All Questions

Naming clockwise, regular pentagon COUNT has vertices C, O, U, N, T, respectively. Point X is right in the center of this pentagon so that line segments from X to each vertex create congruent triangles. If point C is rotated 144° counterclockwise about the point X, what original vertex is the image of point C?

  The four points A (−4, 0), B (0, −4), X (0, 8) and Y (14, k) are graphed on the Cartesian plane. If segment AB is parallel to segment XY, what is the value of k?

  The preimage of square ABCD has its center at (8, −8) and has an area of 4 square units. The top side of the square is horizontal. The square is then dilated with the dilation center at (0, 0) and a scale factor of 2. What are the coordinates of the vertex of the image of square ABCD that is farthest from the origin?

A car is scheduled to make a 616-mile trip in 9 hours. The car averages 60 mph during the first 240 miles and 80 mph during the next 160 miles. What must the average speed of the car be for the remainder of the trip in order for the car to arrive on schedule?

The new Perry Hotter book will have a cover price of $25. The local bookstore is offering two discounts: $4.00 off and 20% off. A clever shopper realizes that the prices will be different depending on the order in which she claims her discounts. How much more money will she save by taking the better-valued approach rather than the other approach? Express your answer in cents.

The area of square I is 1 square unit. A diagonal of square I is a side of square II, and a diagonal of square II is a side of square III. What is the area of square III?

If a is a greatest 1-digit square number, b is  the greatest the even 1-digit number, what is the answer of b+a:0,5?

Triangle ABC has vertices with coordinates A(2, 3), B(7, 8) and C(−4, 6). The triangle is reflected about line L. The image points are A’(2, −5), B’(7, −10) and C’(−4, −8). What is the equation of line L?

Ayushi has six coins with a total value of 30 cents. The coins are not all the same. Two of Ayushi’s coins will be chosen at random. What is the probability that the total value of the two coins will be less than 15 cents? Express your answer as a common fraction.

Ryosuke is picking up his friend from work. The odometer on his car reads 74,568 when he picks his friend up, and it reads 74,592 when he drops his friend off at his house. Ryosuke’s car gets 28 miles per gallon, and the price of one gallon of gas is $4.05. What was the cost of the gas that was used for Ryosuke to drive his friend home from work?