Algebra 1
Geometry
Algebra 2
Related Technical
Final Jeopardy
100
The cost of having a car towed is given by the linear function C(x) = 3x + 65, where C(x) is in dollars and x is the number of miles the car is towed. Find the cost of having a car towed 8 miles
$89
100
Find the angle measures of angle M and angle B.
m∠M=134°
m∠B=72°
100
Let
665
100
You have a room that is 10 ft x 15ft x 10ft. You want to put up wallpaper in this room. In order to attach the wallpaper, you need to use wallpaper glue. 3 oz of the glue will cover 2 sq ft of the room. If they only sell 16 oz bottles of glue for $6, how much money will you spend on the wallpaper glue? (ignore any doors or windows in the room)
$36
100
A solid, four-inch cube of wood is coated with blue paint on all six sides.
Then the cube is cut into smaller one-inch cubes.
These new one-inch cubes will have either three blue sides, two blue sides, one blue side, or no blue sides. How many of each will there be?
There are:
8 with three sides colored
24 with two sides colored
24 with one side colored
8 with no sides colored.
200
A poster in the shape of a triangle has one side that is five inches more the length of the shortest side, and another side that is three inches less than twice the shortest side. Find the dimensions of the poster if its perimeter is 46 inches.
11 inches
16 inches
19 inches
200
In the triangle ABC shown below, A'C' is parallel to AC. Find the length y of BC' and the length x of A'A. Round to tenths place.
BA is a transversal that intersects the two parallel lines A'C' and AC, hence the corresponding angles BA'C' and BAC are congruent. BC is also a transversal to the two parallel lines A'C' and AC and therefore angles BC'A' and BCA are congruent. These two triangles have two congruent angles are therefore similar and the lengths of their sides are proportional. Let us separate the two triangles as shown below.
We now use the proportionality of the lengths of the side to write equations that help in solving for x and y.
(30 + x) / 30 = 22 / 14 = (y + 15) / y
An equation in x may be written as follows.
(30 + x) / 30 = 22 / 14
Solve the above for x.
420 + 14 x = 660
x = 17.1 (rounded to one decimal place).
An equation in y may be written as follows.
22 / 14 = (y + 15) / y
Solve the above for y to obtain.
y = 26.25
200
How many integers
13
200
You have a solution of 99% Isopropyl Alcohol on hand. You want to make 2 Liters of 70% isopropyl Alcohol. How many milliliters of the 99% solution must you add. (Round to the nearest milliliter)
1414
300
The formula for the perimeter of a rectangle is P = 2L + 2W. Solve the formula for L. Use this formula to find the length of the rectangle if the perimeter, P, is 30 feet and the width, W, is 6 feet.
9 units
300
A research team wishes to determine the altitude of a mountain as follows: They use a light source at L, mounted on a structure of height 2 meters, to shine a beam of light through the top of a pole P' through the top of the mountain M'. The height of the pole is 20 meters. The distance between the altitude of the mountain and the pole is 1000 meters. The distance between the pole and the laser is 10 meters. We assume that the light source mount, the pole and the altitude of the mountain are in the same plane. Find the altitude h of the mountain.
We first draw a horizontal line LM. PP' and MM' are vertical to the ground and therefore parallel to each other. Since PP' and MM' are parallel, the triangles LPP' and LMM' are similar. Hence the proportionality of the sides gives:
1010 / 10 = (h - 2) / 18
Solve for h to obtain
h = 1820 meters.
300
One of the zeros of the function
-5
300
There are 3 rivers and after each river lies a grave. So there are 3 rivers and 3 graves. A man wants to leave the SAME amount of flowers at each grave, and be left with none at the end. What happens though is that each time he passes through one of the rivers the number of flowers he has doubles. So he has to start off with what number of flowers, taking into consideration that they double, so that he is left with no flowers whatsoever at the end?
Let f be the starting number of flowers, and g be the number left at every grave.
((f*2-g)*2-g)*2-g=0
(4f-2g-g)*2-g=0
8f-4g-2g-g=0
8f-7g=0
8f=7g
Assume f and g are nonnegative integers.
f=7g/8, so 7g must be a multiple of 8, so g must be a multiple of 8.
g=8f/7, so 8f must be a multiple of 7, so f must be a multiple of 7.
