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Algebra

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

Algebra

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

3x^{3} - 4x^{2 }- + 2x -1 / x - 3

**2.Perform the indicated operation for the following:**

a. (3x^{2} - 8x + 4) - (6x^{2} + 7x -1)

b. (4x^{7} - 3x^{5} - + 2x + 4) + (12x^{5} - 3x + 2x^{2} + 3)

c. (3x + 4)(5x^{2} - 2x + 3)

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

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

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

**3.**Solve x^{2} + 81= 0

4.Solve ^{3} square root of 7x = 3

Algebra

**1.**Factor using difference of cubes **(a-b)(a**^{2}**+ab+b**^{2}**)**

*8x*^{3}*-27*

**2.**Factor by grouping *2x*^{3}*+7x*^{2}*+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) = 3x*^{5}* - 2x*^{2}* - 7x + 4*

Algebra

**1.Use log properties to condense:**

a. log_{8}x + log8p

b. log_{x}1= 0

**2.Rewrite into log form:**

a. 5^{x} = 25

b. 1^{3}/4 = 1/64

**3.Solve 6**^{3x+5}**= 6**^{x-2}

Algebra

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)

Algebra

12/7y^{2 }*** y**^{5 * }**14y - (**4/5)y^{2 }^{ }*** 5y**^{2}

Algebra

if one large pool hold 320,000 mL of water and a smaller pool holds 22 decaliters of water how many more liters of water can the larger pool hold than the smaller

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?

Algebra

Prove that any even power of a Nonzero integer is positive. That is, if X does not equal to zero in integers, then X^{2n} is positive for every positive integer n.