Answer:
y = -2x
Step-by-step explanation:
For direct variation: y = kx, where k is the constant of proportionality.
Given that Y equals -12 when x equals 6, we have -12 = k(6). Solve this for k by dividing both sides by 6:
k = -12/6 => k = -2
Then the "direct variation equation" here is y = -2x.
Answer:
The number of liters of 25% acid solution = x = 160 liters
The number of liters of 40% acid solution = y = 80 liters
Step-by-step explanation:
Let us represent:
The number of liters of 25% acid solution = x
The number of liters of 40% acid solution = y
Our system of Equations =
x + y = 240 liters....... Equation 1
x = 240 - y
A 25% acid solution must be added to a 40% solution to get 240 liters of 30% acid solution.
25% × x + 40% × y = 240 liters × 30%
0.25x+ 0.4y = 72...... Equation 2
We substitute 240 - y for x in Equation 2
0.25(240 - y)+ 0.4y = 72
60 - 0.25y + 0.4y = 72
Collect like terms
- 0.25y + 0.4y = 72 - 60
0.15y = 12
y = 12/0.15
y = 80 Liters
Solving for x
x = 240 - y
x = 240 liters - 80 Liters
x = 160 liters
Therefore,
The number of liters of 25% acid solution = x = 160 liters
The number of liters of 40% acid solution = y = 80 liters
Answer:
7.66
Step-by-step explanation:
Just open the parenthesis.
4x-4+4x+4x-4=84
Now simplify and solve
12x-8=84
12x=92
x= 7.66
If length of rectangle is 8 cm, breadth is 4 cm, side of square is 3 cm, base of triangle is 3 cm, then the area of figure will be 48.5 
.
Given that length of rectangle is 8 cm, Breadth of rectangle is 4 cm,side of square is 3 cm,base of right angled triangle is 3 cm,height of triangle is 5 cm.
Area of figure=Area of rectangle+Area of square+Area of triangle
Area of rectangle=length*breadth
Area of square=Side*Side
Area of triangle=1/2 *Base*Height
Area of figure=8*4+3*3+1/2 *3*5
=32+9+1/2 *15
=41+15/2
=(82+15)/2
=97/2
=48.5
Hence if length of rectangle is 8 cm, breadth is 4 cm, side of square is 3 cm, base of triangle is 3 cm, then the area of figure will be 48.5 .
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Answer:
18.1 m
Step-by-step explanation:
For this problem, we will simply use the initial height of 0 meters, the height of 25 meters after 2 minutes, the decline of 2.2 meters every minute for 7 minutes, and a final increase of 8.5 meters to find the final altitude of the ballon.
0m + 25m - 2.2m(7) + 8.5m = ?
25m - 15.4m + 8.5m = ?
9.6m + 8.5m = ?
18.1m = ?
Hence, the final altitude of the ballon is 18.1m.
Cheers.
