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Fiesta28 [93]
2 years ago
13

Find the value of y...​

Mathematics
1 answer:
soldier1979 [14.2K]2 years ago
5 0

Answer:

y=0

Step-by-step explanation:

Rewrite Evaluate Powers:

33^{2y-1}+3^{-1}+2*3^{y}*3^{-1}=1

Calculate:

(3^{y})^{2}*\frac{1}{3} +2*3^{y}*\frac{1}{3}=1

Solve using substitution:

(3^{y})^{2}*\frac{1}{3} +\frac{2}{3} *3^{y}=1     t=3^{y}

Solve the equation for t:

t^{2}*\frac{1}{3}+\frac{2}{3}t=1

t=-3

t=1

Substitute back to t=3^y

3^y=-3

3^y=1

y∉R

3^{y}=1

y=0

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Perform the following operations s and prove closure. Show your work.
nadezda [96]

Answer:

1. \frac{x}{x+3}+\frac{x+2}{x+5} = \frac{2x^2+10x+6}{(x+3)(x+5)}\\

2. \frac{x+4}{x^2+5x+6}*\frac{x+3}{x^2-16} = \frac{1}{(x+2)(x-4)}

3. \frac{2}{x^2-9}-\frac{3x}{x^2-5x+6} = \frac{-3x^2-7x-4}{(x+3)(x-3)(x-2)}

4. \frac{x+4}{x^2-5x+6}\div\frac{x^2-16}{x+3} = \frac{1}{(x-2)(x-4)}

Step-by-step explanation:

1. \frac{x}{x+3}+\frac{x+2}{x+5}

Taking LCM of (x+3) and (x+5) which is: (x+3)(x+5)

=\frac{x(x+5)+(x+2)(x+3)}{(x+3)(x+5)}\\=\frac{x^2+5x+(x)(x+3)+2(x+3)}{(x+3)(x+5)} \\=\frac{x^2+5x+x^2+3x+2x+6}{(x+3)(x+5)} \\=\frac{x^2+x^2+5x+3x+2x+6}{(x+3)(x+5)} \\=\frac{2x^2+10x+6}{(x+3)(x+5)}\\

Prove closure: The value of x≠-3 and x≠-5 because if there values are -3 and -5 then the denominator will be zero.

2. \frac{x+4}{x^2+5x+6}*\frac{x+3}{x^2-16}

Factors of x^2-16 = (x)^2 -(4)^2 = (x-4)(x+4)

Factors of x^2+5x+6 = x^2+3x+2x+6 = x(x+3)+2(x+3) =(x+2)(x+3)

Putting factors

=\frac{x+4}{(x+3)(x+2)}*\frac{x+3}{(x-4)(x+4)}\\\\=\frac{1}{(x+2)(x-4)}

Prove closure: The value of x≠-2 and x≠4 because if there values are -2 and 4 then the denominator will be zero.

3. \frac{2}{x^2-9}-\frac{3x}{x^2-5x+6}

Factors of x^2-9 = (x)^2-(3)^2 = (x-3)(x+3)

Factors of x^2-5x+6 = x^2-2x-3x+6 = x(x-2)+3(x-2) =(x-2)(x+3)

Putting factors

\frac{2}{(x+3)(x-3)}-\frac{3x}{(x+3)(x-2)}

Taking LCM of (x-3)(x+3) and (x-2)(x+3) we get (x-3)(x+3)(x-2)

\frac{2(x-2)-3x(x+3)(x-3)}{(x+3)(x-3)(x-2)}

=\frac{2(x-2)-3x(x+3)}{(x+3)(x-3)(x-2)}\\=\frac{2x-4-3x^2-9x}{(x+3)(x-3)(x-2)}\\=\frac{-3x^2-9x+2x-4}{(x+3)(x-3)(x-2)}\\=\frac{-3x^2-7x-4}{(x+3)(x-3)(x-2)}

Prove closure: The value of x≠3 and x≠-3 and x≠2 because if there values are -3,3 and 2 then the denominator will be zero.

4. \frac{x+4}{x^2-5x+6}\div\frac{x^2-16}{x+3}

Factors of x^2-5x+6 = x^2-3x-2x+6 = x(x-3)-2(x-3) = (x-2)(x-3)

Factors of x^2-16 = (x)^2 -(4)^2 = (x-4)(x+4)

\frac{x+4}{(x-2)(x+3)}\div\frac{(x-4)(x+4)}{x+3}

Converting ÷ sign into multiplication we will take reciprocal of the second term

=\frac{x+4}{(x-2)(x+3)}*\frac{x+3}{(x-4)(x+4)}\\=\frac{1}{(x-2)(x-4)}

Prove Closure: The value of x≠2 and x≠4 because if there values are 2 and 4 then the denominator will be zero.

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3 years ago
Is it ture equivalent decimals are decimals that have the same value
tester [92]
Yes that statement is true
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How many 1/4 pound bags of candy can be made from box containing 12 1/2 POUNDS
nikitadnepr [17]

Answer:

50

Step-by-step explanation:

12.5*4=50

5 0
3 years ago
3) This table represents the price of milk for various years. What is the percent of increase from 1980 to 2010 1 Year Price 198
kupik [55]

Answer:

124.375% increase

Step-by-step explanation:

From 1980 to 2010 there was a 124.375% increase

6 0
3 years ago
Express ((-x^4)+4x+87)/(x+1) in the form q(x)+((r(x)/b(x))
ryzh [129]

Answer:

-x^3+x^2-x+5+\dfrac{82}{x+1}

Where q(x)=-x^3+x^2-x+5, r(x)=82, and b(x)=x+1

Step-by-step explanation:

See the attached image for the long division I did to get this answer!

4 0
3 years ago
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