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1. A group of students at Omega High School are using staples and popsicle sticks to build a scale model of the Great Wall of China as part of a project detailing China's military history. The number of staples the students will need is three times the number of popsicle sticks they will need. If the students determine they need 84 staples for this particular project, how many popsicle sticks will they need?
2. A standard parabola in the x,y-coordinate plane intersects the x-axis at (5, 0) and (-5, 0). What is the value of the x-coordinate of this parabola's line of symmetry?
3. Danielle is a civil engineer for Dastis Dynamic Construction, Inc. She must create blueprints for a wheelchair accessible ramp leading up to the entrance of a mall that she and her group are building. The ramp must be exactly 100 feet in length and make a 20° angle with the level ground. What is the horizontal distance, in meters, from the start of the ramp to the point level with the start of the ramp immediately below the entrance of the mall, rounded to the nearest meter? (Disregard units when inputting your answer.)
(Note: sin 20° ≈ 0.324, cos 20° ≈ 0.939, tan 20° ≈ 0.364)
4. If twice a number is equal to that number minus five, what is three times that number plus seventeen minus that number?
5. Given that the equation 3x2 + 2x - 8 = 0 has two distinct solutions, what is the value of the smaller solution subtracted from the larger solution?
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