A scientist needs 60 liters of a 60% acid solution. He currently has a 40% solution and a 70% solution. How many liters of each does he need to make the needed 60 liters of 60% acid solution?
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Equation:
acid + acid = acid
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0.40x + 0.70(60-x) = 0.60*60
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40x + 70*60 - 70x = 60*60
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-30x = -10*60
x = 20 liters
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Gabe needs 20 liters of the 40% solution.
He also needs 40 liters of the 70% solution.
Answer:
15.22
Step-by-step explanation:
The equation of the circumference of a circle is 2(pi)r
This is actually because 2pi is angle of the arc that makes up the full circle (radians of course)
so a simple formula is:
arc length in radians X radius
radius = 4 cm
the area that the question wants is the oposite
of the 142 degree section so 360 - 142 = 218
218 degrees * (pi/180) = 3.80482 rad
3.80482 * 4 = 15.21928 cm
Answer:
The equations that represent the equation of the line are:
y = -2x + 16 ⇒ A
2x + y = 16 ⇒ D
y - 6 = -2(x - 5) ⇒ E
Step-by-step explanation:
The slope intercept form of the linear equation is y = m x + b, where
- m is the slope of the line
- b is the y-intercept (y at x = 0)
The formula of the slope is 
∵ The line is passing through points (5 , 6) and (4 , 8)
∴
= 5 and
= 4
∴
= 6 and
= 8
- Substitute them in the formula of the slope to find it
∵ 
∴ m = -2
- Substitute it in the form of the equation
∴ y = -2 x + b
- To find b substitute x and y in the equation by the coordinates
of any point in the line
∵ x = 5 and y = 6
∴ 6 = -2(5) + b
∴ 6 = -10 + b
- Add 10 to both sides
∴ 16 = b
∴ y = -2 x + 16
∴ The equation of the line is y = -2x + 16
∴ A represents the equation of the line
∵ 2x + y = 16
- Subtract 2x from both sides
∴ y = -2x + 16
∴ D represents the equation of the line
∵ y - 6 = -2(x - 5)
∴ y - 6 = -2x + 10
- Add 6 to both sides
∴ y = -2x + 16
∴ E represents the equation of the line
The equations that represent the equation of the line are:
y = -2x + 16 ⇒ A
2x + y = 16 ⇒ D
y - 6 = -2(x - 5) ⇒ E