Answer: x" = 5.69
Step-by-step explanation:
The graphic solution is attached.
Verifying the solution:
Existence condition: x > 0
2x - 4 = √x + 5
√x =2x - 4 - 5
√x =2x - 9 (²)
x = (2x - 9)²
x = 4x² - 36x + 81
4x² - 36x - x + 81 = 0
4x² - 37x + 81 = 0
Δ = -37² - 4.4.81 = 1369 - 1296 = 73
x = 37 ±√73/8
x' = 3.55
x" = 5.69
checking:
2*3.55 - 4 = 3.1
√3.55 + 5 = 6.88 Its not the same ∴ 3.55 is not a solution
2*5.69 - 4 = 7.39
√5.69 + 5 = 7.39 ∴ it's the only solution
The answer is 10 as the diameter because it says to estimate pi as 3. Since we know the circumference is 30 we can reverse it to find the diameter, since Circumference is pi time diameter.
Since you already know BC is 23inches, you can minus it from 83 inches first.
Next, you have to realise that since angle ABC and angle ACB are both 65 degrees and equal, the triangle is an isosceles triangle it means that AC is equals to BC.
Thus, it means that you can divide (83-23) by 2, which is 30 inches