Which equation represents the solution of the linear equation - 4x + 5 = 9?
2 answers:
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The angles m∠ABC = (3·x - 2)° and m∠ABD formed by the ray , which is an angle bisector of angle m∠CBD = (5·x + 18)°, indicates that m∠ABD is 64°
An angle bisector is a line, segment or ray that divides an angle into two congruent angles.
The information in the question are;
The ray that bisects ∠CBD =
The measure of angle, m∠CBD = (5·x + 18)°
The measure of angle, m∠ABC = (3·x - 2)°
Therefore;
(5·x + 18)° = 2 × (3·x - 2)° (definition of angle formed by an angle bisector)
(5·x + 18)° = (6·x - 4)°
(6·x - 5·x)° = (18 + 4)°
x = 22°
m∠CBD = m∠ABD + m∠ABC (angle addition postulate)
m∠ABD = m∠ABC (angles formed by angle bisector )
m∠ABC = (3·x - 2)°
Therefore; m∠ABC = (3 × 22 - 2)° = 64°
m∠ABD = m∠ABC = 64°
Learn more about the angle addition postulate here:
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Answer:
20 years
Step-by-step explanation:
Answer:
<h3>3.5ft</h3>Step-by-step explanation:
The question is incomplete. Here is the complete question.
Find the complete question in the diagram attached.
Area of a sector = θ/360 * πr² where;
r is the radius
θ is the angle substended by the sector
Given parameters
Area of the sector = 9ft²
central angle θ = 1.5 radians
Since 1 radians = 57.2958°
1.5 radians = (1.5 * 57.2958)
1.5 rad = 85.9437°
Substituting the given values into the formula;
Area of a sector = θ/360 * πr²
9 = 85.9437/360 * (3.14)r²
9 = 0.2387325 * 3.14r²
9 = 0.74962005r²
r² = 9/0.74962005
r² = 12.00608
r = √12.00608
r = 3.4641
r = 3.5 ft (to the nearest tenth)
Hence the radius of the circle is 3.5ft
