9514 1404 393
Answer:
a) x = -3
b) 1/250
Step-by-step explanation:
The applicable rule of exponents is ...
a^-b = 1/a^b
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a) It is helpful to know that 216 = 6^3.* Then you would realize that ...
If you don't know that, then you can solve the equation using logarithms. Taking the log of both sides, you have ...
x·log(6) = log(1/216)
x = log(1/216)/log(6) = -3
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b)
_____
* This would be on your list of cubes of small integers that you might want to memorize, along with squares of numbers less than 20.
<h3>
Answer:</h3>
- 32 kg of 30% copper
- 48 kg of 55% copper
<h3>
Step-by-step explanation:</h3>
Let x represent the mass of 55% copper alloy that is to be used in the mix. Then 80-x is the mass of 30% copper alloy to be used. The total amount of copper in the mix is then ...
... 0.55x + 0.30(80-x) = 0.45·80
... 0.25x = 12 . . . . . . simplify, subtract 24
... x = 48 . . . . . . . . . divide by the coefficient of x
... 80-x = 32 . . . . . . the mass of 30% copper alloy required
The metalworker should combine 32 kg of 30% copper alloy with 48 kg of 55% copper alloy to make 80 kg of 45% copper alloy.
Answer:
Step-by-step explanation:
Given:
To find: points of intersection of the given lines
Solution:
In substitution method, the system of equations is solved by expressing one variable in terms of another, as a result, removing one variable from an equation.
Put 
in the equation 
![2x+8y=7\\2[\frac{1+2y}{5}]+8y=7\\ 2+4y+40y=35\\44y=35-2\\44y=33\\y=\frac{33}{44}\\ =\frac{3}{4}](https://tex.z-dn.net/?f=2x%2B8y%3D7%5C%5C2%5B%5Cfrac%7B1%2B2y%7D%7B5%7D%5D%2B8y%3D7%5C%5C%202%2B4y%2B40y%3D35%5C%5C44y%3D35-2%5C%5C44y%3D33%5C%5Cy%3D%5Cfrac%7B33%7D%7B44%7D%5C%5C%20%3D%5Cfrac%7B3%7D%7B4%7D)
Put 
in the equation
![x=\frac{1+2y}{5}\\=\frac{1}{5}[1+2(\frac{3}{4})]\\=\frac{1}{5}[1+(\frac{3}{2})]\\\\=\frac{1}{5}(\frac{2+3}{2}) \\\\=\frac{1}{5}(\frac{5}{2})\\\\=\frac{1}{2}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B1%2B2y%7D%7B5%7D%5C%5C%3D%5Cfrac%7B1%7D%7B5%7D%5B1%2B2%28%5Cfrac%7B3%7D%7B4%7D%29%5D%5C%5C%3D%5Cfrac%7B1%7D%7B5%7D%5B1%2B%28%5Cfrac%7B3%7D%7B2%7D%29%5D%5C%5C%5C%5C%3D%5Cfrac%7B1%7D%7B5%7D%28%5Cfrac%7B2%2B3%7D%7B2%7D%29%20%5C%5C%5C%5C%3D%5Cfrac%7B1%7D%7B5%7D%28%5Cfrac%7B5%7D%7B2%7D%29%5C%5C%5C%5C%3D%5Cfrac%7B1%7D%7B2%7D)
Therefore,
A the width is 17.7777778
Steps:
4+5 =9
40÷9= 4.44444444
Width: 4.44444444 times 4 = 17.7777778
Length: 4.44444444 times 5 = 22.2222222
Answer:
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Step-by-step explanation:
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