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3 years ago

Write 0.126126126... as a fraction

Mathematics

1 answer:

Alchen [17]3 years ago

4 0

Answer:

x = 126/999

Step-by-step explanation:

Let x = .126126126 repeating

Multiply each side by 1000

1000x = 126.126126126 repeating

subtract the first equation from the second

1000x = 126.126126126 repeating

- x = .126126126 repeating

999x = 126

Divide each side by 999

999x/999 = 126/999

x = 126/999

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Farmer Jones owns a triangular plece of land.

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Write 30x3+5x in factored form.

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2 years ago

A cash box contains $74 made up of quarters, half-dollars, and one-dollar

Strike441 [17]

Answer:

25 one-dollar coins, 16 half-dollar coins, and 164 quarters

Step-by-step explanation:

First, set up equations based on the information given:

$0.25q+0.50h+1.00d=74$

$\displaystyle{h=\frac{3}{5}d+1}$

$q=4(d+h)$

Then, substitute q in the first equation with the expression from the third equation:

$0.25[4(d+h)]+0.50h+1.00d=74\\1d+1h+0.50h+1.00d=74\\2d+1.5h=74$

Next, substitute h in that equation with the expression from the second equation:

$\displaystyle{2d+1.5(\frac{3}{5}d+1)=74}$

$2d+0.9d+1.5=74\\2.9d+1.5=74$

Solve for d, the number of one-dollar coins:

$2.9d+1.5=74\\2.9d=72.5\\d=25$

Substitute 25 for d in the second equation to find h, the number of half-dollar coins:

$\displaystyle{h=\frac{3}{5}d+1}$

$\displaystyle{h=\frac{3}{5}(25)+1}$

$h=15+1\\h=16$

Substitute 25 for d and 16 for h in the third equation to find q, the number of quarters:

$q=4(d+h)\\q=4(25+16)\\q=4(41)\\q=164$

Then, verify that the coins total $74:

$0.25(164)+0.50(16)+1.00(25)=74\\41+8+25=74\\74=74\\\text{Check.}$

Next, verify that the number of half-dollar coins is one more than three-fifths of the number of one-dollar coins:

$\displaystyle{h=\frac{3}{5}d+1}$

$\displaystyle{16=\frac{3}{5}(25)+1}$

$16 = 15 + 1\\16 = 16\\\text{Check.}$

Finally, verify that the number of quarters is four times the number one-dollar and half-dollar coins together:

$q=4(d+h)\\164=4(25+16)\\164=4(41)\\164=164\\\text{Check.}$

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3 years ago

One of two complementary angles measures 30 degrees more than three times the other. Find each angle.

Leviafan [203]

The two complementary angles are:

95° and 15°

Step-by-step explanation:

Let x be one angle

then the other angle will be 90-x

As the sum of complementary angles is 90

So,

then according to statement

$x = 3(90-x)+30\\x = 270-3x +30\\x = 300-3x\\x+3x = 300\\4x = 300\\x = \frac{300}[4}\\x = 75\\and\\90 -x = 90 - 75 = 15$

The two complementary angles are:

95° and 15°

Keywords: Angles, triangles

Learn more about angles at:

#LearnwithBrainly

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2 years ago

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Kay [80]

From least to greatest
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3 years ago

Write 0.126126126... as a fraction​

Write 0.126126126... as a fraction