There are 30 students in class
<em><u>Solution:</u></em>
Let "x" be the total number of students in class
Given that,
The number of boys represents 54% of the class
Therefore,
Number of boys = 54 % of total number of students
Number of boys = 54 % of x
![\text{Number of boys } = \frac{54}{100} \times x\\\\\text{Number of boys } = 0.54x](https://tex.z-dn.net/?f=%5Ctext%7BNumber%20of%20boys%20%7D%20%3D%20%5Cfrac%7B54%7D%7B100%7D%20%5Ctimes%20x%5C%5C%5C%5C%5Ctext%7BNumber%20of%20boys%20%7D%20%3D%200.54x)
Given that, There are 14 girls in a class
Therefore,
Number of girls = 14
Thus we get,
Number of boys + number of girls = total number of students
0.54x + 14 =x
x - 0.54x = 14
0.46x = 14
Divide both sides by 0.46
![x = 30.43 \approx 30](https://tex.z-dn.net/?f=x%20%3D%2030.43%20%5Capprox%2030)
Thus there are 30 students in class
Answer:
Equation 5 + 2(3 + 2x) = x + 3(x + 1) has no solution.
Step-by-step explanation:
We are looking at two lines.
4(x + 3) + 2x = 6(x +2)
4x + 12 + 2x = 6x + 12
6x + 12 = 6x + 12
These are two identical lines, with an infinite number of solutions. (All points on the lines are the exactly the same).
5 + 2(3 + 2x) = x + 3(x + 1)
5 + 6 + 4x = x + 3x + 3
4x + 11 = 4x + 3
Both lines have the same gradient but have a different incline with the y axis. By definition, they are parallel to each other and there fore have zero solutions. Equation 5 + 2(3 + 2x) = x + 3(x + 1) has no solution, which is the answer we are looking for.
5(x + 3) + x = 4(x +3) + 3
5x + 15 + x = 4x + 12 + 3
6x + 15 = 4x + 15
These are two different lines with exactly one solution.
4 + 6(2 + x) = 2(3x + 8)
4 + 12 + 6x = 6x + 16
6x + 16 = 6x + 16
These are two identical lines, with an infinite number of solutions. (All points on the lines are the exactly the same).
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N'(-2,2)
G'(-2,-4)
H'(6,-4)