Philip Luukkonen

Simpson University
Teacher

Biography

Hi my name is Mr. Luukkonen! I have been teaching math for 19 years. I love helping students understand how to solve math problems and overcome the difficulties they encounter. I explain the problems in a way that is easy to understand and to achieve the quickest success!

Education

BA Mathematics
Simpson University

Educator Statistics

Numerade tutor for 5 years
21 Students Helped

Topics Covered

The Power of Algebraic Language: Unlocking Mathematical Potential
Mastering Equations and Inequalities: Your Guide to Mathematical Success
Understanding Complex Numbers: A Comprehensive Guide

Philip's Textbook Answer Videos

1

Philip's Quick Ask Videos

03:43
Geometry

Complete the proof. Use the figure shown below.

Quadrilateral DCBA has vertices D on the top left, C on the top right, B on the bottom right, and A on the bottom left. A diagonal line segment connects A to C, dividing DCBA into two triangles: â–³ABC and â–³CDA.

Given:
DC ∥ AB and AD ∥ BC

Prove: △ABC ≅ △CDA

Statements Reasons
1. DC ∥ AB 1. Transitive Property of Parallel Lines
2. ∠DCA ≅ ∠BAC 2. Transitive Property of Congruence
3. AD ∥ BC 3. Given
4. ∠DAC ≅ ∠BCA 4. Alternate Interior Angles Theorem
5. AC ≅ AC 5. Reflexive Property of Congruence
6. △ABC ≅ △CDA 6. ASA (Angle-Side-Angle) Congruence Theorem

Philip Luukkonen
02:54
Algebra

Let p represent a true statement and let q represent a false
statement. Find the truth value of the given compound
statement.
~[~p ∨ (~q ∧ p)]

Philip Luukkonen
02:22
Algebra

Find the rational zeros and then the other zeros of the polynomial function f(x) = 3x^3 + 7x^2 + 147x + 343, that is, solve f(x) = 0. Factor f(x) into linear factors. Select the correct choice below and fill in any answer box(es) within your choice. (Type an exact answer; using radicals and i as needed. Use integers or fractions for any numbers in the expression. Use commas to separate answers as needed.)

Philip Luukkonen
03:14
Algebra

A clothing business finds there is a linear relationship between the number of shirts, n, it can sell and the price, p, it can charge per shirt. In particular, historical data shows that 3000 shirts can be sold at a price of $8, while 4000 shirts can be sold at a price of $4. Give a linear equation in the form p = mn + b that gives the price p they can charge for n shirts.
Answer: p =
Round the value of your slope to three decimal places. Be careful to use the proper variable and use the Preview button to check your syntax before you submit your answer.
Check Answer

Philip Luukkonen
01:20
Algebra

3. Solve the following systems of equations using Gaussian elimination.
(a) 2x1 - 3x2 + 2x3 = 0
x1 - x2 + x3 = 7
-x1 + 5x2 + 4x3 = 4
(b) -x1 - x2 + x3 = 2
2x1 + 2x2 - 4x3 = -4
x1 - 2x2 + 3x3 = 5
(c) -x1 - 3x2 + 2x3 = -2
2x1 + x2 + 3x3 = 9/2
5x1 + 4x2 + 6x3 = 12
(d) 2x1 + 4x2 - 2x3 = 4
x1 - 2x2 - 4x3 = -1
-2x1 - x2 - 3x3 = -4
(e) x1 + x2 + 4x3 = 4
2x1 + x2 + 3x3 = 5
5x1 + 2x2 + 5x3 = 11
(f) 2x1 - 3x2 - x3 = 2
3x1 - 5x2 - 2x3 = -1
9x1 + 6x2 + 4x3 = 1

Philip Luukkonen
03:43
Geometry

Complete the argument, giving a reason for each step.

7. Given: HI = 8, IJ = 8, IJ ≅ JH
Prove: HI ≅ JH

Statements
1. HI = 8
2. IJ = 8
3. HI = IJ
4. HI ≅ IJ
5. IJ ≅ JH
6. HI ≅ JH

Reasons
1. ?
2. ?
3. ?
4. ?
5. ?
6. ?

8. Given: AL = SK
Prove: AS = LK

Statements
1. AL = SK
2. LS = LS
3. AL + LS = SK + LS
4. AL + LS = AS
5. SK + LS = LK
6. AS = LK

Reasons
1. ?
2. ?
3. ?
4. ?
5. ?
6. ?

9. Write an argument for Exercise 7 in the form of a paragraph proof.

Philip Luukkonen
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