Algebra Answers

3.1. Simplify the following algebraic expressions  -5xy^2 (6xy^2 - 5xy^2 + 6x)?

1.Divide the polynomials using the division method of your choice (long or synthetic)

3x³ - 4x² - + 2x -1 / x - 3

2.Perform the indicated operation for the following:

a. (3x² - 8x + 4) - (6x² + 7x -1)

b. (4x⁷ - 3x⁵ - + 2x + 4) + (12x⁵ - 3x + 2x² + 3)

c. (3x + 4)(5x² - 2x + 3)

d. (3 + 4i) + (1-2i)

e. (2-i) (5-6i)

f. (3-7i) ( 1-2i)

3.Solve x² + 81= 0

4.Solve ³ square root of 7x = 3

1.Factor using difference of cubes (a-b)(a²+ab+b²)

8x³-27

2.Factor by grouping 2x³+7x²+2x+7

3.List the possible roots using the Rational Root Theorem x= +- p/q where q is the leading coefficient and p is the constant

f(x) = 3x⁵ - 2x² - 7x + 4

1.Use log properties to condense:

a. log₈x + log8p

b. log_x1= 0

2.Rewrite into log form:

a. 5^x = 25

b. 1³/4 = 1/64

3.Solve 6^3x+5= 6^x-2

This time, our immune system is the best defense. With this, a Melagail wishes to mix two types of foods in such a way that vitamin contents of the mixture contain at least 8 units of vitamin A and 10 units of vitamin C. Food A contains 2 units/kg of vitamin A and 1 unit/kg of vitamin C. Food B contains 1 unit/kg of vitamin A and 2 units/kg of vitamin C. It costs ₱50 per kg to purchase Food A and ₱70 per kg to purchase Food B. Formulate this problem as a linear programming problem to minimize the cost of such a mixture.

A. Define the decision variables

B. Write the LP Model

C. Determine the feasible region

D. Determine the optimal solution

E. Final Answer: (interpret the result)

12/7y² * y^{5 *} 14y - (4/5)y² * 5y²

16. For each of the following, write the probability in symbolic form and give the answer. 

a) The probability that a female student is in the band but does not have a drivers’ license. 

b) The probability that a female student has a drivers’ license but is not in the band. 

c) The probability that a female student is not in the band and does not have a drivers’ license. 

d) The probability that a female student is in the band or has a drivers’ license. 

​​There are 680 female students on the roster at Neil Armstrong High School. Out of these 680 female students, 68 are in the band and 187 have a drivers’ license. 51 female students have a drivers’ license and are in the band. 

11. How can you tell that this information can be represented with a Venn diagram? 

​​​   

12. What is the probability of a female student being in the band? 

13. What is the probability of a female student having her drivers’ license?  

14. What is the probability of a female student having her drivers’ license and being in the band?