Disscusion Questions Math 209

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MATH 209 — FINAL EXAM

This is an open book quiz – feel free to use all the material at your disposal.

Please remember to show your methodology as well as the answer. How you solve the problems counts almost as much as your correct answer – in other words, even if you get the wrong answer, partial credit is available if you can show that you know how to approach the problem!

These are not difficult – just remember to follow logical rules

AND PLEASE BE CAREFUL — CHECK YOUR ARITHMETIC

WATCH OUT FOR THOSE QUESTIONS THAT NEED ± SOLUTIONS

There are 20 questions.

For questions 1 through 5, perform the indicated operations. If possible, simplify the answer.

1. [2 – 5(6 – 2)²] ÷ (8 – 4•3)
parens
[2-5(4)^2]/(8-12)
Powers
[2-5(16)]/-4
multiplication
(2-80)/-4
parens
-78/-4
Cancel the minus
78/4
simplify
39/2

2.
Expand:
27x^6 * 2x^-3 / 6x^3
Simplify:
54x^3 / 6x^3
Cancel x^3:
54/6
Simplify:
9

3.
Common denominators:
3x/x + 3/x
-------------
4x/x + 4/x

Simplify:
(3x+3)/x
-----------
(4x+4)/x

Cancel the x:
(3x+3)/(4x+4)

Factor:
3(x+1)/4(x+1)

Cancel the x+1:
3/4

4.

Factor:
(y-3)(y-1) / (y-3)(y+3)
---------------------------
(y+6)(y+1) / (y+6)(y-3)

Flip the second fraction and multiply:
(y-3)(y-1)(y+6)(y-3)
-------------------------
(y-3)(y+3)(y+6)(y+1)

Cancel like terms:
(y-3)(y-1)
---------------
(y+3)(y+1)

5.
= 1 / 16^3/4
= 1 / 2^3
= 1/8

6.Solve the equation: T = (3a + b)/2 for a.
Multiply by 2:
2T = 3a+b
Subtract b:
3a = 2T-b
Divide by 3:
a = (2T-b)/3

7.Factor completely: x³ + 1
Sum of cubes:
(x+1)(x^2-x+1)

For problems 8 – 11, solve each equation, inequality or system of equations. Choose whatever method you like, but remember to show your methodology along with your answer.

8.(x + 2)/3 = (x – 1)/4
Cross multiply:
3(x-1) = 4(x+2)
Distribute:
3x-3 = 4x+8
Subtract 3x:
-3 = x + 8
Subtract 8:
X = -11

9.
Square both sides:
x-1 = x^2-2x+1
Subtract x-1:
0 = x^2-3x+2
Factor:
0 = (x-2)(x-1)
X = 2 or 1

10.(7x –6)² = 48
Square root:
7x-6 = ± √48
Add 6:
7x = 6 ± √48
Divide by 7:
x = (6 ± √48)/7 = (6 ± 4√3)/7

11.a) 170 is what percent of 20?
170/20 = 8.5 = 850%

b) 20 is what percent of 170?
20/170 = about 0.117647 = about 11.7647%

12.Select the graph that best satisfies the equation: y = x² – 2x – 3 U shape, through (-1, 0) and (3, 0)

(c)

13. Select the equation that best fits the following graph:

Choice (d): y = (x/3)(|x – 4|), since it has a cusp

14.Write a quadratic equation for which the following are solutions for x: 7 and – 3, (x-7)(x+3)
x^2-4x-21

15.Write a quadratic equation for which the following are solutions for x: ± 3i. (x-3i)(x+3i)
x^2+9

Questions 16 through 20 are word problems. Take your time to make sure that your equations fit the words before you start solving them.

16.Hector can shovel show off the sidewalks in three hours (He doesn’t live in Southern California, of course). Oliver can shovel snow off the same sidewalks in 2 hours. How long will it take them to shovel the snow off the sidewalks if they work together?

1/(1/3+1/2)
= 1/(5/6)
= 6/5
6/5 hours = 72 minutes

17.Park rangers catch, tag and then release 140 elk back into a National Park. One month later, they’re able to round up 130 elk, and find that 91 of them have been tagged. Assuming the ratio of tagged elk to the total in the sample that was rounded up is the same as the ratio of all tagged elk to the total elk population in the park, how many elk are in the park? By the way, they’re beautiful animals. I’ve seen them at the Grand Canyon.

91/130 = 140/x
Cross multiply:
91x = 130*140
X = 130*140/91
X = 200
200 elk

18.Staying on the animal theme, a tourist visits the zoo, and is interested in knowing how many birds and lions are on display. The Zookeeper tells him that between...
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