Answer:
32.50
Step-by-step explanation:
I took the test
Check the picture below.
bear in mind that, the "bases" are the two parallel sides, and the height is the distance between them.
![\bf \textit{area of this trapezoid}\\\\ A=\cfrac{AB(BC+AD)}{2}\\\\ -------------------------------\\\\ \textit{distance between 2 points}\\ \quad \\ \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) A&({{ -1}}\quad ,&{{ 5}})\quad % (c,d B&({{ 3}}\quad ,&{{ 2}}) \end{array}\qquad % distance value d = \sqrt{({{ x_2}}-{{ x_1}})^2 + ({{ y_2}}-{{ y_1}})^2} \\\\\\ AB=\sqrt{[3-(-1)]^2+[2-5]^2}\implies AB=\sqrt{(3+1)^2+(2-5)^2} \\\\\\ AB=\sqrt{16+9}\implies AB=\sqrt{25}\implies \boxed{AB=5}](https://tex.z-dn.net/?f=%5Cbf%20%5Ctextit%7Barea%20of%20this%20trapezoid%7D%5C%5C%5C%5C%0AA%3D%5Ccfrac%7BAB%28BC%2BAD%29%7D%7B2%7D%5C%5C%5C%5C%0A-------------------------------%5C%5C%5C%5C%0A%5Ctextit%7Bdistance%20between%202%20points%7D%5C%5C%20%5Cquad%20%5C%5C%0A%5Cbegin%7Barray%7D%7Blllll%7D%0A%26x_1%26y_1%26x_2%26y_2%5C%5C%0A%25%20%20%28a%2Cb%29%0AA%26%28%7B%7B%20-1%7D%7D%5Cquad%20%2C%26%7B%7B%205%7D%7D%29%5Cquad%20%0A%25%20%20%28c%2Cd%0AB%26%28%7B%7B%203%7D%7D%5Cquad%20%2C%26%7B%7B%202%7D%7D%29%0A%5Cend%7Barray%7D%5Cqquad%20%0A%25%20%20distance%20value%0Ad%20%3D%20%5Csqrt%7B%28%7B%7B%20x_2%7D%7D-%7B%7B%20x_1%7D%7D%29%5E2%20%2B%20%28%7B%7B%20y_2%7D%7D-%7B%7B%20y_1%7D%7D%29%5E2%7D%0A%5C%5C%5C%5C%5C%5C%0AAB%3D%5Csqrt%7B%5B3-%28-1%29%5D%5E2%2B%5B2-5%5D%5E2%7D%5Cimplies%20AB%3D%5Csqrt%7B%283%2B1%29%5E2%2B%282-5%29%5E2%7D%0A%5C%5C%5C%5C%5C%5C%0AAB%3D%5Csqrt%7B16%2B9%7D%5Cimplies%20AB%3D%5Csqrt%7B25%7D%5Cimplies%20%5Cboxed%7BAB%3D5%7D)
![\bf -------------------------------\\\\ \textit{distance between 2 points}\\ \quad \\ \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) A&({{ -1}}\quad ,&{{ 5}})\quad % (c,d D&({{ -13}}\quad ,&{{ -11}}) \end{array} \\\\\\ AD=\sqrt{[-13-(-1)]^2+[-11-5]^2} \\\\\\ AD=\sqrt{(-13+1)^2+(-16)^2}\implies AD=\sqrt{144+256} \\\\\\ AD=\sqrt{400}\implies \boxed{AD=\sqrt{20}}](https://tex.z-dn.net/?f=%5Cbf%20-------------------------------%5C%5C%5C%5C%0A%5Ctextit%7Bdistance%20between%202%20points%7D%5C%5C%20%5Cquad%20%5C%5C%0A%5Cbegin%7Barray%7D%7Blllll%7D%0A%26x_1%26y_1%26x_2%26y_2%5C%5C%0A%25%20%20%28a%2Cb%29%0AA%26%28%7B%7B%20-1%7D%7D%5Cquad%20%2C%26%7B%7B%205%7D%7D%29%5Cquad%20%0A%25%20%20%28c%2Cd%0AD%26%28%7B%7B%20-13%7D%7D%5Cquad%20%2C%26%7B%7B%20-11%7D%7D%29%0A%5Cend%7Barray%7D%0A%5C%5C%5C%5C%5C%5C%0AAD%3D%5Csqrt%7B%5B-13-%28-1%29%5D%5E2%2B%5B-11-5%5D%5E2%7D%0A%5C%5C%5C%5C%5C%5C%0AAD%3D%5Csqrt%7B%28-13%2B1%29%5E2%2B%28-16%29%5E2%7D%5Cimplies%20AD%3D%5Csqrt%7B144%2B256%7D%0A%5C%5C%5C%5C%5C%5C%0AAD%3D%5Csqrt%7B400%7D%5Cimplies%20%5Cboxed%7BAD%3D%5Csqrt%7B20%7D%7D)
so, the area for this trapezoid is then
Take 3 out of both of them
3(5x+2)
See attachment although I gather this is not your question. I did the graph(s) for the function,
[] signs mean that the number is included in the domain and () mean that the number is not included. Now,
1. [-1,5)
Because x is greater than or equal to -1 (included) but less than 5 (excluded
2. [-5,13)
When we plug in x = -1, we get the minimum value of -5, which is included because its x-value was included. The, we plug in x = 5 to find the range's maximum and this is excluded because its x-value was excluded.
3. 218
x = 6 lies in the domain of the first function so we will use it to evaluate the value of x = 6. We do this by simply substituting x into the function.
4. 12
x = 9 is included in the domain of the second function and the value of the second function at all points is 12.
5. 103
x = 10 is included in the domain of the second function so we will use it to evaluate the value of x = 10. This is done by substituting x into the equation.
