Answer:
The cost would be same after 3 months.
Step-by-step explanation:
Given that:
Charges of first company;
Sign up fee = $76
Per month charges = $40
Let,
x be the number of months
y be the total cost.
y = 40x + 76 Eqn 1
Charges of second company;
Sign up fee = $136
Per month charges = $20
y = 20x + 136 Eqn 2
For same cost,
Eqn 1 = Eqn 2
40x + 76 = 20x + 136
40x-20x = 136 - 76
20x = 60
Dividing both sides by 20
![\frac{20x}{20}=\frac{60}{20}\\x=3](https://tex.z-dn.net/?f=%5Cfrac%7B20x%7D%7B20%7D%3D%5Cfrac%7B60%7D%7B20%7D%5C%5Cx%3D3)
Hence,
The cost would be same after 3 months.
For this case we have the following data:
The original dimensions of the drawing are:
If the copier zoom is at 120%, we can find the new dimensions of the drawing by making a rule of three:
Width:
3 ----------> 100%
x ----------> 120%
Where x represents the new width of the drawing:
![x=\frac{(120*3)}{100}\\x=3.6cm](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B%28120%2A3%29%7D%7B100%7D%5C%5Cx%3D3.6cm)
Long:
5 ----------> 100%
y ----------> 120%
Where y represents the new long of the drawing:
![y=\frac{(120*5)}{100}\\y=6cm](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B%28120%2A5%29%7D%7B100%7D%5C%5Cy%3D6cm)
Thus, the new dimensions are 3.6 cm wide and 6 cm long
Answer:
the longer dimension of the new drawing is 6cm
Answer:
![=\frac{64}{3v}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B64%7D%7B3v%7D)
Step-by-step explanation:
One is given the following equation:
![\frac{(4v^-^3)^3}{3v^-^8}](https://tex.z-dn.net/?f=%5Cfrac%7B%284v%5E-%5E3%29%5E3%7D%7B3v%5E-%5E8%7D)
Simplify the numerator, remember to raise every number inside the parenthesis to the exponent outside of the parenthesis. Bear in mind, an exponent raised to another exponent is equal to the exponent times the exponent it is raised to. Then simplify by multiplying the number by itself the number of times that the exponent indicates.
![\frac{(4v^-^3)^3}{3v^-^8}](https://tex.z-dn.net/?f=%5Cfrac%7B%284v%5E-%5E3%29%5E3%7D%7B3v%5E-%5E8%7D)
![=\frac{4^3(v^-^3)^3}{3v^-^8}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B4%5E3%28v%5E-%5E3%29%5E3%7D%7B3v%5E-%5E8%7D)
![=\frac{4^3v^-^9}{3v^-^8}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B4%5E3v%5E-%5E9%7D%7B3v%5E-%5E8%7D)
![=\frac{64v^-^9}{3v^-^8}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B64v%5E-%5E9%7D%7B3v%5E-%5E8%7D)
Bring the variable (v) in the denominator (value under the fraction bar) to the numerator (value ontop of the fraction bar) by multiplying its exponent by (-1). This can be done simply because all operations in this equation are multiplication or division, remember, an exponent is another form of multiplication.
![=\frac{64v^-^9}{3v^-^8}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B64v%5E-%5E9%7D%7B3v%5E-%5E8%7D)
![=\frac{(64v^-^9)(v^(^-^1^)^(^-^8^))}{3}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B%2864v%5E-%5E9%29%28v%5E%28%5E-%5E1%5E%29%5E%28%5E-%5E8%5E%29%29%7D%7B3%7D)
Simplify, remember, multiplying two numbers with the same base that have an exponent is the same as adding the two exponents,
![=\frac{(64v^-^9)(v^(^-^1^)^(^-^8^))}{3}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B%2864v%5E-%5E9%29%28v%5E%28%5E-%5E1%5E%29%5E%28%5E-%5E8%5E%29%29%7D%7B3%7D)
![=\frac{(64v^-^9)(v^8)}{3}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B%2864v%5E-%5E9%29%28v%5E8%29%7D%7B3%7D)
![=\frac{64v^-^9^+^8)}{3}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B64v%5E-%5E9%5E%2B%5E8%29%7D%7B3%7D)
![=\frac{64v^-^1}{3}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B64v%5E-%5E1%7D%7B3%7D)
Now bring the variable to the denominator so that there are no negative exponents. Use a similar technique that was used to bring variables with exponents to the numerator.
![=\frac{64v^-^1}{3}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B64v%5E-%5E1%7D%7B3%7D)
![=\frac{64}{3(v^(^-^1^)^(^-^1^))}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B64%7D%7B3%28v%5E%28%5E-%5E1%5E%29%5E%28%5E-%5E1%5E%29%29%7D)
![=\frac{64}{3v^1}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B64%7D%7B3v%5E1%7D)
![=\frac{64}{3v}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B64%7D%7B3v%7D)