Study Guide Part 1
Evaluate the radical expression and express the result in the form a + bi: √―2 ∙ √―18
-6
Evaluate the product, and write the result in the form. a + bi: (7 – 3i)(7 + 3i)
58
Solve the following inequality: |𝑥―4| ≥ 5
x≥9 or x≤-1
Solve graphically:
𝑥+ 1 = √( 𝑥+ 3)
x=1
Find the center and radius of the circle:
(𝑥+ 3)2 + (𝑦―4)2 = 12
Center: (-3,4)
Radius= 2√3
Find all solutions of the equation. Simplify your answer completely leaving in radical form: 6𝑥2 +12𝑥+ 7= 0
-1 +(- i√6)/6
A rental company charges $80 a day and 25 cents a mile for renting a truck. Michael rents a truck for 3 days, and his bill came to $331. How many miles did he drive?
364 miles
Solve using your calculator. Give answers to 2 decimal places: 𝑥4 = 16 ―𝑥
x=-2.31, 1.79
Write the equation of the line through the points (-4,2) and (2, -8).
y=-5/3x-14/3
Find the equation of the line through the point (-7, 2) with slope of -3.
y=-3x-19
Using a graphing calculator for the following question. Solve the equation:
5𝑥2 ―𝑥3 = ―𝑥2 +3𝑥+ 8. Round answers to 2 decimal places.
x=-0.88, 1.78, 5.11
Find the x & y intercept(s) of the equation: 𝑥2𝑦+ 16𝑦2 = 80
x-int: none
y-int: (0,√5) and (0,-√5)
Randy invested $7,500, a portion earning a simple interest rate of 4.5% per year and the rest earning a rate of 5% per year. After one year the total interest earned on these investments was $360.00. How much money did he invest at each rate?
$3,000 at 4.5%
$4,500 at 5%
Solve the following inequality: (𝑥+ 4)(𝑥―1) < 0
(-4, 1)
Determine the type of symmetry: 𝑥3𝑦―𝑥2𝑦2 = 8
Only has symmetry about the origin
Graph the function h(x) = 𝑥3 ―5𝑥―4 in each of the given viewing rectangles. Select the viewing window
that produces the most appropriate graph of the function.
a) [-2,2] by [-2, 2]
b) [-3,3], [-10,10]
c) [-3,3] by [-10,5]
d) [-10,10] by [-10,10]
C
17. The graph of y = 𝑥3 ―6𝑥2 +11𝑥―6 is shown above (show on study guide). Use the graph to answer the question: Find the solutions of the equation 𝑥3 ―6𝑥2 +11𝑥―6 = 0
x= 1,2,3
Find the x- and y- intercepts of the following equation: 16𝑥2 +64𝑦2 +6𝑥𝑦= 64
x-ints: (2,0) and (-2,0)
y-ints: (0,1) and (0,-1)
The graph of y = 𝑥3 ―6𝑥2 +11𝑥―6 is shown above. Use the graph to answer the following
questions: Find the solutions of the inequality. 𝑥3 ―6𝑥2 +11𝑥―6 ≥0 Write your answer using intervalnotation.
[1,2] u [3,∞)
Solve the following inequality: (𝑥+ 3)/(𝑥―1) ≥0
(-∞,-3] u (1,∞)
What amount of a 65% acid solution must be mixed with a 35% solution to produce 600 mL of a 40% solution?
100 mL
Find an equation of the circle that satisfies the given conditions: Endpoints of a diameter are P(-1,2) and Q(7,8)
(x-3)2+(y-5)2=25
Candy and Tim share a paper route. It takes Candy 95 minutes to deliver all the papers, and it takes Time 55
minutes. How long does it take the two when they work together?
34 minutes, 50 seconds
Find an equation of the line that passes through. (5, -2) and is perpendicular to the line:
3x - 5y + 15 = 0
y=-5/3x+19/3
A pair of points is given: (-6, 3) and (4,-2)
Find the distance and midpoint
d= 5√5
midpoint= -1,1/2