The 82nd term for the sequence would be -4
<span> the equation of this circle is (x - 3)² + (y + 1)² = 4²</span>
X= 100°
180° - 57° = 123
x + 23°= 123°
x = 100°
<u>We are given:</u>
An even number 'n', multiplied by the next consecutive even number is 168
<u>Solving for n:</u>
From the given statement, we can say that:
n(n+2) = 168 [<em>n multiplied by the next even number 'n+2'</em>]
n² + 2n = 168
n² + 2n - 168 = 0 [<em>subtracting 168 from both sides</em>]
We can see that we now have a quadratic equation, solving using splitting the middle term
n² + 14n - 12n - 168 = 0
n(n + 14) -12(n + 14) = 0 <em>[factoring out common terms</em>]
(n-12)(n+14) = 0
Here, we can divide both sides by either (n-12) OR (n+14)
Checking the result in both the cases:
(n + 14) = 0/(n-12) (n-12) = 0/(n+14)
n + 14 = 0 n - 12 = 0
n = -14 n = 12
Both these values are even and since we are not told if the number 'n' is positive or negative, both 12 and -14 are the possible values of n
Answer:
A
Step-by-step explanation:
Cosine is the ratio of "adjacent" to "hypotenuse"
With respect to the Angle E, the adjacent side is FE and the hypotenuse (always opposite side to 90 degree angle) is DE.
We are given DE = 26, but we need FE. We will solve for FE using Pythagorean Theorem, which tells us:
leg^2 + another leg^2 = hypotenuse^2
So, we will have:
10^2 + FE^2 = 26^2
Now, we solve for FE:
So,
Cos(E) = adj/hyp = 24/26
Correct answer is A
