To solve this problem, you must know that an inscribed angle equals 1/2 of the arc that it intercepts.
Therefore, because <ABC intercepts arc ADC, we know that
the measure of angle ABC = 1/2 * (measure of Arc ADC)
OR, when the values are substituted into the equation
165 = (1/2) (5)(x-3)
When simplified, this equation equals
330 = 5x - 15
345 = 5x
x = 69
Therefore, your answer is the second option, that x = 69 degrees.
1/3 ln(<em>x</em>) + ln(2) - ln(3) = 3
Recall that 
, so
ln(<em>x</em> ¹ʹ³) + ln(2) - ln(3) = 3
Condense the left side by using sum and difference properties of logarithms:
Then
ln(2/3 <em>x</em> ¹ʹ³) = 3
Take the exponential of both sides; that is, write both sides as powers of the constant <em>e</em>. (I'm using exp(<em>x</em>) = <em>e</em> ˣ so I can write it all in one line.)
exp(ln(2/3 <em>x</em> ¹ʹ³)) = exp(3)
Now exp(ln(<em>x</em>)) = <em>x </em>for all <em>x</em>, so this simplifies to
2/3 <em>x</em> ¹ʹ³ = exp(3)
Now solve for <em>x</em>. Multiply both sides by 3/2 :
3/2 × 2/3 <em>x</em> ¹ʹ³ = 3/2 exp(3)
<em>x</em> ¹ʹ³ = 3/2 exp(3)
Raise both sides to the power of 3:
(<em>x</em> ¹ʹ³)³ = (3/2 exp(3))³
<em>x</em> = 3³/2³ exp(3×3)
<em>x</em> = 27/8 exp(9)
which is the same as
<em>x</em> = 27/8 <em>e</em> ⁹
Answer:
Step-by-step explanation:
Triangle RST is a right angle triangle.
From the given right angle triangle
RT represents the hypotenuse of the right angle triangle.
With 26 degrees as the reference angle,
ST represents the adjacent side of the right angle triangle.
RS represents the opposite side of the right angle triangle.
1) To determine RS, we would apply trigonometric ratio
Sin θ = opposite side/hypotenuse Therefore,
Sin 26 = RS/9.1
RS = 9.1Sin26 = 9.1 × 0.4384
RS = 4.0
2) To determine ST, we would apply trigonometric ratio
Cos θ = adjacent side/hypotenuse Therefore,
Cos 26 = ST/9.1
ST = 9.1Cos26 = 9.1 × 0.8988
ST = 8.1
3) The sum of the angles in a triangle is 180 degrees. Therefore,
∠R + 26 + 90 = 180
∠R = 180 - (26 + 90)
∠R = 64 degrees
Answer:
answer is option b 70
Step-by-step explanation:
A=b×h = A= 14×5= 70
Answer:
The distance from point A to the line of reflection is the same as the distance from point AGH to the line of reflection. This means that the line of reflection bisects .
1) 4 2 2
2) 5.77 2.89 2.89
3) 7.9 3.95 3.95
Step-by-step explanation:
