Rationalizing
Radicals
Systems
Conic Sections
Rational exponents
100
Look at the problem 1. What do you multiply to rationalize the numerator?
square root (2x)
100
For problem 4: Add
13sqrt(2)
100
Define variables, and set-up a system of equations. DO NOT SOLVE. A company sells hats a t-shirts. Hats are sold for 10 each, t-shirts are 15 dollars each. If they sold 100 items, and brought in a total of $1100, how many of each were sold?
x = number of hats, y = number of t-shirts, x+y = 100 AND 10x + 15y = 1100
100
Which of the conic sections is a circle?
#1 (x^2 = 3 - y^2)
100
Write sqrt(5) with fractional exponents.
5^(1/2)
200
Look at the problem 1. What would you multiply by to rationalize the denominator?
Square root (3) + 4
200
For question 5: Multiply.
11 - 6sqrt(2)
200
Define variables, and set-up the system (But DO NOT SOLVE) A rowing team wants to now how fast they can row. In a stream they can row 5 miles in 3 hours downstream, but only 4 miles in 6 hours upstream.
x = speed of boat, y = speed of current, 5=(x+y)*3, 4=(x-y)*6
200
Which of the conic sections is an ellipse?
#5 (4x^2 = 3 - y^2)
200
Write (x)^(2/3) as a radical
cube root (x^2)
300
Look at problem 2: What would you multiply by to rationalize the denominator?
cube root (9y) Also acceptable: cube root (9y^4) or cube root(3y^2)*cube root(3y^2), however this option requires more simplifying.
300
For problem 6: Multiply
18x
300
Define variables and write the system. Do not solve. Two angles are complementary if they sum to 90 degrees. If the larger angle of two complementary angles is 5 less then 3 times the smaller angle, what are the angles?
x=larger angle, y = smaller angle, x+y=90, x = 3y-5.
300
Which of the conic sections is a parabola opening up/down?
#4 (x^2 = 3 - y)
300
simplify: sqrt ( cuberoot(x))
x^ (1/6) = sixth root of x.
400
Looking at problem 2: What would you multiply by to rationalize the numerator?
cube root(2x^2) Also acceptable: cube root (16x^2) or cube root(4x)*cube root(4x), however this option requires more simplifying.
400
For problem 7: Solve Problem: 4 - 3 sqrt(2x+1) = x - 9
{4}
400
Define variables, set-up the system. Do not solve: You have 8,000 dollars to invest. You will put some in a low risk account earning 1%, and some in a high risk account claiming to earn 12%. How much should you put in each to earn $500 by the end of the year?
x= principle in low risk (1% account), y = principle in high risk (12% account), x + y = 8000, .01x+.12y = 500. Note x = 1% is NOT acceptable. y = 12% is NOT acceptable.
400
Which of the conic sections is a parabola opening right/ left?
#3 (x = 3 - y^2)
400
SImplify sqrt(x) divided by cuberoot(x)
x^(1/6) = sixth root of x
500
Rationalize the denominator of problem 3.
Multiply by 3sqrt(2)+sqrt(3) Numerator: 6(3sqrt(2) + sqrt(3)) Denominator: (3sqrt(2)-sqrt(3))(3sqrt(2)+sqrt(3)) = 18-3 = 15 The problem reduces: Answer: [6sqrt(2) + 2sqrt(3)]/5
500
For question 8: Solve
{1}
500
The three angles in a triangle always sum to 180 degrees. If the largest angle is twice the sum of the smaller angles, and the middle angle is the difference of the larger angle and the smaller angle, find the measure of the angles.
x=largest angle, y = middle angle, z = smallest angle, x+y+z=180, x=2(y+z), y = x - z
500
Which of the conic sections is a hyperbola?
#2 (x^2 = 3 + y^2)
500
Multiply: sqrt(x)*cuberoot(x)=
x^(5/6)= sixth root of x^5
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