/8x = 9/8 + x
x = 3
18. Solve using the multiplication system. -2x > 1/9 The solution set is?
x <
19. Solve. -0.3x < -24 The solution set is?
x > 80
20. Solve using the multiplication & addition principles. 2 + 5x < 37 The solution set is?
x < 7
21. Find the slope, if an exists, of the line containing the pair of points (6, 8) & (10, -5) The slope m = ?
m =
22. Solve using the elimination method. 3x + 4y = 5, 6x + 8y = 10
3x + 4y = 5
6x + 8y = 10
Multiply the first equation by -2,
-6x - 8y = -10
6x + 8y = 10
Add the two equations side by side,
0 = 0
There are infinitely many solutions.
23. Determine if (-5, -4) is a solution of 9x - 4y = -6
9(-5) - 4(-4) = -29 ≠ -6
it is not a solution.
24. Find the slope if it exists. x = -3 m = ?
Slope is undefined. There is no slope.
25. Use the distributive property to solve the equation. 8(w-6) = 16 w = ?
w = 8
26. Solve. 8x - (6x + 7) = 3 The solution is x = ?
x = 5
27. Use the multiplication system. 10x = -70 The solution is x = ?
x = -7
28. Collect like terms. 15a + 6b - 12a - 8b = ?
3a - 2b
29. Find the domain of the function. g(x) = 2/3-5x
{x | x ≠ }
30. Solve by the elimination method. 7r - 9s = -46, 9r + 7s = 108 What is the solution of the system?
7r - 9s = -46
9r + 7s = 108
Multiply the first equation by 7 and the second equation by 9,
49r - 63s = -322
81r + 63s = 972
Add the two equations side by side to eliminate s,
49r - 63s + 81r + 63s = -322 + 972
130r = 650
r = 5
Now plug r = 5 in the first equation to get s,
7(5) - 9s = -46
s = 9
So the solution is r = 5, and s = 9,
or in ordered pair notation (5, 9)
31. 25% of what number is 10?
40