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
9514 1404 393
Answer:
$12,720
Step-by-step explanation:
The amount is given by the formula ...
A = P(1 +rt)
where P is the principal, invested at rate r for t years.
A = $12,000(1 +0.06·1) = $12,720
The total amount after 1 year is $12,720.
The correct answer is A) $75.85.
A discount of 20% means that the cost is 80% of the original. 80%=80/100=0.8
0.8(129) = 103.20
A discount of 30% means that the cost is 70% of the amount before discount. 70%=70/100=0.7
0.7(103.20) = 72.24
A sales tax of 5% means that it is 105% of the amount pre-tax. 105%=105/100=1.05
1.05(72.24) ≈ 75.85
Answer:
36 possible ways
Step-by-step explanation:
Range of digit : 0 up to 9
To obtain the number of strings of 4 decimal digits that have exactly 3 digits that are 9s ; we use the multiplication rule :
In other to have exactly 3 digits from 4 that are 9s :
Say:
We have 3 9s and the last number could be any of the 10 possible digits except 9
First 9 = 1 possible way (since we have only one 9 between (0 to 9)
Second 9 = 1 possible way
Third 9 = 1 possible way
4th digit = 9 ways (could be any digit between 0 and 9, except 9)
Also, we consider the 4th digit's position ; as it could take up any of different positions in between the 9s = 4 ways
Using the product rule :
1 * 1 * 1 * 9 * 4 = 36 possible ways
Given expression : 
.
We need to apply power property of logs to rewrite it.
According to log rule of exponents:
If we compare given expression with the rule the exponent part is f, base is 6.
Therefore, we need to bring exponent f in front of log.
Therefore, 
.
<h3>And correct option is second option
</h3>
