What is the equation of the line that is perpendicular to y=2x+1 at point (1,3)?
The slope of the line y = 2x + 1 is 2. A line perpendicular to y = 2x + 1 will have a slope that is the negative reciprocal of 2, or -1/2. Using the point slope form at (1, 3), we get the equation y-3 = -1/2x + ½. Solving for y, we get y = -1/2x + 7/2.
What is 3 1/3 divided by 2 2/9?
Convert the mixed numbers to improper fractions. 3 1/3 becomes 10/3. 2 2/9 becomes 20/9. Multiply 10/3 by the reciprocal of 20/9, or 9/20. The answer is 3/2, or 1 1/2
A movie theater offers a special promotion. You can purchase refillable popcorn bucket for $10. After that, it costs $2 to fill it. Otherwise, a bag of popcorn costs $4. How many times will you need to use the bucket to justify the $10 investment?
Let x be the number of visits to the movie theater. The total cost of popcorn using the bucket is 10 + 2x. The total cost of the popcorn without the bucket is 4x. Setting these equations equal to each other gives 10 + 2x = 4x. Solving for x gives, x = 5. Thus, you need to use the bucket more than 5 times to save money.