If the volume of a cube is x3 cubic units, what is the number of square units in the surface area of the cube?
Answer(s): D
If the volume of the cube is x3, then one edge of the cube is x. The surface area of a cube is six times the area of one face, which is x times x. The total surface area is 6x2.
If x – 3 is a multiple of two, what is the next larger multiple of two?
Answer(s): C
The next larger multiple of two would be x – 3 + 2, which is x – 1. In this case, remember that any even number is a multiple of two and all evens are two numbers apart. If x – 3 is a multiple of two, you can assume that it is also an even number. This number plus two would also produce an even number.
If 3x + 1 = 81, then x – 1 =
Answer(s): A
Solve for x first. Since 3x+1 = 81, and 81 is 34, make an easier equation just based on the exponents. This would be x + 1 = 4. x = 3. Therefore, x – 1 = 3 – 1 = 2.
For dinner at a restaurant, there are x choices of appetizers, y + 1 main courses, and z choices of dessert. How many total possible choices are there if you choose 1 appetizer, 1 main course, and 1 dessert for your meal?
Answer(s): B
Use the counting principle: Take the number of choices you have for each course and multiply them together to get the total possible combinations. x × (y + 1) × z. Use the distributive property to simplify to xyz + xz.
If x $ y is defined as 2(x + y) 2, then what is the value of 2 $ 3?
For this type of problem, substitute the values you are given for x and y. In this case, x = 2 and y = 3. The expression becomes 2 (2 + 3)2. Using the order of operations, perform the operation within the parentheses first and then the exponent. 2 (5)2 = 2 (25).Multiply to get 50.
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