Answer:
1) -1/4
2) -1/2
3) 1/3
Step-by-step explanation:
perpendicular lines' slopes are opposite reciprocals so you flip it and change the positive or negative sign
parallel lines have the same slope
1. --> d
2. --> b
3. --> a
4. --> c
1 is d because that is the only piece of information that sounds like a given.
2 is b because we know that from the given, m∠1 is complementary to m∠2 and in the first problem, m∠1 + m∠2 = 90, they are added together. The definition of complementary angles is "Two angles with measures that, when added together, equal 90 degrees". Same thing with m∠3 and m∠2.
3 is a because since both of the problems equal 90 degrees, you can just take away the 90 and put an equal sign in between the two problems because they equal the same thing.
4 is c because you are subtracting m∠2 from the problems and ending up with just m∠1 = m∠3.
Hope this helps! :)
Think of ratios as fractions.
5:8 is the same as 5/8
6:7 is the same as 6/7
Divide each fraction
5/8 = 0.625
6/7 = 0.857
-------------------------------------------------------------------------------------------------------------------
0.857 > 0.625 ∴ 6:7 is greater, and is your answer
-------------------------------------------------------------------------------------------------------------------
hope this helps
Length of side BM is 30 yd
Step-by-step explanation:
- Step 1: Find the value of ∠S using the property that sum of angles of a triangle is 180°
⇒ ∠B + ∠M + ∠S = 180°
⇒ 35° + 102° + ∠S = 180°
∴ ∠S = 180° - 137° = 43°
- Step 2: Use the law of sines to find the length of BM.
Law of sines ⇒ a/sin A = b/sin B = c/sin C
Here, let BM be a then, sin A = sin S = sin 43° = -0.83
Also, b = 18 yd, then sin B = sin 35° = -0.43
⇒ BM/-0.83 = 18/-0.43
⇒ BM = -0.83 × 18/-0.43 = 14.94/0.43 = 34.74 yd = 30 yd (rounded to nearest tenth)
