Perfect squares follow this pattern:
![(a\pm b)^2 = a^2\pm 2ab+b^2](https://tex.z-dn.net/?f=%20%28a%5Cpm%20b%29%5E2%20%3D%20a%5E2%5Cpm%202ab%2Bb%5E2%20)
So, two terms must be perfect squares of two certain roots. If so, the remaining term must be twice their product. Let's analyse the trinomials one by one:
1) x^2 is the square of x. -64 is not a perfect square. So, the trinomial is not a perfect square.
2) 4x^2 is the square of 2x. 9 is the square of 3. The remaining term, 12x, is indeed twice their product. So, we have
![4x^2 +12x +9 = (2x+3)^2](https://tex.z-dn.net/?f=%204x%5E2%20%2B12x%20%2B9%20%3D%20%282x%2B3%29%5E2%20)
3) x^2 is the square of x. 100 is the square of 10. The remaining term, 20x, is indeed twice their product. So, we have
![x^2 +20x +10 = (x+10)^2](https://tex.z-dn.net/?f=%20x%5E2%20%2B20x%20%2B10%20%3D%20%28x%2B10%29%5E2%20)
4) x^2 is the square of x. 16 is the square of 4. The remaining term, 4x, is not twice their product (it's only the product of 4 and x, so it should be doubled). So, this trinomial is not a perfect square.
The area of circle having radius 3cm is 28.27 cm², diameter 5cm is 19.63 cm², radius 8 ft is 201.06 ft², diameter is 113.1 cm², diameter 20 km is 314.16 km², diameter 15 mm is 176.71 mm² and radius 16 yd is 804.25 yd².
Given the radius and diamtere are (a) Radius (r) = 3 cm (b) Diameter (d) = 5 cm (c) Radius (r) = 8 ft. (d) Diameter (d) = 12 cm (f) Diameter (d) = 20 km (g) Diameter (d) = 15 mm (i) Radius (r) = 16 yd.
We will calculate the area of circle by using the formula A=πr² or π(d/2)².
(a) Radius (r)=3cm
The area of circle is
Area=π(3)²
Area =9π
Here, π=3.14, we get
Area =9×3.14
Area=28.27cm²
(b) Diameter (d)=5cm
The area of circle is
Area=π(5/2)²
Area =π(2.5)²
Area=6.25π
Here, π=3.14, we get
Area =6.25×3.14
Area=19.63cm²
(c) Radius (r)=8 ft
The area of circle is
Area=π(8)²
Area =64π
Here, π=3.14, we get
Area =64×3.14
Area=201.06ft²
(d) Diameter (d)=12cm
The area of circle is
Area=π(12/2)²
Area =36π
Here, π=3.14, we get
Area =36×3.14
Area=113.1cm²
(e) Diameter (d)=20km
The area of circle is
Area=π(20/2)²
Area =100π
Here, π=3.14, we get
Area =100×3.14
Area=314.16km²
(f) Diameter (d)=15mm
The area of circle is
Area=π(15/2)²
Area =56.25π
Here, π=3.14, we get
Area =56.25×3.14
Area=176.71mm²
(g) Radius (r)=16yd
The area of circle is
Area=π(16)²
Area =256π
Here, π=3.14, we get
Area =256×3.14
Area=804.25yd²
Hence, the area of circle having radius and diameter is radius 3cm is 28.27 cm², diameter 5cm is 19.63 cm², radius 8 ft is 201.06 ft², diameter is 113.1 cm², diameter 20 km is 314.16 km², diameter 15 mm is 176.71 mm² and radius 16 yd is 804.25 yd².
Learn more about the area of circle from here brainly.com/question/17096708
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I'm pretty sure y is 47 and x is 46... hope that helps!
The pair of numbers that have a sum of zero is 5, -5. -5 + 5 = 0
![5 \sqrt{18} - \sqrt{32} \\= 5 \sqrt{9 \times 2} - \sqrt{4 \times 4 \times 2} \\ = 5 \times 3 \times \sqrt{2} - 2 \times 2 \times \sqrt{2} \\ = 15 \sqrt{2} - 4 \sqrt{2} \\ = \boxed{11 \sqrt{2} }](https://tex.z-dn.net/?f=5%20%5Csqrt%7B18%7D%20%20-%20%20%5Csqrt%7B32%7D%20%20%5C%5C%3D%205%20%5Csqrt%7B9%20%5Ctimes%202%7D%20%20-%20%20%5Csqrt%7B4%20%5Ctimes%204%20%5Ctimes%202%7D%20%5C%5C%20%20%3D%205%20%5Ctimes%203%20%5Ctimes%20%20%5Csqrt%7B2%7D%20%20%20%20-%202%20%5Ctimes%202%20%5Ctimes%20%20%5Csqrt%7B2%7D%20%20%5C%5C%20%20%3D%2015%20%5Csqrt%7B2%7D%20%20-%204%20%5Csqrt%7B2%7D%20%5C%5C%20%20%3D%20%20%5Cboxed%7B11%20%5Csqrt%7B2%7D%20%7D)
<h3>11√2 is the right answer.</h3>