What number is a solution of the inequality x(7-x)>8

Step-by-step explanation:

The inequality can be put in vertex form.

  -x^2 +7x > 8

  x^2 -7x +3.5^2 < -8 +3.5^2 . . . . . multiply by -1, complete the square

  (x -3.5)^2 < 4.25  . . . .  show as a square

  |x -3.5| < √4.25  . . . .  take the square root

  -√4.25 < x -3.5 < √4.25 . . . . solve as absolute value problem

  3.5 -√4.25 < x < 3.5 +√4.25

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In the attached graph, the solutions are x-values between the x-intercepts of the graphed function.

question:

could we have options?

option a, c,d are correct.

step-by-step explanation:

from the given figure, it is given that z is equidistant from the sides of the triangle rst, then from triangle tzb and triangle szb, we have

tz=sz(given)

bz=zb(common)

therefore, by rhs rule,δtzb ≅δszb

by cpctc, sz≅tz

also, from δctz and δasz,

tz=sz(given)

∠tcz=∠saz(90°)

by rhs rule, δctz ≅ δasz, therefore by cpctc, ∠ctz≅∠asz

also,from δasz and δzsb,

zs=sz(common)

∠zbs=∠saz=90°

by rhs rule, δasz ≅δzsb, therefore, by cpctc, ∠asz≅∠zsb

hence, option a, c,d are correct.