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goldfiish [28.3K]
3 years ago
11

For the function F(x) = 2x^2-31x-51, where is the function increasing and positive? ( for all X values greater than what number

)
Mathematics
1 answer:
Ulleksa [173]3 years ago
7 0
ANSWER
x \: > \: 17

EXPLANATION

The given function is

f(x) = 2 {x}^{2} - 31x - 51
Let us split the middle term to get,

f(x) = 2 {x}^{2} -34x + 3x- 51

We factor to obtain,

f(x) = 2x(x - 17) -+3(x - 17)

f(x) = (2x -+3)(x -17)

Let us find the zeros of f(x),

(2x +3)(x - 17) = 0

Either

2x +3 = 0 \: or \: x - 17 = 0
x = -\frac{3}{2} \: or \: x = 17

We need to find the x-value of the vertex, which is the midpoint of the x-intercepts.

This gives us,

\frac{- \frac{3}{2} + 17}{2} = 7.75
Hence the axis of symmetry of the parabola has equation,

x = 7.75

Since the given function has minimum turning point, it will decrease and then increase.

The function will be increasing for
x \: > \: 7.75

The function will be increasing and positive for
x \: > \: 17
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Hi, help will be appreciated
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Answer:

KM=9

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ML=18.97

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Step-by-step explanation:

Triangle JKM is a 45, 45, 90 degree triangle so that means both side lengths are equal and the hypotenuse is square root of 2 times a side length. This means, KM will be equal to 9 and JK will be equal to 9 times square root of 2. For triangle KML, you know that the triangle is a 30,60,90 degree triangle. This means the hypotenuse is a^2+b^2=c^2 where c is the hypotenuse.  Since you know that a is 9 and c is 21, plug them into the equation to get 81+b^2=441. Subtract 81 from both sides to isolate b^2 to get 360. b^2 = 360. Then find the square root of 360 which is about 18.97. Therefore, b or ML is equal to 18.97. Also, because we know that MKL is a 30, 60, 90 triangle, we know that angle MKL is equal to 60 degrees. Because we know the angles of MKL(60) and KML (90), we do 180-90-60 to find angle L. Simplify 180-90-60 to 30 and that means that angle L is equal to 30 degrees.  Since we know that JKM is a 45, 45, 90 degree triangle, we know that JKM is equal to 45 degrees. Therefore, KM is equal to 9, JK is equal to 9 times square root of 2 or 9 times 1.41 which is 12.69. Angle JKM is 45 degrees, ML is 18.97, angle MKL is 60 degrees, and angle L is 30 degrees.

If this answer has helped you, please mark this answer as the brainliest

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