Answer:
85/7
Step-by-step explanation:
log2 + log7(x-5) = 2
log(14(x-5)) = 2
14x - 70 = 10²
14x = 170
x = 170/14
x = 85/7 or 12 1/7
<h2><em>Width=w
</em></h2><h2><em>Length=l
</em></h2><h2><em>Perimeter=p
</em></h2><h2><em>
</em></h2><h2><em>p=2w+2l
</em></h2><h2><em>l=20+w
</em></h2><h2><em>p=2w+20+w+20+w
</em></h2><h2><em>p=4w+40
</em></h2><h2><em>
</em></h2><h2><em>4w+40=160
</em></h2><h2><em>4w=160-40=120
</em></h2><h2><em>w=120:4=30
</em></h2><h2><em>w=30
</em></h2><h2><em>l=20+w
</em></h2><h2><em>l=20+30=50</em></h2>
<span>he total number of internal degrees is (n-2)*180 = 4*180 = 720 degrees.
-----
let a = one of the congruent angles.
you have:
angles 1, 2, and 3 = a.
-----
if a = 2 * angle 4, then angle 4 = 1/2 * a
-----
if a = 1/2 * angle 5, then angle 5 = 2 * a
-----
we have:
angle 1 = a
angle 2 = a
angle 3 = a
angle 4 = 1/2 * a
angle 5 = 2 * a
angle 6 = 115
</span><span>-----
since the sum of the angles is equal to 720, we have:
3*a + 2*a + 1/2*a + 115 = 720
combine like terms to get:
5.5 * a + 115 = 720
subtract 115 from both sides to get:
5.5 * a = 720 - 115 = 605
divide both sides by 5.5 to get:
a = 720/5.5 = 110
-----
angle 1, 2, and 3 are each 110 degrees.
angle 4 = 55 degrees
angle 5 = 220 degrees
angle 6 = 115 degrees
-----
the question is:
What is the measure of the smallest angle?
the answer is:
55 degrees.</span>
Applying the trigonometric ratios, the equations that can be used are:
sin 45 = BC/9
cos 45 = BC/9
<h3>How to Apply the Trigonometric Ratio?</h3>
In the given image below, to find the unknown lengths of the triangle, we would apply the following trigonometric ratios:
To find AC, use the cosine ratio, CAH.
To find BC, use the sine ratio, SOH.
sin 45 = opp/hyp = BC/9
sin 45 = BC/9
cos 45 = adj/hyp = BC/9
cos 45 = BC/9
Learn more about the trigonometric ratios on:
brainly.com/question/10417664
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