Algebra Answers

Given that 𝑇 = ³√ 32𝑐⁴−𝑞/2 . Show that 𝑐 = 1/2 ⁴√2𝑇² + 𝑞   

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. 

Express the following in rectangular and polar form, if Z1 = 3+ 4i

Z2= 2+3i

1. Z1*Z2

2. Z1-Z2

3. Z1/Z2

4. |Z1|

5. |Z2|

(2)if Z1=50<30°and Z2=30<60°find in rectangular form the following

1. |Z1|

2. |Z2|

3. |Z1|-|Z2|

4. Z1*Z2

5. |Z2-Z1|

6. |Z2|/|Z1|

The shopkeeper brought a box containing x files for $20. he could have brought 5 more files if each file cost 20 cents less.(a) Form an equation in x and show that it reduces to x^2 + 5x - 500 = 0

Given that 𝑇 = 3√ 32𝑐⁴−𝑞 /2 . Show that 𝑐 = 1/2 4√2𝑇³ + 𝑞   

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.