LKM≈TEJ since it makes the triangles congruent, although the angles in each triangle are not corresponding equal angles
You just need to find distance between two points
d=
![\sqrt{(y2-y1)^2+(x2-x1)^2}](https://tex.z-dn.net/?f=%20%5Csqrt%7B%28y2-y1%29%5E2%2B%28x2-x1%29%5E2%7D%20)
d=6
Remember that the area of a rectangle is the length of the rectangle multiplied by the width of the rectangle.
In this case, we could say (where
is the area of the rectangle):
![A(x) = L(x) \cdot W(x)](https://tex.z-dn.net/?f=A%28x%29%20%3D%20L%28x%29%20%5Ccdot%20W%28x%29)
Substituting the values the problem gave us for
and
, we can find the formula for
in terms of
, which is:
![A(x) = (5x) \cdot (2x^2 - 4x + 13) = (10x^3 - 20x^2 + 65x)](https://tex.z-dn.net/?f=A%28x%29%20%3D%20%285x%29%20%5Ccdot%20%282x%5E2%20-%204x%20%2B%2013%29%20%3D%20%2810x%5E3%20-%2020x%5E2%20%2B%2065x%29)
The formula for the area of the rectangle would be A(x) = 10x³ - 20x² + 65x.
Part A:
Given that <span>Starlight tree farms sells Douglas Firs and Noble First.
Let </span>n be the number of Noble Fir trees sold, then<span> if they sold 139 more Douglas First than Noble Firs, this means that the number of Douglas First trees sold is n + 139.
Given that the total number of trees sold was 377, then we have, n + n + 139 = 377, which means that 2n + 139 = 377
Therefore, the equation that could be used to solve for n, the number of Noble Fir trees sold is 2n + 139 = 377.
Part B:
</span><span>Given that you are driving 55 miles per hour and you must drive a total of 440 miles. If you already driven 275 miles, then, the equation representing the number of hours, h, it will take to reach your destination is given by 55h + 275 = 440.
Subtracting 275 from both sides of the equation gives:
</span>
![55h+275-275=440-275 \\ \\ \Rightarrow55h=165](https://tex.z-dn.net/?f=55h%2B275-275%3D440-275%20%5C%5C%20%20%5C%5C%20%5CRightarrow55h%3D165)
<span>
Dividing both sides by 55 gives:
</span>
![\frac{55h}{55} = \frac{165}{55} \\ \\ \Rightarrow h=3](https://tex.z-dn.net/?f=%20%5Cfrac%7B55h%7D%7B55%7D%20%3D%20%5Cfrac%7B165%7D%7B55%7D%20%20%5C%5C%20%20%5C%5C%20%5CRightarrow%20h%3D3)
<span>
Therefore, the time it will take you to reach your destination is 3 hours.</span>