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What is the factor of x2y-xyb-abx plus ab2?
(b - x)(ab - xy)
Triangle abc is a right triangle if ac equals 4 and bc equals 10 find ab?
The question is poorly specified, since the given triangle can be right angled at A or C. If it is right angled at A, then bc2 = ab2 + ac2 so that ab2 = 100 - 16 = 84 and ab = sqrt(84) = 9.165 Or it is right angled at C, and ab2 = bc2 + ca2 = 100 + 16 = 116 so that ab = sqrt(116) = 10.770
What is the LCM of 14ab to the second power and 42a to the second power?
The LCM is 42a2b2.
Why does b times ab equal ab squared and not equal ab plus b squared?
b*ab = ab2 Suppose b*ab = ab + b2. Assume a and b are non-zero integers. Then ab2 = ab + b2 b = 1 + b/a would have to be true for all b. Counter-example: b = 2; a = 3 b(ab) = 2(3)(2) = 12 = ab2 = (4)(3) ab + b2 = (2)(3) + (2) = 10 but 10 does not = 12. Contradiction. So it cannot be the case that b = 1 + b/a is true for all b and, therefore, b*ab does not = ab + b2
Why is the long leg the square root of 3 times bigger then the short leg in a 30 60 90 triangle?
I guess you are asking of the two sides which are not the hypotenuse, why the longer is root 3 times the shorter. Consider a 30, 60, 90 triangle ABC with ∠A = 30o, ∠B = 90o and ∠C = 60o and so side AC is the hypotenuse and BC is the shortest side. Reflect the triangle ABC in side BC to create triangle ABE. ∠EAB will be 30o, ∠ABE 90o and ∠BEA 60o. Side AE = AC. ∠EAC = ∠EAB + ∠BAC = 30o + 30o = 60o So triangle ACE is an equilateral triangle and thus side EC = AC Since EC = AC and EB = BC, EC=EB + BC ⇒ AC = BC + BC ⇒ AC = 2BC Using Pythagoras on triangle ABC to find length AB gives: AB2 + BC2 = AC2 ⇒ AB2 + BC2 = (2BC)2 ⇒ AB2 = 4BC2 - BC2 ⇒ AB2 = 3BC2 ⇒ AB = √3BC ie the shortest side is root 3 times the other non-hypotenuse side.
