Answer: 24
A hyperbola is the locus of a point in a plane which moves in the plane in such a way that the ratio of its distance from a fixed point in the same plane to its distance from a fixed line is always constant, which is always greater than unity.
the fixed point is called the focus and the fixed line is directrix and the ratio is the eccentricity.
The general equation for the vertical hyperbola is
[ (y-k)^2 / a^2 ] – [ (x-h)^2 / b^2 ] = 1
The conjugate axis of the vertical hyperbola is y = k
Length of the conjugate axis = 2b
According to the question k = 2, h = -1, a = 4, b = 12
Length of the conjugate axis = 2b = 2 * 12 = 24
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The statement that is true regarding the sides of a triangle is the last one because the top and bottom have to be identical to each other and the sides have to be identical to each other.
3 consecutive means
x, x+1, x+2
OR
x, x-1, x-2
the equation based on givens and first equation is:
2(x) + 2(x+1) = 69 - (x+2)
4x + 2 = 67 - x
5x = 65
x = 13
so the largest would be x+2 or 15
Try this:
1) note that weight of pure antifreeze before mixing and after mixing is the same. So, if 'x' is weight of pure antifreeze in 50% solution, it is possible to make up equation before mixing: 0.5x+0.2*90.
2) there are 0.2*90=18 gal. of pure antifreeze in the 20% solution. If 'x' gal. is the weight of pure antifreeze in 50% sol. and 18 gal. is the weight of pure antifreeze in 20% sol., it is possible to make up an equation after mixing: 0.4(x+18).
3) using the both parts: 0.5x+0.2*90=0.4(x+18) ⇒ x=54 gal. of <u>pure</u> weight.
4) to find 50% solution of 54 gal. pure weight just 54:0.5=108 gal.
Answer: 108 gal.
The angles of a triangle always equal to 180 degrees.
Knowing this, you can solve this by this equation
Angle A + Angle B + Angle C = 180
43 + 85 + Angle C = 180
Angle C = 180 - 43 - 85
Angle C = 52
