x^2 + 10x = - 5
To complete the square, we need to add a constant on the
left side that makes the expression on the right a perfect square trinomial. We
need to add the same value on the right side to keep the equation equal. So,
x^2 + 10x + a = -5 + a
where a is the square of one-half the coefficient of x, therefore:
a = (10 / 2)^2 = 25
x^2 + 10x + 25 = -5 + 25
(x + 5)^2 = 20
Taking the square root of both sides:
x + 5 = ± 4.47
x = -5 ± 4.47
<span>x = -9.47, -0.53</span>
The answers is A because the dice rolls on the same lane as A
Let x be that number
We know x + 5 = 12 ( the number plus five equals to 12)
=> x = 12-5 = 7
So, that number is 7.
As the sum of the angles of a triangle is 180 degrees, we can find the measure of Angle A.
180 - 102.9 - 18.6 = 58.5
Now that we know angle A, we can use the Law of Sines to find AB. The angle opposite BC is 58.5 degrees, which we found above. The angle opposite AB is angle C, which is 18.6 degrees.
By the Law of Sines,
AB / sin (18.6) = 943 / sin (58.5)
AB / .31896 = 943 / 0.85264
AB / .31896 = 1105.97652 by simplifying the right side
AB = 1105.97652 * .31896 by multiplying both sides by .31896 and clearing fractions
AB = 352.7622, which is 353 rounded to the nearest whole number.
Thus, AB is 353 feet and choice A is the best answer.