Algebra Answers

Which is the complete fractorization of 5y3-125y?

What are the (x:y) coordinates of the point of intersection of the lines determined by the equation 2x-3y=4 and y = x?

An element with mass 590 grams decays by 19.5% per minute. How much of the element is remaining after 15 minutes, to the nearest 10th of a gram?

Given the functions 𝑔(𝑥) = 𝑥 − 5 and 𝑓(𝑥) = 𝑒

𝑥

Determine (𝑓 ∘ 𝑔)(5)

for h(x) = 2/3 x -5 find the value of x for which h(x) = -7

Directions: find (f-g) (x) using the two functions given in each number.

1. F(x) = 3x+3

g(x) = -4x+1

2. F(x) = 2x+5

g(x) = 4x² +2x-2

3.f(x)=5x+1

g(x) =3x-2

4.f(x) -15 x² -2x+5

g(x) = 3x2+x-7

5.f(x) = 3x² - 2x+1

g(x) = 4x² +5x-4

BAT Industries is a manufacturer of orange juice in Jamaica. In 2022 it sold a bottle of orange juice to wholesalers for $100 and its variable costs is $40 and fixed costs is $100,000 monthly:

Using the information provided. 

i. How many bottles of orange juice must the company sell in order to break even and what is the breakeven revenue? 

ii. If the company sold 1,500,000 bottles of orange juice for the year 2022, what was its profit? 

iii. Due to inflation, in 2023 fixed costs are expected to rise to $175,000 monthly. What will be the NEW break-even quantity and revenue? 

iiii. If the company will sell the same number of orange juice as it did in 2022 and it wants to make the same profit as in 20222, what price should they sell each bottle of orange Juice for in 2023? 

 Can some working out be shown please?

3400 dollars is placed in an account with an annual interest rate of 8.25%. How much will be in the account after 25 years, to the nearest cent?

prove that sin (degree(m)) is an algebraic number of any integer m.

prove that sin (degree(1)) is an algebraic number