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kenny6666 [7]
3 years ago
9

Finding the roots by completing the square

Mathematics
1 answer:
Andrej [43]3 years ago
6 0
For y=x^2-6x-11

complete the square

so roots
set y=0
0=x^2-6x-11

group x terms
0=(x^2-6x)-11
take 1/2 of linear coefient (-6) and square it
-6/2=-3, (-3)^2=9
add positive and neative to inside of parenthasees
0=(x^2-6x+9-9)-11
complete square
0=((x-3)^2-9)-11
expand
0=(x-3)^2-9-11
0=(x-3)^2-20
add 20 to both sides
20=(x-3)^2
sqrt both sides
remember positive and negative roots

+/-2√5=x-3
add 3 to both sides
3+/-2√5=x

so
x=3+2√5 and 3-2√5
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If mike Kevin and Dustin all collect baseball cards and Dustin and Kevin has 81 altogether and Dustin and Mike have 96 altogethe
jek_recluse [69]

Answer:

Dustin has 42 cards.

Mike has 54 cards.

Kevin has 39 cards

Step-by-step explanation:

subtract (Dustin + Mike) – (Dustin + Kevin) or 96 – 81.

Think of it like....

Dustin + Mike – Dustin – Kevin

Dustin – Dustin + Mike – Kevin

Mike – Kevin

Since 96 – 81 = 15, Mike – Kevin = 15

Add (Kevin + Mike) + (Mike – Kevin) or 93 + 15.

Think of it like...

Kevin + Mike + Mike – Kevin

Kevin – Kevin + Mike + Mike

Mike + Mike

Since 93 + 15 = 108, Mike + Mike = 108. If you divide, Mike had 54 cards. That means that you can find Kevin’s cards by using 93 – 54 or 39. You can then find Dustin’s cards by using 81 – 39 = 42.

Check:

Dustin’s cards + Kevin’s cards = 42 + 39 = 81

Dustin’s cards + Mike’s cards = 42 + 54 = 96

Mike’s cards + Kevin’s cards = 54 + 39 = 93

5 0
3 years ago
On one side of a football stadium are 30 suites on the circle level. Fourteen of the suites have 24 seats each, and the rest hav
hram777 [196]
<span>The simplest form of a fraction occurs when the numerator and denominator cannot get any smaller (while still being integers)

In the stadium there are 30 suites.

14 suites.............24 seats
16 suites..............18 seats

The suites with 24 seats are 14 out of 30 which can be represented as 14/30.

However, the simplest fraction would be 

  7*2        7
------- = ------ 
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This is why Tyler is incorrect</span>
5 0
3 years ago
Sarah's grape vine grew 15 inches in 6 weeks, write an equation to represent its growth after x weeks
mixer [17]
6x = 15

I apologize if this is wrong!
5 0
3 years ago
What is the exact volume of the cylinder? height 9 in. width 6 in.
boyakko [2]
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3 0
3 years ago
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How many different ways can 13 questions on true-false test be answered if a student answers every question?
Darya [45]
Each question has 2 possible answers.

There are 13 questions.

Number of different ways = 2^{13} = 8192

Answer: There are 8192 different ways.
4 0
3 years ago
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