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Functions and equations

I need help answering these practice questions. I have attached the questions that I need help with. Please explain your answers in detail.

1. Which of the ordered pairs (3, 1), (0, -4), (-4, 0), (-3, -7)are solutions for the equation x - y = 4?
2. Given f(x) = 5x - 1, find f(a + 3).
3. Solve by completing the square. x2 = 5x + 2
4. Find the slope of the line passing through the points (-10, 4) and (-4, -1).
5. Graph the inequality.
6. Find the axis of symmetry.
7. Solve. x2 + 9 = 34
8. A roof rises 2.75 ft over a horizontal distance of 20.91 ft. What is the slope of the roof to the nearest hundredth?
9. Write the equation of the line with slope 5 and y-intercept (0, -3).
10. Match the graph with one of the equations.
11. Simplify.
12. Find the y-intercept.
13. Solve the system by addition or substitution.
14. Determine whether is rational or irrational.
15. Find the x-intercepts.
16. Determine which two equations represent parallel lines.
17. Solve. 5(x - 2)2 = 3
18. Write the equation of the line that passes through point (-6, -2) with a slope of 0.
19. Lane invested $28,000, part at 18% and part at 9%. If the total interest at the end of the year is $3,240, how much did she invest at 18%?
20. Solve the following system of linear inequalities by graphing.
21. Find the length x. Express your answer in simplified radical form.
22. Simplify.
23. Is the following trinomial a perfect square? x2 - 6x - 9

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1. Which of the ordered pairs

(3, 1), (0, -4), (-4, 0), (-3, -7)

are solutions for the equation x - y = 4?
Substituting each of the ordered pair to the equation to check:
(3, 1): it means x = 3 and y = 1, so x - y = 3 - 1 = 2 ≠ 4, not a solution
(0, -4): x - y = 0 - (-4) = 4, solution
(-4, 0): x - y = -4 - 0 = - 4 ≠ 4, not solution
(-3, -7): x - y = - 3 - (-7) = 4, solution
A) (0, -4), (-4, 0), and (-3, -7)
B) (-4, 0) and (-3, -7)
C) (0, -4) and (-3, -7)
D) (3, 1) and (-4, 0)

2. Given f(x) = 5x - 1, find f(a + 3).
Treat a + 3 as one variable and replace x with a + 3 in the function:
f(a + 3) = 5(a + 3) - 1 = 5a + 15 - 1 = 5a + 14
A) 5a + 14
B) 5a + 2
C) a + 7
D) a + 14

3. Solve by completing the square.
x2 = 5x + 2

Then take the square root on both sides

A)

B)

C)

D)

4.
Find the slope of the line passing through the points A(-10, 4) and B(-4, -1).
The slope is defined as the rate of change in y in terms of x:
So

A)

B)

C)

D)

5. Graph the inequality.
y  -2
The line y = -2 is the horizontal line passing through (0, -2). y  -2 should be the half-plane below the line y = - 2. The boundary line y = -2 should be solid since y = - 2 is part of the inequality.
A)

B)

C)

D)

6. Find the axis of symmetry.
y = x2 - x + 5
By completing the squares:
Thus, the axis of symmetry is ...

Solution Summary

This provides several examples of working with functions, equations, and graphing, including slope, inequalities, symmetry, and determining solutions.

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