I'm begging 100 ! i need answers karen has been working on her math homework for a very long time. dakota asked about the methods karen was using to solve each equation. part i: evaluate take a look at karen's work and then show her a more efficient way of finding each solution. part ii: compare and contrast choose two of the equations to compare and contrast problem-solving strategies and solutions. did karen get the correct answers? why do you think it took her over two hours?

Well what you do is look at her answer then read part one and then  explain your answer and do the following :)

Problem 1

2x² = 200

/2        /2     divide both sides by 2

x² = 100

√      √        get square root of both sides

x = + or - 10

Problem 2  easier to factor

x² - 4x -5

what times to -5 and adds to -4?  -5 and 1

(x-5) (x+1) = 0

x = 5 and -1

Problem 3 Is a difference of squares

x² -144

diff of squares factor easily

(x+12)(x-12)

x = -12, +12

Problem 4 use radical

(x-4)² = 25

√          √   square root each side

x-4  = + -  5

+ 4        + 4   add 4 to both sides

x  = + 5 + 4  and -5 +4

x = 9 and -1

Problem 5 factor

x² -16x + 64 = 0

what times to +64 and adds to -16? -8 and -8

x = 8

Part 2

Karen got the right answers but did so much more work than necessary.

on number one by dividing out the coefficient 2 you notice you have two squares so you can square root.  On problem 2 you should always try factoring before completing the square of quadratic formula

x = 10.1

step-by-step explanation:

all of the angles of a tirangle add up to 180º

180 - 65 = 115 (since we already know the value of one angle)

(2x + 7) + (8x + 7) = 115

(combins like terms) 10x + 14 = 115

(isolate the variable subtract 14 from both sides): 10x = 101

(find the variable divide both sides by 10): x = 101/10

x = 10.1