<span>Simplifying
4x2 + 8xy + 4y2
Reorder the terms:
8xy + 4x2 + 4y2
Factor out the Greatest Common Factor (GCF), '4'.
4(2xy + x2 + y2)
Factor a trinomial.
4((x + y)(x + y))
Final result:
4(x + y)(x + y)</span>
Answer:
20
Step-by-step explanation:
Answer:
c and d are correct
Step-by-step explanation:
<h3>Answer: As a fraction, HC is 21/4 units long</h3><h3>In decimal form, HC is 5.25 units long.</h3>
==============================================
Work Shown:
Let x = HC and y = BH
AH = 12-x since AH = 12-HC and x = HC
---------------
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.
---------------
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
Answer:
750kmph
Step-by-step explanation:
Average is sum of all parts divided by the number of parts.
Let Stot be average speed for total trip (800kmph).
Let S1 be speed for first quarter of trip (950kmph).
Let S2, S3, and S4 be the speeds of each of the remaining quarters respectively.
Let Sans be the average speed for the remaining three quarters of the trip (a.k.a. The Answer!).
Stot = (S1 + S2 + S3 + S4) / 4
800kmph = (950kmph + S2 + S3 + S4) / 4
3200kmph = 950kmph + S2 + S3 + S4
3200kmph - 950kmph = 2250kmph = S2 + S3 + S4
Divide both sides by 3.
2250kmph / 3 = (S2 + S3 + S4) / 3 = Sans
Sans = 750kmph