3(2x - 5) = 4x + 33
6x - 15 = 4x + 33
6x - 4x = 33 + 15
2x = 48
x = 48/2
x = 24
The shape which describe the shape of the sandbox is "A quadrilateral, because angle c and angle x are acute."
<h3>
What is Quadrilateral?</h3>
A quadrilateral is a four-sided polygon, having four edges and four corners.
Here, Diagonal = 14 ft.
Length = 12 ft.
Width = 8 ft.
14² = 196, 12² = 144, 8² = 64
8² + 12² ≠ 14²
so it is not a rectangle.
Now, 14² < 12² + 8²
this condition does not occur in rectangle, so it will be a quadrilateral and here sum of square of two adjacent side is greater than the square of third side (Diagonal). So that is an acute angle.
From this situation we can conclude that:
Thus, the shape which describe the shape of the sandbox is "A quadrilateral, because angle c and angle x are acute."
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<h3>
Answer:</h3>
6√2 ≈ 8.485 inches
<h3>
Step-by-step explanation:</h3>
The radii and the chord together make an isosceles right triangle with legs 6 inches long. The hypotenuse of such a triangle is √2 times the leg length. So, the chord will be 6√2 in long.
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<em>Comment on isosceles right triangle</em>
It is worth remembering that the hypotenuse of an isosceles right triangle is √2 times the leg length. This is easily found using the Pythagorean theorem:
... c² = a² + b²
... c² = 1² + 1² = 2 . . . . for legs of length 1
... c = √2 . . . . . . . . . . take the square root.
Scale this result as needed for any particular problem. Here, the scale factor is 6 inches.
(2j+7)(2j−7)
=(2j+7)(2j+−7)
=(2j)(2j)+(2j)(−7)+(7)(2j)+(7)(−7)
=4j2−14j+14j−49
=4j2−49
The function f(x) = 5(x)⁴, and f(x) = 5(4)ˣ represents the function that passes through the point (2, 80) option second and fourth are correct.
<h3>What is a function?</h3>
It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
We have; an exponential function that passes through the point (2, 80).
f(x) = 4(x)⁵
Plug (2, 80) in the abovew function:
f(2) = 4(2)⁵ = 128 (false)
f(x) = 5(x)⁴
Plug (2, 80) in the abovew function:
f(2) = 5(2)⁴ = 80 (true)
f(x) = 4(5)ˣ
f(2) = 4(5)² = 100 (false)
f(x) = 5(4)ˣ
f(2) = 5(4)² = 80 (true)
Thus, the function f(x) = 5(x)⁴, and f(x) = 5(4)ˣ represents the function that passes through the point (2, 80) option second and fourth are correct.
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