The equation of a circle is written as ( x-h)^2 + (y-k)^2 = r^2
h and k is the center point of the circle and r is the radius.
In the given equation (x+3)^2 + (y-1)^2 = 81
h = -3
k = 1
r^2 = 81
Take the square root of both sides:
r = 9
The center is (-3,1) and the radius is 9
Answer:
A
Step-by-step explanation:
The triangle shown has all 3 sides equal in length, hence it is an equilateral triangle.
A property of equilateral triangles is the angles are congruent.
The sum of the 3 angles = 180°, hence the measure of each angle is
= 60° → A
Answer:
x = -1
Step-by-step explanation:
Step 1: Simplify both sides of the equation.
−46+23=46x+23
(−46+23)=46x+23(Combine Like Terms)
−23=46x+23
−23=46x+23
Step 2: Flip the equation.
46x+23=−23
Step 3: Subtract 23 from both sides.
46x+23−23=−23−23
46x=−46
Step 4: Divide both sides by 46.
46x/46 = -46/46
Answer: 6 goes on 6/// 83 goes on 9///// 40goes on 6///// 64 goes on8///and the 7.5 will go between 7 and 8
Step-by-step explanation:
go onto a calculator and type in the number and decide it by the square root
Answer:
z' = 2iz +11 -2i
Step-by-step explanation:
Dilation multiplies each point by the scale factor. Rotation by 90° CCW is equivalent to multiplication by i.
When the center is not the origin, the transformation is applied to the difference from the center, then the result is added to the center.
z' = 2i(z -(3+4i)) + (3+4i)
Simplifying gives ...
z' = 2iz -6i +8 +3 +4i
z' = 2iz +11 -2i
_____
<em>Check</em>
For example, consider the point 1 unit east of the center of dilation/rotation. That point is z = 4+4i. Applying the transformation moves this point to ...
z' = 2i(4 +4i) +11 -2i = 8i -8 +11 -2i
z' = 3 +6i . . . . . 2 units north of the center of dilation/rotation
This is where it is expected to be after dilation by a scale factor of 2 and rotation 90° CCW.
