# Solving Equations

**D.**

1. Write 4x • 5y • 3x • x in exponential form .

2. Translate the following into an equation :

Three times the difference of a number x and 7 is 6

3. Find the sum of the matrices :

4. Find the difference of the matrices:

5. Graph the inequality :

6. Write the inequality for the half -planed graph:

7. Simplify : (-3x^{2}y^{3})(5xy^{3})

8. Simplify:

9. Simplify: (-2x^{3}y^{2})(3xy^{3})^{2}

Use the quadratic formula to solve each equation:

10. x^{2} + 4x = 5

11. 3x^{2} – 4x - 2 = 0

12. 6x^{2} + x – 2 = 0

13. x^{2} + 6x + 4 = 0

**E.
**Name the opposite and reciprocal of each:

1. 3

2. -7

3. 4/5

4. -6/7

Evaluate for x = 2 and x = -2

5. 2x^{2} – x

6. -3x^{2}

7. - x^{2}

8. ½x -2

9. (-x) ^{2}

Evaluate for x = 7 and y = -3

10. (x + y)^{2}

11. x^{2} + y^{2}

12. (x - y)^{2}

13. x^{2} - y^{2}

Write algebraic expressions for each .

14. The difference between a and m ____________________

15. Seven less than a number, y ____________________

16. Eight more than five times a number c ____________________

17. Twice the sum of a number, x, and nine ____________________

Graph the following equations.

18. y = 2x – 1

19. y = -2

20. x = 3

21. 2x – 4y = 8

22. y = -2/3x + 2

**F.
**Write the equation of each line.

1. Slope = 3, passing through (1, 2)

2. m = -1, passing through (1, 2)

3. m = 4, passing through (-2, 3)

Perform the indicated operations and simplify .

**G.
**Solve each of the systems of linear equations.

1. –4x + 2y = 2

4x + 3y = -12

2. x – 2y = 16

x + y = 10

3. 3x + 2y = 11

x = 3y

4. 3x – 5y = 63

2x + 3y = -15

Rewrite in the following in decimal form .

Rewrite the following in scientific notation form.

8. 2450

9. 0.000372

10. 1.78

11. 47.2

Simplify.

**H.
**Simplify and leave in radical form.

Identify whether the parabola opens up or down and find the vertex.

**Graph.**

Determine whether the information defines a function.

11. {(3, 4), (5, 4), (7, 3), (2, 8)}

12.

Identify the domain and range of the function.

13. {(2, 4), (5, 4), (7, 3), (9, 8)} Domain: _____________ Range: _____________

Evaluate the function.

14.

**I.
**Use the Pythagorean Theorem to find the missing length of a right triangle.

Use the distance formula to find the distance between the two points.

6. (6, 9) and (14, 24)

7. (-5, 8) and (2, -16)

8. (-3, -5) and (-11, 5)

9. (5, 6) and (7, -10)

Find one of the many proofs of the Pythagorean Theorem. Write the solution , draw the solution and explain it in your own words.

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