Answer:
Apply the sine theorem in triangle ABC:
sin C = AB/AC = 4/5
=> C = arcsin(4/5) = 53.13 deg
As shown in picture, AB//CD. Using the same side interior angles theorem:
=> angle BCD = angle ABC = 90 deg
=> angle ACD = 90 - angle ACB = 90 - C = 90 - 53.13 = 36.87 deg
Apply the cosine theorem in triangle ACD:
cos C = AC/CD
=> CD = AC/cos C = 5/cos(36.87) = 5/0.8 = 6.25
=> Option C is correct
Hope this helps!
:)
Let the weight of the first alloy will be x grams.
Weight of gold will be 0.1x grams, weight of lead will be 0.15x grams.
Let the weight of the second alloy <span>will be y grams.
</span><span>Weight of gold will be 0.3y grams, weight of lead will be 0.4y grams.
</span>Summarizing:
0.1x+<span>0.3y=60 - gold
</span><span>0.15x+0.4y=88 - lead
</span>
0.1x+<span>0.3y=60 * 10
</span><span>0.15x+0.4y=88 * 100
</span>
x+3y=600 * 15
15x+40y=8800
15x+45y=9000
<span>15x+40y=8800
</span>
<span>15x+45y=9000 /15
</span>45y-40y=9000-8800
x+3y=600
5y=200
x+3y=600
y=40
y=40
x=600-3*40=480
y=40
<span>x=480</span>
↑The answers.
The answer is false, it is because a continuous variable is where the given values have no end or in other words, infinite. The students in a room has only provided a limited set of values-- in which it it has a fixed number of values, therefore, it is not a continuous variable, so it is false.<span />
