What is the product of the complex numbers
(3 +i) and (3 −i)?
10
100
M is in the interior of angleLPN. L is in the ineterior of angle KPM. Then L is also in the interior of what angle?
angle KPN
100
A wheel has a diameter of x inches and a second wheel has a diameter of y inches. The first wheel covers a distance of d feet in 100 revolutions. How many revolutions does the second wheel make in covering d feet?
100x / y
100
If 8x = 2 and 3x+y = 81, then y =
11/3
200
What is A 120-foot-long rope is cut into 3 pieces. The
first piece of rope is twice as long as the second
piece of rope. The third piece of rope is three
times as long as the second piece of rope.
What is the length of the longest piece of rope?
60 feet
200
What is is the solution to the equation 5^x =17
x=log(subscript10) 17 / log(subscript10) 5
200
Trevor has 16 CDs and Hannah has 20 CDs. What is the ratio of the number of CDs Trevor has to the total number of CDs?
4 to 9
200
The y coordinates of all the points of intersection of the parabola y2 = x + 2 and the circle x2 + y2 = 4 are given by
0, rad(3), -rad(3)
200
In a plane there are 6 points such that no three points are collinear. How many triangles do these points determine?
20
300
A pharmacist mixed some 10%-saline solution
with some 15%-saline solution to obtain
100 mL of a 12%-saline solution. How much of
the 10%-saline solution did the pharmacist use
in the mixture?
60mL
300
Solve the equation for theta. Round to the nearest degree. cos(theta)=.4 pi<theta<2pi.
294 degrees
300
What is the geometric mean of 4 and 12?
4sqroot3
300
What value of x makes the three terms x, x/(x + 1) and 3x/[(x + 1)(x + 2)] those of a geometric sequence?
-1/2
300
2x - y + z = 8
x + 2y + z = -3
x - 2y - z = 7
What is the magnitude of the vector drawn from the origin to the point at which these lines intersect? Simplify your answer. Use radicals.
rad(14)
400
Write the quadratic function f(x) = -2x^2 -12x - 20 in standard form (or vertex form)
f(x)=2(x + 3)^2 - 2
400
What is the sum of the first 30 terms of the series: 7,16,25,34...
4,125
400
In Triangle XYZ, XY=12, YZ=14, ZX=8. In Triangle MNP, MN=6, NP=7, and PM=4. Name the similarity postulate or theorem that can be used to prove the two triangles are similar.
SSS Similarity Theorem
400
What is the equation of the horizontal asymptote of function
f(x) = 2/(x + 2) - (x + 3)/(x + 4)?
-1
400
A cylinder of radius 5 cm is inserted within a cylinder of radius 10 cm. The two cylinders have the same height of 20 cm. What is the volume of the region between the two cylinders?
1500Pi cm^3
500
A rectangular picture measuring 10 cm by 15 cm is surrounded by a frame with uniform width x. Write a quadratic function that gives the area A of the frame as a function of x
.A = 4x^2 + 50x
500
What is the standard form of the equation of the circle that passes through the point (4,-3) with the center at the origin?
x^2 + y^2 =25
500
An Isosceles trapezoid ABCD has legs AB and CD and base BC. If AB=3x-1, BC=2x+3 and CD=4x-6, find the value of x.
5
500
In the xy-coordinate plane, the graph of x = y^2 - 4 intersects line b at (0, p) and (5, t). What is the greatest possible value of the slope of b?
1
500
A particular disc can be made to rotate at 2 different speeds. If it were made to rotate slower by 135 revolutions per hour, it would require an additional 2.7-hour to make 315 revolutions. Find the higher speed at which it can operate.