MayFlowers
12.11.2020 •
Mathematics
After simplifying the following expression, the coefficient of the m^2 term will be .
6mn^2 + 3m^2 + 16m^2 - 6m^2 - 5nm^2
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Ответ:
Answers:
After simplifying the following expression, the coefficient of the m^2 term will be 13
The solution is 13m^2 + 6mn^2 - 5nm^2
Explanation:
Highlight all the terms that have m^2 in them and nothing else (so that means no variables of n or n^2)
You should highlight 3m^2, 16m^2 and -6m^2 as the three terms.
The coefficients 3, 16 and -6 combine to 3+16-6 = 13
Meaning that 3m^2+16m^2-6m^2 = 13m^2
There are no other like terms that pair up.
The 6mn^2 and -5nm^2 are different because the exponent 2 is over a different letter each time. Put another way: mn^2 is not the same as nm^2
So we cannot combine 6mn^2-5nm^2. We leave it as is.
Overall, the entire expression simplifies to 13m^2 + 6mn^2 - 5nm^2
Ответ:
9m^3 of soil with 50% clay and 2m^3 of soil with 28% clay is required
Step-by-step explanation:
Let x represent the quantity of the soil containing 50% clay that you would use.
Let y represent the quantity of the soil containing 28% clay that you would use.
To build the garden of your dreams you need 11 m^3 of soil.
x + y = 11 - - - - - - - - -1
Since the soil must contain 46% clay, the total amount of clay required is 46/100 × 11 = 5.06 m^3.
you have two types of soil you can combine to achieve this: soil with 50% clay and soil with 28% clay. This means that the quantity of both soils required to achieve 5.06 m^3 will be
0.5x + 0.28y = 5.06 - - - - - - - -2
Substituting x = 11 - y into equation 1, it becomes
0.5(11 - y) + 0.28y = 5.06
5.5 - 0.5y + 0.28y = 5.06
- 0.5y + 0.28y = 5.06 - 5.5
- 0.22y = - 0.44
y = - 0.44/ -0.22 = 2
Substituting y = 2 into x = 11 - y, it becomes
x = 11 - 2 = 9