Answer:
∠7 = 34°
Step-by-step explanation:
Since a and b are parallel lines then
∠3 and ∠7 are corresponding angles and congruent, so
∠7 = ∠3 = 34°
Answer:
C. 1:27
Step-by-step explanation:
a²/b²=1/9 => a=1 and b=3
a³/b³=1³/3³=1/27
C. 1:27
Answer: 0 in the 1-20 range, 1 in the 21-40 range, 3 in the 41-60 range, 2 in the 61-80 range, and 2 in the 81-100 range.
Explanation:
No change, 0 in the 1-20 range
33: 1 in the 21-40 range
43, 44, 52: 3 in the 41-60 range
75, 79: 2 in the 61-80 range
86, 89: 2 in the 81-100 range.
<h3>Answer: As a fraction, HC is 21/4 units long</h3><h3>In decimal form, HC is 5.25 units long.</h3>
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Work Shown:
Let x = HC and y = BH
AH = 12-x since AH = 12-HC and x = HC
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See the attached drawing below. The altitude BH forms three similar triangles which makes the proportion below possible
HC/BH = BH/AH
x/y = y/(12-x) ... substitution
x(12-x) = y^2 ... cross multiply
y^2 = -x^2+12x
note how I isolated y^2 instead of y. We will use this equation later.
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Focus on triangle AHB. Use the pythagorean theorem
(BH)^2 + (AH)^2 = (AB)^2
(y)^2 + (12-x)^2 = (9)^2
y^2 + 144-24x+x^2 = 81
-x^2+12x + 144-24x+x^2 = 81 ... replace y^2 with -x^2+12x
-x^2+12x + 144-24x+x^2-81 = 0
-12x + 63 = 0
-12x = -63
x = -63/(-12)
x = 5.25 <<-- answer in decimal form
x = 5 + 0.25
x = 5 + 1/4
x = 20/4 + 1/4
x = 21/4 <<-- answer as a fraction