9514 1404 393
Explanation:
<h3>8.</h3>
An exterior angle is equal to the sum of the remote interior angles. Define ∠PQR = 2q, and ∠QPR = 2p. The purpose of this is to let us use a single character to represent the angle, instead of 4 characters.
The above relation tells us ...
∠PRS = ∠PQR +∠QPR = 2q +2p
Then ...
∠TRS = (1/2)∠PRS = (1/2)(2q +2p) = q +p
and
∠TRS = ∠TQR +∠QTR . . . . . exterior is sum of remote interior
q +p = (1/2)(2q) +∠QTR . . . . substitute for ∠TRS and ∠TQR
p = ∠QTR = 1/2(∠QPR) . . . . . subtract q
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<h3>9.</h3>
For triangle ABC, draw line DE parallel to BC through point A. Put point D on the same side of point A that point B is on the side of the median from vertex A. Then we have congruent alternate interior angles DAB and ABC, as well as EAC and ACB. The angle sum theorem tells you that ...
∠DAB +∠BAC +∠CAE = ∠DAE . . . . a straight angle = 180°
Substituting the congruent angles, this gives ...
∠ABC +∠BAC +∠ACB = 180° . . . . . the desired relation
Answer:
f(5) = 16.5
Step-by-step explanation:
Substitute x = 2.5 into f(x) , that is
f(2.5) = 6(2.5) + 1.5 = 15 + 1.5 = 16.5
14/74 in the simplest form is 7/37
Answer:
<em>Option </em><em>3</em>
Step-by-step explanation:
Rewriting input as fractions if necessary:
3/8, 3/20
For the denominators (8, 20) the least common multiple (LCM) is 40.
LCM(8, 20)
Therefore, the least common denominator (LCD) is 40.
Calculations to rewrite the original inputs as equivalent fractions with the LCD:
3/8 = 3/8 × 5/5 = 15/40
3/20 = 3/20 × 2/2 = 6/40
Answer:
0.5
Step-by-step explanation:
0.35 is 0.15 away from 0.5
0.35 is 0.35 away from 0
0.35 is 0.65 away from 1
