Given that (2, –8) and (–3, 2) are points on a line. Do the following:

a) Write the equation of the line in point–slope form and simplify any fractions completely

b) Write the equation of the line in slope–intercept form

c) Plot the point (–3, 2) and graph the line by using the slope to find two other points

d) On your graph, label the change in the y–value (rise) and the change in the x–value (run)

# Category: Algebra

## The number of hours required to build a fence is inversely proportional to the number of people working on the fence. If it takes 3 people, 48 hours to complete the fence, then how long will it take 14 people to build the fence? (round answer to 2 decimal places if needed)

## three siblings are comparing their ages. Jenna is the youngest. Her brother arl is 6 years older than her. Her sister eve is twice her age. The sum of their ages is 42. Let j represent hennas age. What expressions for both carls age and eves age in terms of j.

## The exponential function N = 500 × 0.74t, where t is measured in years, shows the amount, in grams, of a certain radioactive substance present. (a) Calculate N(3). (Round your answer to one decimal place.) N(3) = Explain what your answer means. After years there are grams of the radioactive substance present. (b) What is the yearly percentage decay rate? (Round your answer to one decimal place.) % (c) What is the monthly decay factor rounded to three decimal places? What is the monthly percentage decay rate? (Round your answer to one decimal place.) % (d) What is the percentage decay rate per second? (Note: For this calculation, you will need to use all the decimal places that your calculator can show. Round your answer to eight decimal places.)

The exponential function *N* = 500 × 0.74^{t}, where *t* is measured in years, shows the amount, in grams, of a certain radioactive substance present.

*N*(3). (Round your answer to one decimal place.)

*N*(3) =

Explain what your answer means.

(b) What is the yearly percentage decay rate? (Round your answer to one decimal place.)

%

(c) What is the monthly decay factor rounded to three decimal places?

What is the monthly percentage decay rate? (Round your answer to one decimal place.)

%

(d) What is the percentage decay rate per second? (*Note:* For this calculation, you will need to use all the decimal places that your calculator can show. Round your answer to eight decimal places.)

%

## American Dollars and British Pounds Assume that at the current exchange rate, the British pound is worth $1.65 in American dollars. You have some dollar bills and several British pound coins. There are 17 items altogether, which have a total value of $20.25 in American dollars. How many American dollars and how many British pound coins do you have? Solve using matrices.

**American Dollars and British Pounds**Assume that at the current exchange rate, the British pound is worth $1.65 in American dollars. You have some dollar bills and several British pound coins. There are 17 items altogether, which have a total value of $20.25 in American dollars. How many American dollars and how many British pound coins do you have?**Solve using matrices.**

## You invested $7000 in two accounts paying 6% and 8% annual interest. If the total interest earned for the year was $520, how much was invested at each rate?

You invested $7000 in two accounts paying 6% and 8% annual interest. If the total interest earned for the year was $520, how much was invested at each rate?

Fully explain how you would go about finding the solution. Please explain all steps in a way that a struggling classmate could understand and learn from your methods. Question and or compliment your classmates’ work at least twice during the discussion period. See the file attached below for the problem assigned you to this week

## In 1998 the population of Los Angeles California was a perfect square. Ten years later, as Gov Brown takes over the helm, and after an increase of 150 people, the population was 9 more than a perfect square. Now in 2018, with a new Governor,(Gov Newsom) and with an increase of another 150 people,the population is once again a perfect square. How many people lived in the town in 1998, 2008 and 2018?

In 1998 the population of Los Angeles California was a perfect square. Ten years later, as Gov Brown takes over the helm, and after an increase of 150 people, the population was 9 more than a perfect square. Now in 2018, with a new Governor,(Gov Newsom) and with an increase of another 150 people,the population is once again a perfect square. How many people lived in the town in 1998, 2008 and 2018?

## The formulas below are the cost and revenue functions for a company that manufactures and sells small radios. C(x)=140,000+36x and R(x)=50x a. Use the formulas shown to write the company’s profit function, P, from producing and selling x radios. b. Find the company’s profit if 25,000 radios are produced and sold.

and R(x)=50x

radios are produced and sold.

## Shawn is training for a triathlon. He starts his workout by riding his bicycle for 1 hour and then he switches to running, which he does for an hour and a half. Shawn rides his bicycle 10 miles per hour faster than he can run. If he traveled a total of 27.5 miles, how fast does Shawn ride his bicycle?

Shawn is training for a triathlon. He starts his workout by riding his bicycle for 1 hour and then he switches to running, which he does for an hour and a half. Shawn rides his bicycle 10 miles per hour faster than he can run. If he traveled a total of 27.5 miles, how fast does Shawn ride his bicycle?

## L.A. Wedding Caterers offers a wedding reception buffet. Suppose a menu is planned around three different salads, six entrees, five side dishes, and eight desserts. There are eight different choices of salads, ten different choices of entrees, eight different choices of side dishes, and ten different choices of desserts. How many menus are possible?

L.A. Wedding Caterers offers a wedding reception buffet. Suppose a menu is planned around three different salads, six entrees, five side dishes, and eight desserts. There are eight different choices of salads, ten different choices of entrees, eight different choices of side dishes, and ten different choices of desserts. How many menus are possible?