Shannon was born on 04/02/2004. How many eight-digit codes could she make using the digits in her birthday?
1 answer:
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The volume of a cube with side length equal to x, is 
,
thus, the volume of a cube shaped box, whose side length is (5a+4b) is :
,
The volume is already expressed in terms of a and b, but we can expand the expression
, as follows:
![(5a+4b)^{3} =(5a+4b)(5a+4b)^{2}= (5a+4b)[ (5a)^{2}+2(5a)(4b)+ (4b)^{2}]](https://tex.z-dn.net/?f=%285a%2B4b%29%5E%7B3%7D%20%3D%285a%2B4b%29%285a%2B4b%29%5E%7B2%7D%3D%20%285a%2B4b%29%5B%20%285a%29%5E%7B2%7D%2B2%285a%29%284b%29%2B%20%284b%29%5E%7B2%7D%5D)
![=(5a+4b)[ 25a^{2}+40ab+ 16b^{2}]](https://tex.z-dn.net/?f=%3D%285a%2B4b%29%5B%2025a%5E%7B2%7D%2B40ab%2B%2016b%5E%7B2%7D%5D)
![=(5a)[ 25a^{2}+40ab+ 16b^{2}]+(4b)[ 25a^{2}+40ab+ 16b^{2}]](https://tex.z-dn.net/?f=%3D%285a%29%5B%2025a%5E%7B2%7D%2B40ab%2B%2016b%5E%7B2%7D%5D%2B%284b%29%5B%2025a%5E%7B2%7D%2B40ab%2B%2016b%5E%7B2%7D%5D)
Answer:
,
or
thus, the volume of a cube shaped box, whose side length is (5a+4b) is :
The volume is already expressed in terms of a and b, but we can expand the expression
Answer:
or
In this question, they gave you the system of equations. You just need to use the two of them.
We want to find the m or the number of the multiple-choice questions. So we need to turn our last equation in the form of 'm's by translating the 'f's into 'm's.
If we know the m form of f, we can convert the second equation and find the answer:
Plug in the m value of f:
Distribute the 5:
Subtract -75 from both sides:
Combine like terms:
Divide both sides by -2:
So, we learned that the number of the multiple-choice questions is 12.
We want to find the m or the number of the multiple-choice questions. So we need to turn our last equation in the form of 'm's by translating the 'f's into 'm's.
If we know the m form of f, we can convert the second equation and find the answer:
Plug in the m value of f:
Distribute the 5:
Subtract -75 from both sides:
Combine like terms:
Divide both sides by -2:
So, we learned that the number of the multiple-choice questions is 12.
Answer:
The price of one pound of coffee is 32 pesos
The price of one pound of sugar is 7 pesos
Step-by-step explanation:
The question in English is
6 pounds of coffee and 5 pounds of sugar cost 227 pesos and 5 pounds of coffee and 4 pounds of sugar (at the same prices) cost 188 pesos Find the price of one pound of coffee and one pound of sugar.
Let
x-----> the price of one pound of coffee
y-----> the price of one pound of sugar
we know that
6x+5y=227 -----> equation A
5x+4y=188 ----> equation B
Solve the system of equations by graphing
Remember that the solution of the system of equations is the intersection point both graphs
The solution is the point (32,7)
see the attached figure
therefore
The price of one pound of coffee is 32 pesos
The price of one pound of sugar is 7 pesos
