Prime Factorization = Divide by factors that are prime number
147 ÷ 3 = 49
49 ÷ 7 = 7
7 ÷ 7 = 1
147 = 3 x 7 x 7
147 = 3 x 7²
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Answer: 147 = 3 x 7²
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Answer: 4/12
Step-by-step explanation: 4 over 12
Let x, y, z be the number of hours that Tom spent in service in Salvation Army, Red Cross, and Rescue Mission, respectively. From the statement above, the sum of the numbers should be 100.
x + y + z = 100
The equations that can be derived from the given and the assigned variables,
y = x + 19
z = y + 8
Expressing the times in terms of variable x,
y = x + 19
z = (x + 19) + 8 = x + 27
Solving for the value of x,
x + (x + 19) + (x + 27) = 100
The value of x from the equation is 18.
y = 18 + 19 = 37
z = 18 + 27 = 45
The number of hours he spent in three charities are 18, 37, and 45, respectively.
A revolution is once around the outside measure of the tire. This is also known as the circumference of a circle. The circumference of this tire is found in the formula
where r is the radius of the tire and pi is given as the fraction equivalent 22/7. If we fill in the formula accordingly, we have
and the circumference is . This means for us that the tire travels a total of 88/7 feet in 1 revolution. If the tire travels 8,800 feet in one minute, we need to find out how moany revolutions this is equal to. We find this out by dividing 8,800 by 88/7. Doing this looks like this:
.
Remember that when we divide fractions, we bring up the bottom fraction and flip it to multiply. That means that the tire makes 700 revolutions in 1 minute. In 3 minutes it makes 700 times 3 which is 2100 revolutions.
We have 3⁴ = 81, so we can factorize this as a difference of squares twice:
Depending on the precise definition of "completely" in this context, you can go a bit further and factorize as yet another difference of squares:
And if you're working over the field of complex numbers, you can go even further. For instance,
But I think you'd be fine stopping at the first result,