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yulyashka [42]
3 years ago
8

Theo can paint a fence three times as fast as his sister can. Working together, they can paint a fence in 9 hours. How many hour

s would it take Theo’s sister to paint the fence by herself?
Mathematics
1 answer:
Deffense [45]3 years ago
8 0

Answer:

12 hours

Step-by-step explanation:

Let Theo's siste can paint a fence in x times

Given.

Theo can paint a fence three times as fast as his sister can. Working together, they can paint a fence in 9 hours.

\frac{1}{x}+\frac{1}{3x} =\frac{1}{9}\\\frac{3+1}{3x} =\frac{1}{9} \\\frac{4}{3x}=\frac{1}{9}

Apply cross multiplication

x=\frac{9\times 4}{3}\\x=\frac{36}{3} \\x=12hours

Theo’s sister to paint the fence in 12 hours.

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Given the system of equations:
uranmaximum [27]

Answer:

x=4

y=2

Step-by-step explanation:

2x+2y=12

x−y=2

​In order to solve by elimination, coefficients of one of the variables must be the same in both equations so that the variable will cancel out when one equation is subtracted from the other.

2x+2y=12,x−y=2

To make 2x and x equal, multiply all terms on each side of the first equation by 1 and all terms on each side of the second by 2.

2x+2y=12,2x+2(−1)y=2×2

Simplify.

2x+2y=12,2x−2y=4

Subtract 2x−2y=4 from 2x+2y=12 by subtracting like terms on each side of the equal sign.

2x−2x+2y+2y=12−4

Add 2x to −2x. Terms 2x and −2x cancel out, leaving an equation with only one variable that can be solved.

2y+2y=12−4

Add 2y to 2y.

4y=12−4

Add 12 to −4.

4y=8

Divide both sides by 4.

y=2

Substitute 2 for y in x−y=2. Because the resulting equation contains only one variable, you can solve for x directly.

x−2=2

Add 2 to both sides of the equation.

x=4

The system is now solved.

x=4,y=2

Correct choice is B) x=4.

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2 years ago
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Y=log x + 2 <br>how can I solve it
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3 years ago
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Ostrovityanka [42]

Answer:

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Step-by-step explanation:

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4 0
2 years ago
Suppose you have a light bulb that emits 50 watts of visible light. (Note: This is not the case for a standard 50-watt light bul
natali 33 [55]

Answer:

0.049168726 light-years

Step-by-step explanation:

The apparent brightness of a star is

\bf B=\displaystyle\frac{L}{4\pi d^2}

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<em>L = luminosity of the star (related to the Sun) </em>

<em>d = distance in ly (light-years) </em>

The luminosity of Alpha Centauri A is 1.519 and its distance is 4.37 ly.

Hence the apparent brightness of  Alpha Centauri A is

\bf B=\displaystyle\frac{1.519}{4\pi (4.37)^2}=0.006329728

According to the inverse square law for light intensity

\bf \displaystyle\frac{I_1}{I_2}=\displaystyle\frac{d_2^2}{d_1^2}

where

\bf I_1= light intensity at distance \bf d_1  

\bf I_2= light intensity at distance \bf d_2  

Let \bf d_2  be the distance we would have to place the 50-watt bulb, then replacing in the formula

\bf \displaystyle\frac{0.006329728}{50}=\displaystyle\frac{d_2^2}{(4.37)^2}\Rightarrow\\\\\Rightarrow d_2^2=\displaystyle\frac{0.006329728*(4.37)^2}{50}\Rightarrow d_2^2=0.002417564\Rightarrow\\\\\Rightarrow d_2=\sqrt{0.002417564}=\boxed{0.049168726\;ly}

Remark: It is worth noticing that Alpha Centauri A, though is the nearest star to the Sun, is not visible to the naked eye.

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Answer:THXXXXXXXSSSSS FOR THE POINTS

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