Triangles and Circles
What is the center of the circle: (x +10)2 + (y - 23)2 = 49?
(-10,23)
What is the area of a circle with a diameter of 10? (Leave answer in terms of pi)
25pi
The International Space Station orbits Earth at an average speed of 4.76 miles per second. What is the space station’s average speed in miles per hour?
17136
What is the slope of the graph y = 1/4(27x +15) +7x in the xy-plane?
55/4 OR 13.75
The central angle of a circle is 135 degrees and its radius is 4 cm. What is the area of the region created by the central angle?
6pi
What is the radius of a cylinder with a volume of 98pi and a height of 2?
7
A rocket contained 467,000 kilograms (kg) of propellant before launch. Exactly 21 seconds after launch, 362,105 kg of this propellant remained. On average, approximately how much propellant, in kg, did the rocket burn each second after launch?
4995
A line in the xy-plane passes through the point (4,-1) and is perpendicular to the line with equation y=x+5. Which of the following is an equation of the line ?
a) y = x + 3
b) y = x - 3
c) y = -x +3
C
The length of a rectangle's diagonal is 3sqrt(17), and the length of the rectangle's shorter side is 3. What is the length of the rectangle's longer side?
12
What is the length of one side of a square that has the same area as a circle with radius 2 ?
2sqrt(pi) or 3.545
25
Line p is defined by 2y + 18x = 9. Line r is perpendicular to line p in the xy plane. What is the slope of line r? (answer in fraction form!)
1/9
A right triangle has sides of length 2sqrt(2), 6sqrt(2), and sqrt(80) units. What is the area of the triangle, in square units?
12
A certain park has an area of 11,863,808 square yards. What is the area, in square miles, of this park? (1 mile = 1760 yards)
3.83
A garden is 85 square feet. How many square meters is the garden? (1 meter = 3.28 feet)
7.9
For the function f, if f(3x) = x - 6 for all values of x, what is the value of f(6)?
-4
Points Q and R lie on a circle with center P. The radius of this circle is 9 inches. Triangle PQR has a perimeter of 31 inches. What is the length, in inches, of QR?
13
A rectangle has an area of 155 square inches. The length of the rectangle is 44 inches less than 7 times the width of the rectangle. What is the width of the rectangle, in inches?
5
The area of a rectangular region is increasing at a rate of 250 square feet per hour. Which of the following is closest to this rate in square meters per minute? (Use 1 meter=3.28 feet.)
0.3873
In the xy plane, line s passes through the point (0, 0) and is parallel to the line represented by the equation y = 18x + 2. If line s also passes through the point (4, d), what is the value of d?
A) 2
B) 18
C) 72
D) 74
72