Answer:
∠ ADC = 110°
Step-by-step explanation:
∠ CDE = 90° ( angle between perpendicular lines ) , then
∠ CDB + ∠ BDE = 90°
∠ CDB + 20° = 90° ( subtract 20° from both sides )
∠ CDB = 70°
∠ ADC and ∠ CDB are adjacent angles on a straight line and sum to 180° , so
∠ ADC + ∠ CDB = 180° , that is
∠ ADC + 70° = 180° ( subtract 70° from both sides )
∠ ADC = 110°
The distance between the ground and the kite to the nearest foot is 64 ft.
<h3>What is a right angle triangle?</h3>
A right angle triangle is a triangle that has one of its sides as 90 degrees. The situation forms a right angle triangle.
Hence,
The length of the kite string is the hypotenuse side of the triangle formed.
The height between the ground and the kite is the opposite side of the triangle formed.
Therefore, using trigonometric ratio,
sin 40 = opposite / hypotenuse
sin 40 = h / 100
cross multiply
h = 100 sin 40
h = 100 × 0.64278760968
h = 64.2787609687
h = 64 ft
Therefore, the distance between the ground and the kite to the nearest foot is 64 ft.
learn more on right triangle here: brainly.com/question/27482803
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36,00÷ 12= 3,000 so that would be the average monthly loss.
<h3>
Answer: n = -11</h3>
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Explanation:
Since x-2 is a factor of f(x), this means f(2) = 0.
More generally, if x-k is a factor of p(x), then p(k) = 0. This is a special case of the remainder theorem.
So if we plugged x = 2 into f(x), we'd get
f(x) = x^3+x^2+nx+10
f(2) = 2^3+2^2+n(2)+10
f(2) = 8+4+2n+10
f(2) = 2n+22
Set this equal to 0 and solve for n
2n+22 = 0
2n = -22
n = -22/2
n = -11 is the answer
Therefore, x-2 is a factor of f(x) = x^3+x^2-11x+10
Plug x = 2 into that updated f(x) function to find....
f(x) = x^3+x^2-11x+10
f(2) = 2^3+2^2-11(2)+10
f(2) = 8+4-22+10
f(2) = 0
Which confirms our answer.