So all nonnegative g that are multiples of 8 are solutions. The first few are listed:
f=0, g=0.
f=7, g=8.
f=14, g=16, etc.
Of these, the simplest solution is to start off with zero flowers, and snub each grave.
400
Robin is having her yard landscaped. She obtained an estimate from two landscaping companies. Company A gave an estimate of $210 for materials and equipment rental plus $45 per hour for labor. Company B gave and estimate of $290 for materials and equipment rental plus $35 per hour for labor. Determine how many hours of labor will be required for the two companies to cost the same.
8 hours
400
After finding the y intercept for AB.
You break the area into three parts.
The side of the shaded region is 4 x 7 = 28.
The area of triangle ACE = 4 * (15-7) / 2 = 16
The area of triangle
EBD = (external height)7 * (15-4) / 2 = 38.5
So the total area is 82.5 square units.
400
The following transformations are applied (in the given order) to the graph of
y=-√(x+2)+3
400
3 people carry 5 pails (each with capacity 8L) to a place where there are 3 springs. One of the springs gives 2L/minute and the other two give 1L/minute. It is not possible to use one spring to fill two pails simultaneously. It takes less than 2 minutes and more than 1 minute to take a pail from one spring to another. What is the shortest time it takes for them to fill all five pails?
They can fill the pails in 10 minutes.
First, I'll try to put some bounds on the possible time. The aggregate flow is 4L/minute, and the total pail capacity is 40L, so the best one could hope for is 10 minutes, and then only if water is flowing continuously into all three pails for the full 10 minutes. A simple-minded plan would be to fill one pail each at the slow spring, and 3 pails at the fast spring, which would take 12 minutes. So the answer has to between 10 and 12 minutes, inclusive.
The simple-minded plan fills a bucket at each of the slow springs in 8 minutes, wasting 2 minutes at each spring. To correct this problem, it is necessary to bring a bucket to each of the slow springs with 2L of available capacity in each bucket so they can be filled to the top in the last two minutes.
500
Factor:
(x² + 11x + 9) ÷ (x + 9)
x+2-(9/(x+9))
500
Which pocket will the ball end up in?
n order to find the intersection points,instead of reflect the line, we can "reflect" the rectangles.
Thanks to Rohit Upadhyaya,I found the mistake in my origin solution, the "reflection" times are wrong. Sorry for the confusion caused by the diagram of mine.
Precisely speaking, the "reflection" times in horizontal direction is 67- 1 = 66, and the vertical direction the "reflection" time is 100-1 = 99. When the "reflection" times in horizontal direction is EVEN, so the Line AB still stand at the left side of the rectangle, the "reflection" times in vertical direction is ODD, so the Line BD will at the top side of the rectangle. So the answer is D.
I made a simpler version diagram of the this question, a 4x3 rectangle situation, hope it will help.
500
Evaluate the expression:
∛[∜(16) +√(625)] + ∛{√[√(169) + √(9)] +√[∛(1000) + ∛(216)]}
5
500
I was driving through northern Maine with a couple of my Physics students, and we passed by the wind farm in Mars Hill. "I wonder," one of them said, "how fast the tip of one of those turbine blades is going."
"I wonder," the other one said, "how far we'd fly if we hung on to the blade until it was at its highest point, and then let go."
"Let's figure it out!" I said.
So we did a bit of research, and a bit of estimation. Here's what we found:
Based on doing the 1001-1002-10003 count that you resort to when you don't have a stop watch handy, we concluded that it took about 8 seconds for the turbine to do a complete revolution.
The height of the turbine tower is 262 feet.
The length of the turbine blade is 115 feet.
So...how long would my students go flying if they let go at the blade's highest point?
The total distance around at the tip of the blade is 2πr, where r is the length of the blade. So the tip of the blade travels 772 feet in 8 seconds, which gives it a speed of 96.5 ft/s (That's about 66 mph, which really surprised everyone; the blade motion looks so sedate from a distance!)
At the top of the cycle, the student is 262 + 115 = 377 feet off the ground, and since they let go at the moment when the blade is at its highest point, all 96.5 ft/s is horizontal.
How long does it take them to reach the ground? Use 32.2 ft/s2 as the acceleration, and we find that the trip to the ground takes about 4.8 seconds.
How far does the student travel horizontally in that time? d = vt = 96.5(4.8) = 463.2 feet, or around a twelfth of a mile.