Answer:
x=18
Step-by-step explanation:
Vertical angles are congruent. This means that they are equal to each other. So, to solve set them equal to each other and isolate x. First, set up the equation. Then, subtract x from both sides. Finally, add 11 to both sides and simplify.
1) 
2) 
3)
Answer:
h ≈ 11.9
Step-by-step explanation:
Since the triangle is right we can use the cosine ratio to find h
cos24° = 
= 
Multiply both sides by 13
13 × cos24° = h
⇒ h = 11.9 cm ( to 1 dec. place )
Answer:
the question is incomplete, so I looked for a similar one:
<em>After the release of radioactive material into the atmosphere from a nuclear power plant, the hay was contaminated by iodine 131 ( half-life, 8 days). If it is all right to feed the hay to cows when 10% of the iodine 131 remains, how long did the farmers need to wait to use this hay? </em>
iodine's half life (we are given x, we need to find b):
0.5A₀ = A₀eᵇˣ
x = 8 days
we eliminate A₀ from both sides
0.5 = eᵇ⁸
ln 0.5 = ln eᵇ⁸
-0.69315 = b8
b = -0.69315 / 8 = -0.08664
since the farmers need to wait until only 10% of the iodine remains (we already calculated b, now we need to find x):
0.1A₀ = A₀eᵇˣ
0.1 = eᵇˣ
ln 0.1 = bx
where b = -0.08664
x = ln 0.1 / -0.08664 = -2.302585 / -0.08664 = 26.58 days
Answer:
Your final answer is either
x≥-2 if your initial inequality was
6x+2≤2(5-x)
OR
x≤-2
if your initial inequality was
6x+2≥2(x-2)
Step-by-step explanation:
As shown you have an equality, not an inequality.
-6x+2=2(5-x) distribute through parenthesis
-6x+2=2(5)+2(-x)
-6x+2=10-2x add 2x to both sides
2x-6x+2=10-2x+2x
-4x+2=10 subtract 2 from both sides
-4x+2-2=10-2
-4x=8 divide both sides by -4
-4x/(-4) = 8/(-4)
x = -2
With the ≥ or ≤ sign you would solve the exact same way
except for the point where when dividing both sides by
-4 requires you to reverse the inequality.
Your final answer is either
x≥-2 if your initial inequality was
6x+2≤2(5-x)
OR
x≤-2
if your initial inequality was
6x+2≥2(x-2)
A short-cut to accurately evaluate the given expression above is using a scientific calculator where one can include integrals and evaluate using limits. In this case, using a calculator, the answer is equal to 0.2679. One can verify this by integrating truly letting 1-x^2 as u and use its du to be substituted in the numerator
