In geometry, zero-dimensional figures do not extend in any direction and include 'points', while one-dimensional figures extend in one direction and include 'lines', 'segments', and 'rays'. Therefore, the zero or one-dimensional figures in the given options are 'point', 'line', 'segment', and 'ray'.
In geometry, quantities can be zero, one, two, or three dimensional. Zero-dimensional figures are those that do not extend in any direction. The only such geometric figure is a point (Option A). One-dimensional figures, on the other hand, extend in one direction. These include a line (Option F), a segment (Option E), and a ray (Option C), all of which have length but no breadth or height. Therefore, the zero-dimensional or one-dimensional figures from the given options are point, line, segment, and ray.
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Answer:
Step-by-step explanation:
To maximize the area of the two identical rectangular pens, we need to find the dimensions that will allow us to enclose the largest possible area using the given 480 feet of fencing.
Let's start by assigning variables to the dimensions of the rectangular pen. Let's say the length of the pen is "L" and the width is "W". Since the two pens share one wall, we can divide the available fencing equally between the two long sides and the two short sides.
The equation for the perimeter of a rectangle is: P = 2L + 2W.
In this case, we have two pens, so the total perimeter is 480 feet: 2L + 2W = 480.
We can simplify this equation by dividing both sides by 2: L + W = 240.
To maximize the area, we need to find the dimensions that satisfy this equation while maximizing the product of L and W, which represents the area.
Since the pens are identical, we can express one dimension in terms of the other. Let's solve the equation for L: L = 240 - W.
Now, substitute this expression for L in the equation for the area: A = L * W = (240 - W) * W.
To find the maximum area, we need to find the value of W that maximizes the expression (240 - W) * W.
One way to do this is by graphing the equation or using calculus, but since this is likely a high school-level problem, we can use the concept of symmetry.
Since the equation for the area is quadratic, the maximum area will occur at the midpoint of the symmetry axis. In this case, the symmetry axis is given by W = 240/2 = 120.
So, to maximize the area, each pen should have a width of 120 feet.
Substituting this value back into the equation for the perimeter, we can find the length of each pen: L + 120 = 240, L = 240 - 120 = 120.
Therefore, the dimensions of each pen that will maximize the area are 120 feet by 120 feet.
Keep in mind that this is just one possible answer, as there may be other valid dimensions that also maximize the area. However, for a symmetrical solution, both pens should have equal dimensions.
2(x+3)
2x-3
2x+3
2(x-3)
Answer:
The fourth answer choice is the correct one: 2(x - 3)
Step-by-step explanation:
2x²-18x+36/x-6 should be factored, as follows:
2(x²-9x+18) / (x-6) = 2(x - 3) (x - 6) / (x - 6)
Substituting x = 6 would result in division by zero and is thus not allowed.
Remembering this, we can reduce 2(x - 3) (x - 6) / (x - 6) to 2(x - 3) for x≠6.
2
9±3√5
2
O-9± √117
2
9± √117
2
Answer: (-9 ± 3√5) / 2
Step-by-step explanation:
Since our equation is in the form of ax² + bx + c = 0, we'll use the quadratic formula to solve the equation, plugging our values in:
(-9 ± √9²-4(1)(9)) / 2(1)
(-9 ± √81 - 36) / 2
(-9 ± √45) / 2
Here, we can simplify √45 by finding pairs of factors that equal 45, and have one of the factors be able to be square rooted:
(-9 ± √9·√5) / 2
(-9 ± 3√5) / 2
I hope this helps! :)
reasoning.
Answer:
3b is the answer
3a+2b-3a+b
3a-3a+2b+b
2b+b
Step-by-step explanation:
The first step I did is switch up the equation so that the like terms are next to each other. So the a’s are next to each other and the b’s are next to each other. Then I subtracted 3a-3a and got 0 and in the last step I added the 2b + b and got 3b.
9a^2- 4b^2
First, Apply the distributive property 3a(3a)+3a(−2b)+2b(3a)+2b(−2b)
Second Simplify the term. 3a(3a)+2b(−2b)
Third, Simplify Each term.
3⋅3a2+2b(−2b)
9a2+2b(−2b)
9a2+2⋅−2b2
= 9a2−4b2