Remark
A kite is constructed such that AB = BC and AD = DC. AB = sqrt( (1/2)AC + 18^2) see diagram. AD = sqrt(24^2 + 32^2)
Step One
Solve for AB
1/2 AC = 24 (AC is given as 48)
18 is a given length
AB = sqrt(24^2 + 18^2) = sqrt(576 + 324) = sqrt(900) = 30
Step Two
Find the length of AD
AD = sqrt(32^2 + 24^2) = sqrt(1024 + 576) = sqrt(1600) = 40
Step Three
Find the Perimeter.
P = 2 * 30 + 2*40 = 60 + 80 = 140
P = 140 <<<<< Answer
Answer: Second option.
Step-by-step explanation:
As you can observe in the picture given in the exercise, there are two Right triangles formed inside the rectangle: CDA and ABC.
You need to use the Pythagorean Theorem to solve this exercise. This is:
![a^2=b^2+c^2](https://tex.z-dn.net/?f=a%5E2%3Db%5E2%2Bc%5E2)
Where "a" is the hypotenuse and "b" and "c" are the legs of the Right triangle.
If you solve for one of the legs, you get the following equation:
![a^2-c^2=b^2\\\\b=\sqrt{a^2-c^2}](https://tex.z-dn.net/?f=a%5E2-c%5E2%3Db%5E2%5C%5C%5C%5Cb%3D%5Csqrt%7Ba%5E2-c%5E2%7D)
In this case, you can identify in the figure that:
![a=AC=65\ m\\\\b=BC=x\\\\c=AB=63\ m](https://tex.z-dn.net/?f=a%3DAC%3D65%5C%20m%5C%5C%5C%5Cb%3DBC%3Dx%5C%5C%5C%5Cc%3DAB%3D63%5C%20m)
Finally, you must substitute these known values into the equation
and then evaluate in order to find the value of "x". You get that this is:
![x=\sqrt{(65\ m)^2-(63\ m)^2}\\\\x=16\ m](https://tex.z-dn.net/?f=x%3D%5Csqrt%7B%2865%5C%20m%29%5E2-%2863%5C%20m%29%5E2%7D%5C%5C%5C%5Cx%3D16%5C%20m)
Answer:
x and y are both equal to 57.5°
Step-by-step explanation:
180° - 65° = 115°
115 ÷ 2 = 57.5
Answer: option D) An = 3an - 9a
Justification:
1) That is an arithmetic sequence which you prove by determining the difference between two consecutive terms (which shall be constant if it indeed is an arithmetic sequence):
2)
Second term - first term = -3a - (-6a) = -3a + 6a = 3a
Third term - second term = 0a - (-3a) = 3a
Fourth term - third term = 3a - 0a = 3a
Fith term - fourth term = 6a - 3a = 3a
Therefore, it is an arithmetic sequence with difference d = 3a.
3) the general rule for the nth term of an arithmetic sequence is given by the formula:
An = Ao + d (n - 1)
Where Ao = -6a and d, as determined above, is 3a
=> An = -6a + 3a (n - 1)
Expand the parenthesis (distributive property) =>
An = -6a + 3an - 3a = -9a + 3an = 3an - 9a = option D. <------- answer.
Answer:
9.35
Step-by-step explanation:
because you take 3.5 away from 12.85