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Yanka [14]
1 year ago
11

X^2 - 6 x + 9 = 4 root(x^2 - 6 x + 6)​

Mathematics
2 answers:
kkurt [141]1 year ago
7 0
Answer

X1= 3-2 root3 x2= 1 x3=5 x4= 3 +2 root 3
First swap the sides then simplify the equation
Collect like terms
Move all the expression to the left to equal 0
Then collect like terms again
Reorder the terms from ^2 to ^4
Factor the expression
Change the signs
Separate into possible cases
Then sold the equation to equal 0
Then check solutions by subbing them in as x
Then you should have 4 perfect answers

lapo4ka [179]1 year ago
4 0

Answer:

Hello,

Step-by-step explanation:

x^2-6x+9=4\sqrt{x^2-6x+6} \\\\(x-3)^2=4\sqrt{x^2-6x+9-3} \\\\(x-3)^2=4\sqrt{(x-3)^2-3} \\\\Let's\ say\ y=x-3\\\\y^2=4\sqrt{y^2-3} \ squaring\\\\y^4=16(y^2-3)\\y^4-16y^2+48=0\\\Delta=16^2-4*48=64=8^2\\y^2=4\ or\ y^2=12\\\\(y-2)(y+2)=0\ or\ (y+2\sqrt{3} )(y-2\sqrt{3} )=0 \\\\y=2,x=5\ or\\\ y=-2, x=-1\ or\\\ y=-2\sqrt{3},x=3-2\sqrt{3}\ \\or\ y=2\sqrt{3},x=3+2\sqrt{3}\\\\

Verifying:

1) if\ x=-1\ then\\a)\ x^2-6x+9=1+6+9=16\\b)\ 4\sqrt{x^2-6x+6} =4\sqrt{1+6+6} =4\sqrt{13}:\ False\\\\2)if\ x=5\\a)\ x^2-6x+9=25-30+9=4\\b)\ 4\sqrt{x^2-6x+6} =4\sqrt{25-30+6} =4\sqrt{1}=4:\ True\\

3) if\ x=3-2\sqrt{3}\ x^2=21-12\sqrt{3} \\a)\ x^2-6x+9=21-12\sqrt{3}-18+12\sqrt{3}+9=12\\b)\ 4\sqrt{x^2-6x+6} =4\sqrt{21-12\sqrt{3}-18+12\sqrt{3}+6} =4\sqrt{9}=12:\ True\\\\\\4) if\ x=3+2\sqrt{3}\ x^2=21+12\sqrt{3} \\a)\ x^2-6x+9=21+12\sqrt{3}-18-12\sqrt{3}+9=12\\b)\ 4\sqrt{x^2-6x+6} =4\sqrt{21+12\sqrt{3}-18-12\sqrt{3}+6} =4\sqrt{9}=12:\ True\\

Sol={5,3-2√3,3+2√3}

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The interest is a) $7000

b) $17709.73

c) $18672.62

d) $18901.67

What is the formula for simple and compound interest?

Simple interest = (P× r× t)

Compound interest = P(1+r/n)^nt - P

We will find the interest as shown below:

P=$4,000

t=25 years

a) r=7%=0.07

Simple interest = (P× r× t)

= (4000×0.07×25)

= $7000

b) r=7%=0.07

Compound interest = P(1+r)^t - P

= 4000(1+0.07)^25-4000

= $17709.73056

rounding to nearest cents

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c) r=7%=0.07

n=4

Compound interest = P(1+r/n)^nt - P

= 4000(1+0.07/4)^(25*4)-4000

= $18672.62375

rounding to nearest cent

= $18672.62

d) r=7%=0.07

n=12

Compound interest = P(1+r/n)^nt - P

= 4000(1+0.07/12)^(25*12)-4000

= $18901.6728

rounding to nearest cent

= $18901.67

Hence, the interest is a) $7000

b) $17709.73

c) $18672.62

d) $18901.67

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7 0
2 years ago
3.6 (5 x 4) ÷ 3 + 5.0
Yuliya22 [10]

3.6 (5 x 4)  ÷ 3 + 5.0

use the PEMDAS rule

P - parentheses

E - exponents

M - multiplication

D - division

A - addition

S - subtraction

3.6 (5 x 4)  ÷ 3 + 5.0

= 3.6 (20)  ÷ 3 + 5.0

= 72  ÷ 3 + 5.0

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Step-by-step explanation:

Given that:

Area of square parking lot = 12,996 square yards

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