The standard form form for a circle is
, where h and k are the center's coordinates respectively, and r is the radius. The first circle has a center at the origin, so the center's coordinates are (0, 0). Counting from the center straight across or up or down to a point on the circle tells us that the radius is 5. Our equation then is
, or simplifying,
. The second circle has a center of (5, 4). The radius is 3. So the equation for that circle is
. The last circle has a center of (4, 3) and a radius of 5. The equation for that circle is
. And there you go!
Answer:
15
Step-by-step explanation:
use distance formula
Answer:
(x-3) (x-4)
Step-by-step explanation:
x²- 7x + 12
= x² - 3x -4x +12
=x(x-3) - 4(x-3)
=(x-3) (x-4)
Sometimes when you're given dimensions that differ by some amount, it is easier to work with their average value. Let x represent the average of length and width of the rectangle. The length and width differ from this average value by 1.5 m. Then the area is
.. (x +1.5)*(x -1.5) = 154
.. x^2 -2.25 = 154
.. x^2 = 156.25
.. x = 12.5
The width is 1.5 m shorter than this, or 11 m.
_____
Solved in the conventional way, you are looking for factors of 154 that differ by 3. This means you have to find the factors of 154, or use the quadratic formula.
.. 154 = 1*154 = 2*77 = 7*22 = 11*14 (the pair we want)
Once you have the factorization of 154, you have the answer. No equations are necessary, really.
Angle A = 3x - 10
Angle B = x
Their angle sum = 90° ( complementary angles form 90° )
This can be written in an equation as =
= 3x - 10 + x = 90
= 3x + × + ( -10 ) = 90
= 4x + (-10) = 90
= 4x = 90 + 10 ( transposing-10 from LHS to RHS changes-10 to +10 )
= 4x = 100
= x = 100 ÷ 4 ( transposing ×4 from LHS to RHS changes ×4 to ÷4 )
= x = 25
Angle A = 3x - 10
= 3 × 25 - 10
= 75 - 10
= Angle A = 65°
Angle B = x = 25°
Their sum = 65 + 25 = 90°
Therefore , the complementary angles , Angle A = 65° and Angle B = 25° .