Exam 6: Algebraic Thinking

Find the Celsius temperature when the Fahrenheit temperature is -20 . Use the relationship between Fahrenheit temperature and Celsius temperature, which is given by the formula F = 1.8 C + 32, where F is the Fahrenheit temperature and C is the Celsius temperature. Round your answer to the nearest tenth of a degree. ​

Find four different odd numbers whose sum is 34 . ​

​If 3 books cost $ 30 , a book, three pens, and a notebook cost $ 16 , and a book and pen cost $ 11 . Find the cost of a notebook.

​Hester wants to spend no more than $ 48 at the grocery store. She needs to buy a pound of a salmon for $ 12 . A bag of organic apples costs $ 9 . How many bags of organic apples can she buy?

The value of an investment in a high-tech company after 1 year was $17,000. The increase in value during the year was $3000. Find the amount of the original investment. Note: Use the formula A = P + I , where A is the value of the investment after 1 year, P is the original investment, and I is the increase in value of the investment. ​

Find a pattern from the first 3 equations of the following sequence of equations and predict the 11th equation. ​ 1³ + 2³ = 3² 1³ + 2³ + 3² = 6² 1³ + 2³ + 3³ + 4³ = 10 ²

Find a pattern in the following set of equations and predict the next equation. ​ 1² + 2² + 2² = 3² 2² + 3 ² + 6² = 7² 3² + 4² + 12² = 13² ​

You estimate that your car can travel 440 miles on 12 gallons of gasoline. Find the miles per gallon. Round your answer to the nearest tenth of a mile per gallon. Note: Use the formula ​D = m · g , where D is the total mileage, m is the average mileage, and g is the total number of gallons used. ​

​Mario is driving on the highway at a steady rate. He encounters a construction zone and slows down until he is out of the zone and is able to resume his original steady speed. He then slows down as he approaches his exit and comes to a complete stop at the stop sign at the end of the exit ramp. Sketch a graph of Mario's speed versus time.

What is the next term in the sequence? ​ 1, 4, 7, 10, 13, ... ​

Examine the following phrase made famous by Fred Flintstone: ​ Y a b b a d a b b a d o o ​ If this pattern is repeated over and over, what letter will be in the 66 th position? ​

Consider the graph below which depicts the depreciation of a copy machine over 5 years. Predict when the value of the copy machine will be $ 200 . Round your answer to two decimal places. ​ ​

​Jerry and Elliot raised money selling popcorn. They raised $ 2100 total. Jerry raised $ 100 more than Elliot. How much did Jerry raise?

​Which of the following is a geometric sequence? ​

What is the next term of the sequence? ​ 4 , 5 , 8 , 13 , 20 , 29 , 40 ,..... ​

What is the next term of the sequence? ​ 9 , 16 , 25 , 36 , 49 , .... ​

​A runner begins running at a steady pace on a at path. She speeds up as she starts to run downhill. Once she is at the bottom of the hill, the path is at again, and she resumes a steady pace faster than her previous steady pace. Her run ends with an uphill path, on which she runs slower and slower until she stops at the top of the hill. Sketch a graph of the runner's speed versus time.

Find a pattern in the following set of equations and predict the next equation. ​ 1³+ 2³ = 3² 1³+ 2³+ 3³ = 6² 1³+ 2³+ 3³+ 4³ = 10² ​

​Which of the following is an arithmetic sequence? ​

The original investment in a mutual fund was $ 9,000 . The value of the mutual fund after 1 year was $ 11,670 . Find the increase in value of the investment. Note: Use the formula A = P + I , where A is the value of the investment after 1 year, P is the original investment, and I is the increase in value of the investment. ​