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Anastaziya [24]
3 years ago
8

If line AD is a tangent to circle B at point C, and m ABC = 55°, what is the measure of BAD?

Mathematics
1 answer:
nikdorinn [45]3 years ago
8 0

Answer:

145°

Step-by-step explanation:

There are a couple of ways you can get there:

1. ∠ACB is a right angle, 90°. Hence, ∠BAC is the complement of ∠ABC, so is ...

... ∠BAC = 90° -∠ABC = 90° -55° = 35°

Then, ∠BAC and ∠BAD are a linear pair, so total 180°. That makes ∠BAD the supplement of ∠BAC, so ...

... ∠BAD = 180° -35° = 145°

2. ∠BAD is the exterior angle at A for the triangle ABC. It will have a measure that is the sum of the opposite interior angles: given ∠ABC = 55° and right angle ACB = 90°.

... ∠BAD = 55° +90° = 145°

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We have to show that this is a square, meaning all the sides are perpendicular and the same distance.  

A(3,4), B(2,-2), C(-4,-1), D(-3,5)

For each side we calculate the squared distance and the slope.  We don't have to bother to take the square root.  We'll subtract the points first because that difference, called the direction vector, goes into both the calculation of the slope and of the distance.

AB=B-A=(2 - 3, -2 - 4) = (-1, -6).   slope=-6/-1=6  AB²=(-1)²+(-6)²=37

BC=C-B=(-6, 1).  slope=1/-6=-1/6.   BC²=(-6)²+1²

CD=D-C=(1, 6).   slope=6/1=6    CD²=1²+6²=37

DA=A-D=(6,-1)   slope=-1/6     DA²=37

We see the negative reciprocal slopes, alternating between 6 and -1/6, indicating perpendicular sides.  We see they all have squared distance 37.  Equal perpendicular sides proves its a square.

If we do these problems enough we learn:  There's no point taking the square root.  In fact, there's really no point computing the slopes and the squared distances; we can see it's a square from the pattern of the direction vectors of the sides:  (-1, -6) (-6, 1) (1, 6) (6,-1)

5 0
3 years ago
Find the area of the irregular polygon. Round your answer to the nearest tenth if necessary.
kvasek [131]
The answer is 60 square cm

How to solve:

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3 years ago
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3. What is the molar mass of SO2?
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Answer: 64.066 g/mol

hope this helps :D

Step by Step: To find the molecular mass of SO2, you are going to want to search out the mass of SO2. The mass of sulfur is 32AMU, and also the mass of oxygen is 16AMU, then times two thanks to the subscript, so 32. Add those up, and 32+32=64AMU, which is your mass for the entire.

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2 years ago
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Photo attached please help
aniked [119]
C and E that is the answer
4 0
2 years ago
Please help me on this quick!! Thanks and please show work.
FinnZ [79.3K]
The two parallel bases b1 and b2 are
b1 = 12
b2 = 9
the order of which base you pick doesn't matter

The height is h = 10 and it's perpendicular to each base.

The area is...

A = (1/2)*h*(b1+b2)
A = (1/2)*10*(12+9)
A = (1/2)*10*(21)
A = 5*21
A = 105

Final Answer: B) 105 square centimeters
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3 years ago
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