Answer:
16/21
Step-by-step explanation:
We are given the equation 3x(5 + 2) = 16.
By order of operations, let's add the two numbers in the parentheses first:
3x(5 + 2) = 16
3x(7) = 16
Now, we must multiply 3x by 7:
3x * 7 = 16
21x = 16
Divide both sides by 21:
x = 16/21
The answer is thus 16/21.
<em>~ an aesthetics lover</em>
The difference between constructing and drawing geometric figures is that when constructing a geometric figure, you use compass, protractor, ruler, or any scale with accurate measurement while when drawing geometric figures, you just draw with free-hand. It is not exact in measures.
Answer:
70°
Step-by-step explanation:
Connect the center of the circle with endpoints of the chord. Let the center of the circle be point O and endpoints of the chord be points A (let point A lie on the tangent line too)and B.
From the figure, central angle AOB has the measure of 220°.
Consider triangle AOB. This triangle is isosceles triangle because OA and OB are both radii. In this triangle the measure of angle AOB is 360° - 220° = 140°.
Angles OAB and OBA are angles adjacent to the base AB, so they are congruent. The sum of the measures of all interior angles in triangle is always 180°, so
m∠OAB + m∠OBA + m∠AOB = 180°
m∠OAB = m∠OBA = 1/2 (180° - 140°)
m∠OAB = 20°
Since drawn line is tangent line, then OA is perpendicular to this tangent line and
x° = 90° - 20°
x° = 70°
When
, you're left with
When
or
, you're left with
Adding the two equations together gives
, or
. Subtracting them gives
,
.
Now, you have
By just examining the leading and lagging (first and last) terms that would be obtained by expanding the right side, and matching these with the terms on the left side, you would see that
and
. These alone tell you that you must have
and
.
So the partial fraction decomposition is
