Algebra Answers

If log_𝑎 𝑞 = 1/5 solve the equation , 𝑥 log_𝑎 𝑞 + (𝑥 + 2) log_𝑎 𝑞² = 3 

Given f(x) = ax³ + 2x² + bx − 20 where x − 2 and x − 5 are two of its factors determine the real values of a and b

Describe the two math concepts below that you will use to solve the problem. Converting fractions to decimals. Rounding to the nearest hundreths

graph of the following function .

f(x)=-2^x-2

(1) The table below shows the calories, fat, and carbohydrates per ounce for three brands of cereal, and the total amount of calories, fat, and carbohydrates required for a special diet. Calories Fat Carbohydrates Cereal Brand X 50 0 22 Cereal Brand Y 108 0.1 25.5 Cereal Brand Z 127 5.5 18 Total Required 393 5.7 91 (i) Using the information in the table above, write a system of three equations. (ii) Write a system in matrix form Ax b  . (ii) Using the Cramer's Rule or Inverse Method, find the amount of each brand of cereal that will give the level of nutrition required. 

(2) Determine k such that kx^2 - 4x + 1/2=0 has real and different solutions. (3) (i) What rate of interest compounded annually is needed to make an investment of $6,500 accumulate to an amount of $7166.25 at the end of two years? (ii) How long will it take for the initial amount to double, compounded annually at the rate in (i) above?

(3) Showing all your working, find the solution set which describes the area shown in green below. Problem Set: D (1) State the appropriate formulae used in solving parts (i) and (ii) of this question then demonstrate the use of the formulae in finding your answers. (i) Determine how many rows are in the corner section of a stadium containing 3920 seats if the first row has 10 seats and each successive row has 6 additional seats? (ii) A new machine was purchased for $45,000. For tax purposes, the company depreciates the value by 5% annually. Determine the value of the machine after 7 years of use? 

Consider the following procedure: Pick a number. Add 6 to the number. Multiply the sum by 2. Subtract 12 from the product. Divide the difference by 2. Suppose we pick -8, then what is the resulting number? 

Show that,

1. lim _z->infinity (𝑎𝑧+𝑏) ³/(𝑧+𝑑)³ 
2. lim _z->1 (1−z bar)/(1−z) does not exist

Cheney is ordering pizza for her birthday party breadsticks cost $4.99 and large pizzas cost at $10.99 write an expression to represent the total cost for her party using beef or breadsticks and P for pizzas