36 and 12/25 hope this helps
The expression for the area of a rectangle is given by:
A = (w) * (l)
Where,
l: long
w: width
the length is two less than twice the width:
l = 2w-2
Substituting the values:
420 = (w) * (2w-2)
We rewrite the expression:
210 = (w) * (w-1)
210 = w ^ 2-w
w ^ 2-w-210 = 0
The roots of the polynomial are:
w1 = -14
w2 = 15
We discard the negative root.
Width:
w = 15
Long:
l = 2w-2
l = 2 (15) -2
l = 30-2
l = 28
Answer:
the dimensions of Rosa's garden are:
w = 15 feet
l = 28 feet
Answer:
6.28 gallons
Step-by-step explanation:
first we need to find the area of a half sphere, and then find how much paint will be needed for that area.
The area of a sphere:
thus, the area of half a sphere is:
we know that the radius is:
we substitute this to find the area of the half sphere (the area they need to paint):
now the question is how many gallons of paint are needed to paint 2,513.27 square feet.
We are told that 1 gallon covers 400 square feet
thus, we must divide 2,513.27 by 400:
6.28 gallons of paint are needed.
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.
