Reflecting the point (x, y) over the x-axis transforms it to the point (x, -y). Then the points (x, f(x)) on the graph of f(x) will be transformed to (x, -f(x)) when the graph is reflected over the x-axis.
The reflection of the function f(x) = |x| is -f(x) = -|x|. If we name the reflected function f(x), we have
f(x) = -|x|
Answer:
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Step-by-step explanation:
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Answer:</u></em></h2>
Total Surface Area = 375
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Step-by-step explanation:</u></em></h2>
You need to find the area of the ceiling, floor, the two rectangle walls and the two trapezoid walls
<u>Area of the ceiling:</u>
c = length * width
c = 9*6.5 = 58.5
<u>Area of the 2 rectangle walls:</u>
w = 2(length * width)
w = 2(9 * 8)
w = 2(72)
w = 144
<u>Area of floor:</u>
f = 9 * 7.5
f = 67.5
<u>Area of the two trapezoids:</u>
a = 6.5
b = 7.5
h = 7.5
Total Surface Area = c + w + f + t
Total Surface Area = 58.5 + 144 + 67.5 + 105
Total Surface Area = 375
For example a × b × c = c × a × b
Answer:
Therefore the Commutative Expression is,
11 × w × 3 = 11 × 3 × w
Step-by-step explanation:
Commutative property:
The Commutative property states that order does not matter.
This property allows Two or more factors to be multiplied in any order without Changing the product.
Multiplication and addition are commutative.
For example a × b = b × a
1. 2 × 5 = 5 × 2
Therefore the Commutative Expression is,
11 × w × 3 = 11 × 3 × w
Answer:
Step-by-step explanation:
The ladder, ground, and building form a right triangle where the vertical distance between the top of the ladder and the bottom of the ground is one leg, the horizontal distance between the bottom of the ladder and the building is another leg, and the length of the ladder is the hypotenuse.
For any right triangle, the Pythagorean Theorem states that the sum of the squares of both legs is equal to the hypotenuse squared (), where is the hypotenuse.
Let the length of the ladder be (hypotenuse of right triangle). The distance between the top of the ladder and the ground (vertical distance) can be represented as .
From the Pythagorean Theorem, we then have:
Expand using :
Subtract from both sides and add to both sides:
Combine like terms:
Divide both sides by 2:
Therefore, the length of the ladder is 25 feet.