Tutor profile: Amanda L.
A right triangle has sides a, b and c, where c is the hypotenuse. The values of a and b are 12 and 35. What is c?
All right triangles abide by the pythagorean therorem, which is a^2 + b^2 = c^2, where a and b are the two short lengths and c is the longest (hypotenuse). Since the values of a and b are given as 12 and 35, plug them into the pythagorean theorem and solve for c. Thus, c = 37.
What is 4/3 + 8/5?
To add fractions, you need to find the common denominator of both fractions. Since the denominator of the first fraction is 3 and the denominator of the second fraction is 5, the common denominator is 15 because it is the smallest number that has both 3 and 5 as factors. In order for 4/3 to have 15 as the denominator without changing its value, multiply it by 5/5 (also known as 1) to get 20/15. In order for 8/5 to have 15 as the denominator without changing its value, multiply it by 3/3 (also known as 1) to get 24/15. Now you can add the fractions because they both have the same denominator. When adding fractions, only add the numerator and keep the denominator the same. Thus, the answer is 44/15.
A car averages 22 miles per gallon. If gas costs $2.89 per gallon, which of the following is closest to how much the gas would cost for this car to travel 3,483 typical miles?
It costs $2.89 to fill the car with 1 gallon of gas and the car can travel 22 miles with 1 gallon of gas, therefore it costs $2.89 to travel 22 miles. To travel 1 mile, it costs $2.89/22 = 0.132. Since the car needs to travel 3,483 miles, it costs $0.132 x 3483 = $457.54.
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