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Answer:
Second : 1/6 x + 47
Third : 1 2/3 x + 35 - 1 1/2 x + 12
Fourth : 5 (1/3x) + (5) (7) - (3) (1/2x) + (3) (4)
Step-by-step explanation:
I would start by expanding the expression, showing each step. Then, simplify by collecting like terms.
To expand, you multiply the term outside of the brackets by each term inside the brackets.
5(1/3x + 7) - 3(1/2x - 4)
= 5(1/3x) + (5)(7) - (3)(1/2x) + (3)(4) Showing how to expand
= 5/3x + 35 - 3/2x + 12 Simplified above step by multiplying
= 5/3x - 3/2x + 47 Collected like terms (35 + 12 = 47)
= 10/6x - 9/6x + 47 Change fractions to the common denominator 6
= + 47 Combine fractions with common denominator
= 1/6x + 47 Fully expanded
See which options match the steps I took to expand the original expression.
The second step is the same as option 4.
The last step is the same as option 2.
I bolded those steps that are the same.
Some options use mixed fractions (whole numbers and fractions).
From the third step, I will convert the improper fractions to mixed fractions.
5/3x + 35 - 3/2x + 12
= 1 2/3x + 35 - 1 1/2x + 12
This is the same as option 3.
On the left side, 5 goes into 3 ONE time. The ONE becomes the whole number. After 5 goes into 3, there is 2 left, which becomes the numerator.
On the left side, 3 goes into 2 ONE time. The ONE becomes the whole number. The remainder is 1, which becomes the numerator.
Answer/Step-by-step explanation:
Quotient is simply the ratio of the first numerator to the second numerator:
Let's are two fractions in same terms.
Thus, {Divided by a fraction is equal to multiplied by its reciprocal}
=
Quotient is simply the quotient of their numerators.
Example could be:
2 is first numerator and 3 is the second numerator.
<u><em>~lenvy~</em></u>
Answer:
The number of subscribers in 2008 is 110,845,988
Step-by-step explanation:
The number of cell phone subscribers in Arlington, in t years after 1985, can be modeled by the following equation.
And which N(0) is the number of subscribers in 1985 and r is the rate it increases per year, as a decimal.
In 1985, there were 285 cell phone subscribers in Arlington.
This means that
The number of subscribers increased by 75% per year since 1985.
This means that
So
Find the number of subscribers in 2008.
2008 is 2008-1985 = 23 years after 1985. So we have to find N(23).
The number of subscribers in 2008 is 110,845,988
Answer:
3.189 seconds
Step-by-step explanation:
You want f(t) = 0, so ...
0 = -16t^2 +13.4t +120
0 = t^2 -0.8375t -7.5 . . . . divide by -16
0 = (t^2 -0.8375t +0.41875^2) -7.5 -0.41875^2 . . . . complete the square*
0 = (t -0.41875)^2 -7.6753515625 . . . . write as a square
√7.6753515625 = t -0.41875 . . . . . . . . add 7.67... and take positive root
t = 0.41875 +√7.6753515625 ≈ 3.189192 . . . . add 0.41875
It will take the rock about 3.189 seconds to hit the ground.
_____
* We complete the square by adding the square of half the coefficient of the linear term (= (-0.8375/2)^2) inside parentheses and subtracting the same amount outside parentheses. This gives a form inside parentheses that is ...
(t^2 -2at +a^2) = (t -a)^2
Completing the square is complicated a little bit by a leading coefficient that is not 1. That is why we divided by -16 first.
_____
<em>Comment on the question</em>
We note that the rock "falls" from the 120 foot high balcony by first traveling upward at a rate of 13.4 feet per second. We also note that the height function is written f(x), but uses t as the variable. That is, it should be f(t) = ...
