A circle passes through the four vertices of a rectangle that is 8 feet long and 6 feet wide.How many feet are there in the radius of the circle?
Answer(s): D
If the circle passes through all four vertices of the rectangle, its diameter will be a diagonal of the rectangle.Since a rectangle's angles are right angles, the diagonal for n is a right triangle with two sides of the rectangle.Let x = the length of the diagonal. By the Pythagorean Theorem, in a right triangle the square of the length of the hypotenuse is equal to the sum of the squares of the legs.x2 = 82 + 62x2 = 64 + 36x2 = 100x2 = 100means that x times x=100.Therefore, x = 10 feet.But 10 is a diameter of the circle. A radius of a circle is one-half the diameter. Hence, the radius is 5 feet.
(x + 3)(x + 5) = __________.
Answer(s): C
Use the FOIL method (First, Outside, Inside, Last) to solve.x2 + 3x + 5x + 3 × 5
25 percent of what number is equal to 5?
Answer(s): B
Divide 5 by 25 and then multiply the answer by 100 to find the percent.
Which of the following is the equivalent of 12/25?
The fraction 12/25 is equivalent to 48/100 or 0.48.
Which of the following means 3n + 7 = 16?
Answer(s): A
The expression 3n means 3 times n. The addition sign before the 7 indicates the phrase more than.
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