<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
It is 22 my guy because i think it is 22
Answer:
D: 14q + 21√qr
Step-by-step explanation:
We want to find the product of;
(2√q + 3√r) and 7√q.
Where p and q are integers.
Using distributive property, we have;
(2√q × 7√q) + (3√r × 7√q)
>> 14q + 21√qr
Correct option is D
x=ferns ; y=ivy
12x+8y=260
6x+15y=240
x=60 -(15/6)y
12(60+ (15/6)y + 8y = 260
x=60 -(15/6)y
720 - 30y + 8y = 260
x=60- (15/6)y
-30y +8y= 260-720 ==> -22y= -460
x=60 -(15/6)y
y= (-460)/(-22)= 20.9090909091
y=20.90
x=60 -(15/6)×20.90= 7.75
×(ferns)=7.75$
y(ivy)=20.90$