Step-by-step explanation:
3x+12=45
3x=45-12
3x=33
3x/3=33/3
x=11
Answer:
x² -3/4x +1/4 = 0
Step-by-step explanation:
Consider the two equations in factored and expanded forms:
(x -p²)(x -q²) = x² -(p²+q²)x +p²q² = 0 ⇒ p²+q² = 1, p²q² = 16
and
(x -1/p)(x -1/q) = x² -(1/p+1/q)x +1/(pq) = 0
Consider the squares of the sum and product of roots:
constant term: (1/(pq))² = 1/(p²q²) = 1/16 ⇒ 1/(pq) = √(1/16) = 1/4
x-term: (1/p +1/q)² = (p +q)²/(pq)² = (p² +q² +2pq)/(p²q²)
= (p² +q²)/(p²q²) +2/(pq)
= 1/16 +2/√16 = 9/16 ⇒ (1/p +1/q) = √(9/16) = 3/4
Then the equation with roots 1/p and 1/q is ...
x² -3/4x +1/4 = 0
Since the two angles are equal, hence the angles B and angle 2 are congruent.
<h3>Congruent triangles</h3>
Congruent triangles are triangles that are similar to each other
Since the sum of the interior angles of a triangle is 180°, then
m∠B + 50° + 65° = 180°
Determine the value of <B
m∠B = 180° - (50° + 65°)
m∠B = 180° - 115°
m∠B= 65°.
Similarly, the sum of angle on a straight line is 180 degrees
m∠2 + 50° + 65° = 180°
m∠2 = 180° - (50° + 65°)
m∠2 = 180° - 115°
m∠2= 65°
As we can see that the two angles are equal, hence the angles B and angle 2 are congruent.
Learn more on congruent angles here; brainly.com/question/2938476
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Use Mathpapa or symbolab, they are both very useful resources, and have saved me many times
4p - 9 = -193
4p = -193 = 9
4p = -184
p = -184/4
p = -46
