The expression 4a^2c^2 - (a^2-b^2+c^2)^2 has to be factored.
4a^2c^2 - (a^2 - b^2 + c^2)^2
=> (2ac)^2 - (a^2 - b^2 + c^2)^2
=> (2ac - a^2 + b^2 - c^2)(2ac + a^2 - b^2 + c^2)
=> (b^2 - (a^2 - 2ac + c^2))((a^2 + 2ac + c^2) - b^2)
=> (b^2 - (a - c)^2)((a + c)^2 - b^2)
=> (b - a + c)(b + a - c)(a + b + c)(a - b + c)
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The factorized form of 4a^2c^2 - (a^2-b^2+c^2)^2 is (b - a + c)(b + a - c)(a + b + c)(a - b + c)</span>
Answer: 10 4/5
Convert the mixed numbers to improper fractions
Use the algebraic formula for addition of fractions:
a/b + c/d = (ad + bc) / bd
Reduce fractions and simplify if possible
Answer:
38°
Step-by-step explanation:
The sum of angles that make a line is 180°; the sum of angles in a triangle is 180°. So, we have the following relations:
2x +y +A = 180
2y +x + B = 180
A +B +33 = 180
Adding the first two equations and subtracting the third, we get ...
(2x +y +A) +(2y +x +B) -(A +B +33) = 180 +180 -180
3x +3y -33 = 180
x + y - 11 = 60
x + y = 71
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We know vertical angles are congruent, so in triangle QRK, we have ...
2y +2x +∠K = 180
∠K = 180 -2x -2y = 180 -2(x +y) = 180 -2(71)
∠JKL = 38°
Answer:
Step-by-step explanation:
This is a quadrilateral. A quadrilateral is <em>a plane figure</em> that<u> has four sides or edges</u>, and also <u>has four corners or vertices</u>.
<u>The interior angles</u> of a simple<em> quadrilateral ABCD</em> add up to <u>360 degrees of arc</u>.
Answer:
90x in
Step-by-step explanation:
V≈1696.46
Solution
V=πr2h=π·62·15≈1696.46003