Theta Quads
RSTU is a kite. Its diagonals intersect at RX=UX=XS=5. ST=UT=13. The area of the kite.
A regular hexagon has area 150root3 . The perimeter of this hexagon.
What is 60?
Dhyey is enclosing his dog in a pen. The pen is a right triangle with legs 48 yards and 14 yards. The number of feet of wire to enclose the pen.
What is 336 yards?
Given a repeating decimal of 0.231231231... can be expressed as A/B with A,B as relatively prime positive integers. The value A + B.
What is 410?
The range of f(x)=−x^2 − 4x + 1 in interval notation.
What is (−∞, 5]?
∆RST is an equilateral triangle. SU=UT. m SUT ∠ =140. In quadrilateral RSUT, the measure of angle RSU.
What is 40 degrees?
A cone has dimensions that are each three times a second similar cone. The first cone has volume 27000 cu. ft. The volume of the second cone.
The cube of power is not a cube but a 3-dimensional shape that has 17 edges and 9 faces. To attain its power one needs to know how many vertices this shape has. The vertices this shape has.
What is 10?
Given x + y = 6 and x^3 + y^3 = 23. The value of xy.
What is 193/18?
Define the operation ⊞ as follows: x⊞y = x^y − y^x . The value of (2⊞ 3) ⊞ (2 ⊞ 5).
What is -8/7?
A quadrilateral RSTU is similar to quadrilateral ABCD so that the correspondence is RSTU~ABCD. If RS=12 cm and AB=3 cm, and the area of RSTU is 36 sq. cm, then the area of ABCD. If needed round to the nearest decimal place.
A sphere is inscribed in a right circular cylinder. The sphere has radius 10 cm. The total surface area of the cylinder.
What is 600pi?
It takes Benjy 3 hours to complete a certain differential equation problem. It takes Aarsh 7 hours to do that same problem. Assume they can work simultaneously on independent portions of the problem, and that their rates of work are constant. The time it takes if both of them work together as an improper fraction.
What is 21/10 hours?
The determinant of the denominator matrix for the x and y solutions when applying Cramer’s Rule to the following system of equations: 3x + 2y = 17 5x + 11y = 13
What is 23?
The function d(x) is equal to the number of diagonals in a convex polygon with x sides (that is, a convex x-gon). The value of d(3) is 0 because a triangle has no diagonals. The value of d(16)- d(13).
What is 39?
The bases of a trapezoid are each increased by 10%. The area of the trapezoid is to remain the same. The percent will be altitude be decreased as an improper fraction.
What is 100/11?
A regular hexagon HEXAGN has area 96root3 . T is the midpoint of HE. The area of ∆TGA .
What is 32root3?
Tickets to a University of Florida football game cost $2 for students and $10 for non-students. 30% of the game’s ticket sales will go to a children’s fund. Given that the children’s fund received $2700 from this game and 3500 tickets were sold. The number of students who attended the game.
What is 3250?
Given the following set of equations, the value of x+y+z. 6x + 2y − 3z = 8 3x − 2y + z = 0 2x + 3y − 5z = 7
What is 1?
If 𝑓(𝑥) = 2𝑥 + 3 and 𝑔(𝑥) = 𝑥^2. The values of x where 𝑓(𝑥) > 𝑔(𝑥) in interval notation.
(-1,3)
Let S be a square of side length 20202020. A point P ∋ S is chosen randomly. Given that the probability that P is closer to the center of the square then one of the vertices can be written in the form m/n where m and n are relatively prime positive integers. The sum of m+n
What is 3?
A capsule is constructed by using two hemispheres and a right circular cylinder with concurrent bases. The diameter of the hemispheres are each 12 and the height (h) of the entire capsule is 20. The total surface area of the capsule.
28. The Supreme Court is made of 9 people. Assume each member of the pool is equally likely to be picked. The probability that out of a pool of 8 Democrats, 5 Republicans, and 2 Independents, that 4 are Democrats, 4 are Republicans, and 1 is an Independent will be chosen?
What is 20/143?
Allen drove to work averaging 48 miles per hour (MPH). Returning home on the same road, he averaged 30 MPH. His average speed (in MPH) is a/b, where a and b are relatively prime. The value of a+b
What is 493?
The sum of the coefficients of the terms in the expansion of (2𝑥 + 2)^5.
What is 1024?