<ABD + <DBC = 95
2x + 23 + 9x - 5 = 95
11x + 18 = 95
11x = 77
x = 7
<ABD = 2(7) + 23 = 14 + 23 = 37
<DBC = 9x - 5 = 9(7) - 5 = 63 - 5 = 58
Answer
<ABD = 37°
<DBC = 58°
Example:
1. 2/3,3/4
<span>2. 3/5,1/2 </span>
<span>3. 2/5,1/3 </span>
<span>4. 5.6,4.5 </span>
<span>5. 1/2,2/3 </span>
<span>6. 3/7,2/3 </span>
<span>7. 1/3,3/10 </span>
<span>8. 2/5,3/7
</span>
Answer:
1. 8/12, 9/12
<span>2. 6/10, 5/10 </span>
<span>3. 6/15, 5/15 </span>
<span>4. 25/30, 24/30 </span>
<span>5. 3/6, 4/6 </span>
<span>6. 9/21, 14/21 </span>
<span>7. 10/30, 9/30 </span>
<span>8. 14/35, 15/35</span>
Find <span>tan<span>(<span><span>5π</span>12</span>)</span></span> and sin ((5pi)/12)
Answer: <span>±<span>(2±<span>√3</span>)</span>and±<span><span>√<span>2+<span>√3</span></span></span>2</span></span>
Explanation:
Call tan ((5pi/12) = t.
Use trig identity: <span><span>tan2</span>a=<span><span>2<span>tana</span></span><span>1−<span><span>tan2</span>a</span></span></span></span>
<span><span>tan<span>(<span><span>10π</span>12</span>)</span></span>=<span>tan<span>(<span><span>5π</span>6</span>)</span></span>=−<span>1<span>√3</span></span>=<span><span>2t</span><span>1−<span>t2</span></span></span></span>
<span><span>t2</span>−2<span>√3</span>t−1=0</span>
<span>D=<span>d2</span>=<span>b2</span>−4ac=12+4=16</span>--> <span>d=±4</span>
<span>t=<span>tan<span>(<span><span>5π</span>12</span>)</span></span>=<span><span>2<span>√3</span></span>2</span>±<span>42</span>=2±<span>√3</span></span>
Call <span><span>sin<span>(<span><span>5π</span>12</span>)</span></span>=<span>siny</span></span>
Use trig identity: <span><span>cos2</span>a=1−2<span><span>sin2</span>a</span></span>
<span><span>cos<span>(<span><span>10π</span>12</span>)</span></span>=<span>cos<span>(<span><span>5π</span>6</span>)</span></span>=<span><span>−<span>√3</span></span>2</span>=1−2<span><span>sin2</span>y</span></span>
<span><span><span>sin2</span>y</span>=<span><span>2+<span>√3</span></span>4</span></span>
<span><span>siny</span>=<span>sin<span>(<span><span>5π</span>12</span>)</span></span>=±<span><span><span>√<span>2+<span>√3</span></span></span>2</span></span></span>
Answer:
The total number of U.S. high school students that played on a sports team that year can be estimated to be 7,950,000.
Step-by-step explanation:
From the random sample, we can expect that 
of all students played on a sports team that year. So in the bigger sample of 15900000 high school students, we can expect 
students to have played on a sports team that year.
