Algebra Answers

Lines can be used to approximate a wide variety of functions; often a function can be described using many lines.

If a stock price goes from $10 to $12 from January 1st to January 31, from $12 to $9 from February 1st to February 28th, and from $9 to $15 from March 1st to March 31th is the price change from $10 to $15 a straight line?

It is clear that in each of the three time intervals mentioned there was a complex daily variation of prices as in an electrocardiogram. But what would be a simplified solution for a first naive view of the situation? Would a simple function hold up? What is the simplest function to represent this situation? Does your naïve initial and simplified model allow you to predict the behavior of the stock in the next month?

How can I use three “pieces” of lines to describe the price movements from the beginning of January to the end of March? Show the graph for the price movement.

y = x + 2 {0 < x < 2}

y = –x + 6 {2 < x < 5}

y = 2x – 9 {5 < x < 8}

Reflect on the concept of lines and quadratic functions. What concepts (only the names) did you need to accommodate the concept of lines and quadratic functions in your mind? What are the simplest line and quadratic function you can imagine? In your day to day, is there any occurring fact that can be interpreted as lines and quadratic functions? What strategy are you using to get the graph of lines and quadratic functions?

3. The tank has 700 liters oil and is being drainad ar a constart rate of 25 liters per minute.

a) How do you write a linear function V for the number of liten in the tank after t minutes

Tassuming that the drainage started art-012

bi Compute how many litera are in the tank after 75 minutes and 55 seconds.

The formula for calculating the sum of all natural integers from 1 to n is well-known: Sn = 1 + 2 + 3 + ... + n = n 2 + n 2 Similary, we know about the formula for calculating the sum of the first n squares: Qn = 1 · 1 + 2 · 2 + 3 · 3 + ... + n · n = n 3 3 + n 2 2 + n 6 Now, we reduce one of the two multipliers of each product by one to get the following sum: Mn = 0 · 1 + 1 · 2 + 2 · 3 + 3 · 4 + ... + (n − 1) · n Find an explicit formula for calculating the sum Mn. 

Find the smallest positive integer N that satisfies all of the following conditions: • N is a square. • N is a cube. • N is an odd number. • N is divisible by twelve prime numbers. How many digits does this number N have?

From the function, f(x) = (3x ^ 2 - 8x - 3) / (2x ^ 2 + 7x - 4) ,

a. Construct table of values

b. Find the following:

vertical and horizontal asymptotes

x - ir intercepts or zeroes upstingit)

y- intercept,

Renting a BIXI bike in montreal costs various prices depending on the time frame. Delaney is interested in renting a bike for the 3-day osheaga festival in July. The rate is $5 for a 24-hour period and $1.75 for every 30 additional minutes following that. Write a linear equation to model the cost, C of the rental per hour, H

1.In an enter - baranggay basketball league,the team from baranggay Carolina has won 15 out of 25 games,a winning percentage of 60%. We have seen that they need to win 25 more games consecutively to raise their percentage for at least 80%.

a.what function will represent the winning percentage of baranggay Carolina if x is the number of remaining games?

b.what will be the winning persentage after 15?20?25?30?35 games?

c.plot the ordered pairs you got in questions (a)and(b) in a Cartesian plane and connect it using a smooth curve

The magnitude of an earthquake is given by 𝑀 = log 𝐼

where M is the Richter scale value of an earthquake, and I is the intensity of the earthquake. An earthquake of magnitude 6.4 is measured and the following aftershock has a magnitude or 4.1.

Determine algebraically how many times more intense, to the nearest whole, the earthquake is compared to the aftershock.

You live 25 kilometers from your friend's home. Your parents need to drive you, so how long does it take to get them ready? Use algebra in solving such problem?