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2 years ago

Which number can each term of the equation be multiplied by to eliminate the fractions before solving?

Mathematics

1 answer:

AVprozaik [17]2 years ago

6 0

Answer:

The correct answer is Option 4: 12

Step-by-step explanation:

Given equation is:

$6-\frac{3}{4}x+\frac{1}{3} = \frac{1}{2}x+5$

We have to find a number that is common multiple of all the denominators or least common divisor

So to find the LCM

The numbers in denominator are: 4,3,2

So,

$4=> 4,8,12,16\\3 => 3,6,9,12,15\\2=> 2,4,6,8,10,12$

It can clearly be seen that 12 is the LCM of all three numbers so the equation will be multiplied with 12 to eliminate the fractions.

$12*6-12*\frac{3}{4}x+12*\frac{1}{3} =12* \frac{1}{2}x+12*5\\72-9x+4 = 6x+60$

Hence,

The correct answer is Option 4: 12

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A trapezoid is a quadrilateral with exactly one pair of what sides.

balu736 [363]

Answer:

parallel

Step-by-step explanation:

it has exactly one pair of parallel sides or sides that will never touch

5 0

3 years ago

A large truck has two fuel tanks, each with a capacity of 150 gallons. Tank 1 is half full, and Tank 2 is empty.

12345 [234]

Answer:

1) $G(t) = 75 + \frac{23}{4}t\\$

2) After 8 minutes delivering fuel the tanks will have 121 gallons of fuel

Step-by-step explanation:

1) For generating the equation we have to take into account that in the tanks there is a initial volume of fuel that corresponds to 75 gallons, as it is stated that tank one is half full. As the capacity for tank 1 is of 150 gallons, half of the tank equals to:

$\frac{150}{2} = 75 gallons$

Now we have to convert the rate of delivery that is expressed as a mixed number to an improper fraction so:

$5\frac{3}{4} = \frac{(5x4)+3}{4} = \frac{23}{4}$

Then the pumping rate is of 23/4 gallons per minute, to get how many gallons are in the tank we just need to multiply this rate by the time in minutes, and as there is an initial volume we have to add it, so we have the following equation:

$G(t) = 75 + \frac{23}{4}t\\$

2) To know how much fuel is in the tank after 8 minutes we have to replace this time in the previous equation so we have

$G(t) = 75 + \frac{23}{4}t\\G(8) = 75 + \frac{23}{4}(8)\\G(8) = 75 + 23(2)\\G(8) = 75 + 46\\G(8) = 121 gallons$

After 8 minutes delivering fuel the tanks will have 121 gallons of fuel

8 0

3 years ago

How do i write proofs like this?

kirill115 [55]

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7 0

3 years ago

What is 2 gallons equally divided into nine

SSSSS [86.1K]

Its a repeating decimal 0.22222222222222222222222

3 0

3 years ago

Read 2 more answers

What expression represents the value of x?

pogonyaev

Answer:

Answer A

Step-by-step explanation:

The Pythagorean formula in the small triangle gives

x² = w² + y²

x = √( w² + y² )

By this answer alone, answer C √( w * y ) is defenately false, because w*y is not w² + y², and therefore this answer can be discarded.

Answer B is also defenately wrong because the area indicated by the square on side z is much bigger then the area indicated by the square on side x.

Supose answer D is right, then

w*z must be equal to w² + y².

But from the big triangle we know that

v² = y² + z² , so y² = v² - z²

Since w*z is not v² - z², answer D must be wrong also.

The only answer which we can choose from is answer A, which must be the right answer since it is the only possibility left...

EXTRA

We have already deduced that answer A must be the right one, so we have already finished this question.

How ever, if answer A is right, then x = √( w(w + z) )

x = √( w² + wz )

From Pythagoras we know the next line to be true:

x = √( w² + y² )

From this, w*w = w² , no problem there, but then w*z must be equal to y². This is a problem for me at least...

At this moment I am unable to prove that w*z = y² but this seems at least plausible...

I leave it for now.

6 0

3 years ago