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题目内容
$$x+\frac{1}{x}=2$$

Quantity A

$$x^{2}$$+$$\frac{1}{x^{2}}$$

Quantity B

$$x^{3}$$+$$\frac{1}{x^{3}}$$
$$k+\frac{1}{k}=3$$

Quantity A

$$k+\frac{1}{k^{2}}$$

Quantity B

$$k^{2}$$+$$\frac{1}{k^{3}}$$
$$y=x^{2}+2x-35$$ can be transformed into $$y=(x+m)(x-n)$$ where $$m$$ and $$n$$ are both integers.

Quantity A

$$m$$

Quantity B

$$n$$
What is the product of the two solutions of the equation $$3x^{2}+17x+10=0$$?
The function f is defined by f(x) =$$x^{2}$$-18x+56 for all numbers x. If r and t are two different numbers such that f(r) = f(t) = 0. What is the value of $$\frac{r+t}{2}$$?
An apple falls straight to the ground from a tree branch 8 meters above the ground. The apple's height above the ground, t seconds after it starts falling, is H meters, where H=8-4.9$$t^{2}$$ and t≥0. How many seconds after the apple starts falling does it hit the ground?

Give your answer to the nearest 0.1 second.
The electric power P in a resistor is directly proportional to the square of the electric current I flowing through the resistor. For a given resistor, if the power is 18 watts when the current is 3 amperes, what is the power, in watts, when the current is 4 amperes?
The operation ⭕️ is defined by x ⭕️ y=$$\frac{1}{x}$$+$$\frac{1}{y}$$ for all positive numbers x and y. Which of the following statements must be true for all positive numbers m and r?

Indicate all such statements.
In the xy-plane, the point (3p, 5p-1) lies on the line with equation y=-$$\frac{1}{2}$$x-$$\frac{5}{3}$$. What is the value of p?

Give your answer as a fraction.
How many x-intercepts, and y-intercepts does the graph of the equation $$4x^{2}-9y^{2}=1$$ have?
In the $$xy$$-plane, line $$m$$ passes through the point $$(7, 7)$$ and is perpendicular to the line $$x+y=4$$. The point $$(a, b)$$ is on line $$m$$ and is halfway between the point $$(7, 7)$$ and the line $$x+y=4$$. What is the value of $$a+b$$?
In the xy-plane, S is the set of all points (c, d) for which c and d are both integers.

Quantity A

The number of points in S that are a distance of 2 units from the point (7, 5)

Quantity B

4
There are two parallel lines, and the third line intersects these two lines.

Quantity A

The number of points with equal distance from three lines

Quantity B

3


$$l_{1}$$ is parallel to $$l_{2}$$

Quantity A

x

Quantity B

y
A hexagon with sides of equal length and interior angles of equal measure is inscribed in a circle. If the perimeter of the hexagon is 12, what is the perimeter of an equilateral triangle inscribed in the same circle?


The figure above shows the interior of a propane tank in the shape of a right circular cylinder with a hemisphere at each end. The diameter of the cylinder is 60 centimeters, and the total length of the interior of the tank is 210 centimeters. The tank is filled with propane to 80 percent of its capacity. If the cost of the propane is $0.60 per liter, approximately what is the cost of the propane in the tank?

(Note: 1 liter=1,000 cubic centimeters. The volume of a sphere of radius r is $$\frac{4}{3}πr^{3}$$.)
What is the remainder when $$223^{4}-223^{3}+223^{2}-223$$ is divided by 221?
Set A={x, y, w}

Set B={x+6, y+6, w+6}

Quantity A

The standard deviation of all the numbers in Set A

Quantity B

The standard deviation of all the numbers in Set B

Quantity A

100!

Quantity B

$$(50!)^{2}$$

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