Answer:
24
Step-by-step explanation:
Move all the terms involving the sine to one side, and all the numbers to the other:
Answer:
47.4%
Step-by-step explanation:
It has to be below 50% because those weights fall at or below the average.
Answer:
Explanation:
The formula for calculating the distance between two points is:
d
=
√
(
x
2
−
x
1
)
2
+
(
y
2
−
y
1
)
2
Substituting the values from the points in the problem gives:
d
=
√
(
−
6
−
−
3
)
2
+
(
−
4
−
−
5
)
2
d
=
√
(
−
6
+
3
)
2
+
(
−
4
+
5
)
2
d
=
√
(
−
3
)
2+
1
2
d
=
√
9+
1
d
=
√
10
Or
d
=
3.162
rounded to the nearest thousandth
Answer: C. Definition of an Altitude
Step-by-step explanation:
Given: In triangle MNO shown below, segment NP is an altitude from the right angle.
Let ∠MNP=x
Then ∠PNO=90°-x
Therefore in triangle MNO,
∠MPN=∠NPO =90° [by definition of Altitude]
[Definition of altitude : A line which passes through a vertex of a triangle, and joins the opposite side forming right angles. ]
Now using angle sum property in ΔMNP
∠MNP+∠MPN+∠PMN=180°
⇒x+90°+∠PMN=180°
⇒∠PMN=180°-90°-x
⇒∠PMN=90°-x
Now, in ΔMNO and ΔPNO
∠PMN=∠PNO=90°-x
and ∠MPN=∠NPO =90° [by definition of altitude]
Therefore by AA similarity postulate, we have
ΔMNO ≈ ΔPNO
