|
|
If $$x \ge 0$$ and $${x}=\sqrt{8xy-16y^2}$$ , then, in terms of y, x =
|
|
Magoosh
|
$$(2\sqrt{3}+\sqrt{5})(2\sqrt{3}-\sqrt{5})$$
|
|
Magoosh
|
If the hypotenuse of an isosceles right triangle has length of 8, then the area of the triangle is
|
|
|
 If the area of rectangle ABCD is $$4\sqrt3$$, then what is the area of the square DEFG?
|
|
|
If 3x + 19 = - 3 - x, then x =
|
|
PREP07 Test 1
|
A small water pump would take 2 hours to fill an empty tank. A larger pump would take 1/2 hour to fill the same tank. How many hours would it take both pumps, working at their respective constant rates, to fill the empty tank if they began pumping at the same time?
|
|
PREP07 Test 1
|
The perimeters of square region S and rectangular region R are equal. If the sides of R are in the ratio 2 : 3, what is the ratio of the area of region R to the area of region S ?
|
|
Manhattan
|
If the price of a certain stock increased by $$\frac{1}{5}$$ during the first month and then decreased by $$\frac{1}{4}$$ during the second month, what was the ratio of the stock price at the end of the two months to the original price?
|
|
Manhattan
|
Given that a is the average (arithmetic mean) of the first nine positive multiples of six and b is the median of the first twelve positive multiples of six, what is the ratio of a to b?
|
|
OG18-定量推理
|
A positive integer n is a perfect number provided that the sum of all the positive factors of n, including 1 and n, is equal to 2n. What is the sum of the reciprocals of all the positive factors of the perfect number 28 ?
|
|
OG19-定量推理
|
A positive integer n is a perfect number provided that the sum of all the positive factors of n, including 1 and n, is equal to 2n. What is the sum of the reciprocals of all the positive factors of the perfect number 28 ?
|
|
OG19-定量推理
|
The points R, T, and U lie on a circle that has radius 4. If the length of arc RTU is $$\frac{4\pi}{3}$$ , what is the length of line segment RU?
|
|
OG18
|
If $$(\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+\frac{1}{6}) = r(\frac{1}{9}+\frac{1}{12}+\frac{1}{15}+\frac{1}{18})$$, then r =
|
|
OG17 OG18 OG19 OG20 OG2022
|
City X has a population 4 times as great as the population of City Y, which has population twice as great as the population of City Z. What is the ratio of the population of City X to the population of City Z?
|
|
OG19 OG20 OG2022
|
If($$\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+\frac{1}{6})=r(\frac{1}{9}+\frac{1}{12}+\frac{1}{15}+\frac{1}{18}$$) ,then r=
|
|
181215
|
The four sides of the square is tangent to the circle, as shown in the picture. The radius is 0.5. What is the area of the shaded part?
|
|
190321
|
In the rectangle ABCD, E,F,G and H are the midpoints of each side, BC=x, CD=y. How to express the shaded area with x and y?
|
|
190603
|
As shown in the figure, ABE and CDE are isosceles triangles, BC and AD are parallel, and the sum of the perimeter of ABE and CDE is 32. What is the range of AB length?
|
|
191020
|
As shown in the figure, a semicircle is spliced with a rectangle. The rectangle is x in width and y in length. If the area of semicircle is 1/3 of the area of rectangle. What is the ratio of the arc of the semicircle to x?
|
|
PREP07 Test 1
|
Which of the following equations is NOT equivalent to $${4}{x}^{2}={y}^{2}-{9}$$
|