Answer:
59
Step-by-step explanation:
If we convert from degrees into radians, we can use the formula
, where s is the arc length, r is the radius and θ is the angle in radians.
To convert from degrees to radians, we multiply by 
So 
is our angle in radians, and we have the radius - we can now plug in these two values into our equation.
7x+1 + 4x-3 = 42
11x-2=42
11x=44
Divide by 11 on both sides which equals:
x=4
To find the length of DE just plug 4 in for x into the equation:
(7x+1) —> 7(4)+1= 29
29 is the length of DE
Then plug in 4 to EF’s equation:
(4x-3) —> 4(4)-3=13
13 is the length for EF
29+13= 42
So in the end, your answer will be 29.
Something that is 6ft tall with an 11ft shadow is the same relation as something that is x ft tall with a 33ft shadow. You can set up a proportion and then cross-multiply to solve for x (which is the height of the tree)
y = -3(x<span> - 2)^2 + 1 </span>x<span>-coordinate of vertex: </span>x<span> = -b/(2a) = -12/-6 = 2 y-coordintae of vertex: y(2) = -12 + 24 - 11 = 1 </span>Vertex form: y = -3(x<span> - 2)^2 + 1 Check. Develop y to get back to standard form: y = -3(</span>x^2 - 4x + 4) + 1 = -3x<span>^2 + </span>12x<span> - </span>11<span>. </span>
To answer your question: Rewrite <span>81<span>x2</span></span> as <span><span>(<span>9x</span>)</span>2</span>.<span><span><span>(<span>9x</span>)</span>2</span><span>−49</span></span>Rewrite 49 as <span>72</span>.<span><span><span>(<span>9x</span>)</span>2</span><span>−<span>72</span></span></span> Both terms are perfect squares, factor using the difference of squares formula, <span><span><span>a2</span><span>−<span>b2</span></span></span>=<span><span>(<span>a+b</span>)</span><span>(<span>a<span>−b</span></span>)</span></span></span> where <span>a=<span>9x</span></span> and <span>b=7</span>.<span><span>(<span><span>9x</span>+7</span>)</span><span>(<span><span>9x</span><span>−7</span></span><span>)</span></span></span>
