Answer:
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Step-by-step explanation:
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Step-by-step explanation:
For a quadratic expression ax²+bx + c = 0
The discriminant D = b²-4ac
Given the following quadratic equation;
x^2 - 6x-27 = 0
a = 1, b = -6, c = -27
D = (-6)²-4(-27)
D = 36+108
D = 144
Hence the discriminant is 144
For the roots;
x = -b±√D/2a
x = 6±√144/2
x = 6±12/2
x = 18/2 and -6/2
x = 9 and -3
For the expression x2 - 25 = 0
a = 1, b = 0 and c = -25
D = (0)²-4(-25)
D = 100
Hence the discriminant is 100
For the roots;
x = 0±√100/2
x = ±10/2
x = ±5
x =-5 and 5
Given the following quadratic equation;
x^2 +10x+25 = 0
a = 1, b = 10, c = 25
D = (10)²-4(25)
D = 100-100
D = 0
Hence the discriminant is 0
For the roots
x = -10±√0/2
x = -10/2
x = -5
Given the following quadratic equation;
2x^2 - 5x+3 = 0
a = 2, b = -5, c = 3
D = (-5)²-4(2)(3)
D = 25-24
D = 1
Hence the discriminant is 1
For the roots;
x = 5±√1/2(2)
x = 5±1/4
x = 5+1/4 and 5-1/4
x = 6/4 and 4/4
x = 3/2 and 1
x = 18/2 and -6/2
x = 9 and -3
Notice that in the dotted line above there is an arrowhead.
There is also an arrowhead on the bottom side of the triangle.
Those arrowheads mean that the dotted line and the bottom side of the triangle are parallel.
Since the bottom side is perpendicular to the left vertical side, then the dotted line is also perpendicular to the left vertical side.
The angle formed by the dotted line and the vertical side is 90 deg.
Since the angle shown is 28 deg, then the upper left angle of the triangle is 90 - 28 = 62 deg.
Now you have enough info to answer the question.
For the 62-deg angle, the 350-ft side is the adjacent leg.
y is the opposite leg.
The trig ratio that relates the adjacent and opposite legs is the tangent.
Assume that the larger number is m and the smaller one is n.
the larger is 10 less than twice the smaller, this means that:
m = 2n-10
the sum of the two is 38, this means that:
m+n = 38
substitute by the first equation in the second one:
2n-10+n=38
3n=48
n= 16
substitute by n in the first equation:
m=2n-10=2(16)-10= 22
based on this,
the larger number is 22 while the smaller number is 16