Patrick made tortilla soup in his slow cooker and has turned the heat off to allow the soup to cool slightly before consuming. The temperature, in degrees Fahrenheit, of the soup x minutes after the heat was turned off is represented by the function below. T(x) = 14 + 156e-0.022x What is the approximate average rate of change over the interval [10, 20]?

Three people are traveling and need to exchange the currency of their native country for the currency of the country they are visiting. drag each exchange to the category that shows the ratio of currencies in that exchange.

Statement reason 1. δabc is similar to δced. given 2. 3. definition of slope 4. slope of slope of definition of slope 5. slope of × slope of multiplying the slopes 6. slope of × slope of substitution property of equality 7. slope of × slope of simplifying the right side the table contains the proof of the relationship between the slopes of two perpendicular lines. what is the reason for statement 2? a. parallel line segments that meet a common perpendicular line are proportional in length. b. the lengths of vertical and horizontal sides in congruent triangles are in a common ratio. c. trigonometric identities determine the lengths of the legs in a right triangle. d. corresponding side lengths in similar triangles are proportional in length.

Scenario: susan wants to make 2 square flags to sell at a crafts fair. the fabric she wants to buy is 3 meters wide. she doesn't want any fabric left over. what's the least amount of fabric she should buy? question: which equation will susan solve her problem? note: let x represent the length of 1 side of the flag. options: 1) 3x^2 -2x =0 2) 2x^2 =3x 3) 2 * 2 = 2 * 2 4) 6 +2x = 2(4x)