# math

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16) AB = 3.2cm
BC = 8.4cm
The area of the triangle ABC is 10cm².
Calculate the perimeter and give the answer correct to 3 significant figures.

19) Bill said that the line y=6 cuts the curve x² + y² =25 at two points.
a) By eliminating y, show that Bill is incorrect.
b) By eliminating y, find the solutions to the simultaneous equations
x² + y² = 25
y = 2x - 2

26)
c) Factorise (p+q)² + 5(p+q)
e) Simplify 2t² * 3r³t4

30) It is always possible to draw a circle which passes through all four vertices of a rectangle. Explain why.

(26) (c) factor out the (p+q) term and you get (p+q)(p+q+5)
(d) factor out the t term. I assume the last 4 is supposed to be an exponent.

(30) Draw the intersecting diagonals of the rectangle. Use geometry axioms and theorems to prove that the distance from the intersection of the diagonals to the corners are equal for all 4 corners. Therefore a circle centered on the intersection passes through all corners.

16) AB = 3.2cm
BC = 8.4cm
The area of the triangle ABC is 10cm².
Calculate the perimeter and give the answer correct to 3 significant figures

1--Triangle ABC has a base of BC = 8.4, a left side of AB = 3.2 and an unknown left side of AC.
2--Draw altitude AD perpendicular to BC
3--SInce the area A = 10, A = 8.4h/2 = 4.2h making h == 2.38095.
4--With AB = 3.2 and h == 2.38095, BD = sqrt(3.2^2 - 2.38095^2) = 2.138
5--CD therefore equals 8.4 - 2.138 = 6.262.
6--Thus, AC = sqrt(2.38095^2 + 6.262^2) = 6.699.
7--The perimeter is therefore 8.4 + 3.2 + 6.699 = 18.299.

• math -

because the distance of each vertice is the same distance away from the midpoint of the rectangle as the radius of the circle which passes through all four vertices of the rectangle.
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