Answer:
i
Step-by-step explanation:
Why is i the square root of negative one?
The term "imaginary" is used because there is no real number having a negative square. There are two complex square roots of −1, namely i and −i, just as there are two complex square roots of every real number other than zero, which has one double square root.
A line segment from a vertex to the midpoint of the opposite side is a "median". A median divides the area of the triangle in half, as it divides the base in half without changing the altitude.
AAMC is half AABC. AADC is half AAMC, so is 1/4 of AABC. (By the formula for area of a triangle.)
ABMC is half AABC. ABMD is half ABMC, so is 1/4 of AABC. (By the formula for area of a triangle.)
Then, AADC = 1/4 AABC = ABMC, so AADC = ABMC by the transitive property of equality.
The measure of the ∠LQP is 120°
Step-by-step explanation:
The diagram of the question is as attached in the image.
LMNP is a square. We know that for a square all sides are equal and intersects at 90°
Hence, LM=MP=PN=LN
and ∠LMP= ∠MPN= ∠PNL= ∠NLM= 90°
Δ LMQ is an equilateral triangle
We know that for equilateral triangle all sides are equal and all angles are 60°
LM=LQ=QM=MP=PN=LN and
∠LQM= ∠QML= ∠MLQ= 60°
∠LQP= ∠LQM+ ∠MQP eq 1
In Δ MPQ
∠QPM=90° and ∠PMQ= 90°-60°=30°
Hence, ∠MQP= 180°-(90°+30°)=60°
Putting the value of ∠MQP and ∠LQM in equation 1
∠LQP= 60°+60°= 120°
Thus the measure of ∠LQP=120°
Find the area of the triangle, then multiply that by the depth of the prism.
Area of triangle = 1/2 x base x height = 1/2 x 14 x 16 = 112
Volume = 112 x 32= 3584 ft^3
Answer:
12.5 units
Explanation:
We are given that:
ΔABC ~ ΔDEC
This means that the similarity proportion can be set up as follows:
AB/DE = BC/EC / AC/DC
We have:
CD = 5 units
BC = 6 + 4 = 10 units
EC = 4 units
This means that:
BC/EC = AC/DC
10/4 = AC / 5
Therefore,
AC = (5*10) / (4) = 12.5 units
Hope this helps :)
