Solve for x:
5 - sqrt(x) + sqrt(3 x - 11) = 6
Subtract 5 from both sides:
sqrt(3 x - 11) - sqrt(x) = 1
(sqrt(3 x - 11) - sqrt(x))^2 = -11 + 4 x - 2 sqrt(x) sqrt(3 x - 11) = -11 + 4 x - 2 sqrt(x (3 x - 11)) = 1:
-11 + 4 x - 2 sqrt(x (3 x - 11)) = 1
Subtract 4 x - 11 from both sides:
-2 sqrt(x (3 x - 11)) = 12 - 4 x
Raise both sides to the power of two:
4 x (3 x - 11) = (12 - 4 x)^2
Expand out terms of the left hand side:
12 x^2 - 44 x = (12 - 4 x)^2
Expand out terms of the right hand side:
12 x^2 - 44 x = 16 x^2 - 96 x + 144
Subtract 16 x^2 - 96 x + 144 from both sides:
-4 x^2 + 52 x - 144 = 0
The left hand side factors into a product with three terms:
-4 (x - 9) (x - 4) = 0
Divide both sides by -4:
(x - 9) (x - 4) = 0
Split into two equations:
x - 9 = 0 or x - 4 = 0
Add 9 to both sides:
x = 9 or x - 4 = 0
Add 4 to both sides:
x = 9 or x = 4
5 - sqrt(x) + sqrt(3 x - 11) ⇒ 5 - sqrt(4) + sqrt(3×4 - 11) = 4:
So this solution is incorrect
5 - sqrt(x) + sqrt(3 x - 11) ⇒ 5 - sqrt(9) + sqrt(3×9 - 11) = 6:
So this solution is correct
The solution is:
Answer: x = 9
Convert 3 6/2 to an improper fraction so: 12/2
convert 2 4/5 to 14/5
multiply the numerators of the improper fractions so 12*14, which is 168.
multiple the denominators so 2*5, which is 10.
the new fraction is 168/10, so you divide 168 divided by 10, which is 16.8, or 16 4/5.
Answer:
The number of boys last year will be 50 boys
Step-by-step explanation:
330 members with 240 adults
The number of children will be;
330-240 = 90
2/3 of 90 are boys
= 2/3 * 90 = 60 boys
Number of girls is 90-60 = 30
Ratio of adults:boys:girls
= 240:60:30
divide through by 30
= 8:2:1
b) A year ago, there were 200 adults but the ratio still remains same
Let the number of girls be x, the number of boys will be 2x
Thus, total number is 200 + x + 2x = 200 + 3x
Total ratio is 8 + 2 + 1 = 11
mathematically;
8/11 * (200 + 3x) = 200
8(200 + 3x) = 11(200)
1600 + 24x = 2200
24x = 2200-1600
24x = 600
x = 600/24
x = 25
So the number of boys will be 25 * 2 = 50
B because plants are often identical to or a clone of their parent and one parent is involved.
