46 - 4 = 3b + 3
Simplify the left side:
42 = 3b + 3
Subtract 3 from both sides:
39 = 3b
Divide both sides by 3:
b = 13
Answer:
Step-by-step explanation:
The radius of circle D is the distance from the origin to (-4, -7).
In math, the distance formula gives us the distance between two points, (x₁, y₁) and x₂, y₂):
You are really using Pythagoras' Theorem to find the distance. You are building a right triangle whose hypotenuse connects two given points.
For example, in the blue triangle below, the distance between the points (0,0) and (-4, -7) is
We need to determine the radius and diameter of the circle. If the area of the circle is 10 pi in^2, then, according to the formula for the area of a circle,
A = 10 pi in^2 = pi*r^2. Thus, 10 in^2 = r^2, and r = radius of circle = sqrt(10) in.
Thus, the diam. of the circle is 2sqrt(10) in. This diam. has the same length as does the hypotenuse of one of the triangles making up the square.
Thus, [ 2*sqrt(10) ]^2 = x^2 + x^2, where x represents the length of one side of the square. So, 4(10) in^2 = 2x^2. Then:
40 in^2 = 2x^2, or 20 in^2 = x^2, and so the length x of one side of the square is sqrt(20). The area of the square is the square of this result:
Area of the square = x^2 = [ sqrt(20) ]^2 = 20 in^2 (answer). Compare that to the 10 pi sq in area of the circle (31.42 in^2).
Answer:
height = 2.5 units
Step-by-step explanation:
The volume of a rectangular prism is given by the product of its base area and its height. If the area of the base is 28 square units and the volume is 70 cubic units, we can find the height as follows:
Volume = base area * height
70 = 28 * height
height = 70 / 28
height = 2.5 units
The height of the rectangular prism is 2.5 units.
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