Find b and then solve the equation:(b−5)x2−(b−2)x+b=0, if one of its roots is0.5

b = ⅓

x = ½, -1/7

Step-by-step explanation:

(b−5)x² − (b−2)x + b = 0

(b - 5)(0.5)² - (b - 2)(0.5) + b = 0

0.25b - 1.25 - 0.5b + 1 + b = 0

0.75b = 0.25

b = ⅓

(⅓−5)x² − (⅓−2)x + ⅓ = 0

(-14/3)x² + (5/3)x + 1/3 = 0

14x² - 5x - 1 = 0

14x² - 7x + 2x - 1 = 0

7x(2x - 1) + (2x - 1) = 0

(7x + 1)(2x - 1) = 0

x = 0.5, -1/7

b = 1/3    x = -1/7 and -1/2

Step-by-step explanation:

(b−5)x^2−(b−2)x+b=0

Since we know one of the solutions, we can solve for b

(b−5)(.5)^2−(b−2)(.5)+b=0

(b−5)(.25)−(b−2)(.5)+b=0

Distribute

.25b -1.25 -.5b+1 +b = 0

Combine like terms

.75b -.25 =0

Add .25 to each side

.75b = .25

Divide by .75

b = .25/.75

b =1/3

Substituting this back into the equation

(1/3−5)(x)^2−(1/3−2)(x)+1/3=0

Getting a common denominator

(1/3−15/3)(x)^2−(1/3−6/3)(x)+1/3=0

-14/3 x^2  +5/3x +1/3 =0

Multiplying by 3 to get rid of the fractions

-14x^2 +5x +1 =0

using the quadratic formula

-b ±sqrt( b^2-4ac)

  2a

-5 ±sqrt( 5^2-4(-14)1)

  2(-14)

-5 ±sqrt( 81)

  2(-14)

-5 ±9

  -28

-5+9                  -5-9

  and  

-28                   -28

-4/28     and  14/28

-1/7           and  1/2

no association

step-by-step explanation:

if you have eyes and you can use them efficiently you can see that it just looks like random dots like do a line of best fit and like they're so spread out it's such a weak association you might as well consider it nonexistent

proofs involving isosceles triangles often require special consideration because an isosceles triangle has several distinct properties that do not apply to normal triangles.(more about triangle types) therefore, when you are trying to prove that two triangles are congruent, and one or both triangles, are isosceles you have a few theorems that you can use to make your life easier.

step-by-step explanation:

an isosceles triangle has two congruent sides and two congruent angles. the congruent angles are called the base angles and the other angle is known as the vertex angle. ∠bac and ∠bca are the base angles of the triangle picture on the left. the vertex angle is ∠abc