Answer:
<XWZ is a right angle
Step-by-step explanation:
Since <YWZ and <XWY both equal 45 degrees, So, <XWZ is a right angle.
Answer:
![l = 28](https://tex.z-dn.net/?f=l%20%3D%2028)
Step-by-step explanation:
Given
![S = \sum (2k - 3); k = 4\ to\ l](https://tex.z-dn.net/?f=S%20%3D%20%5Csum%20%282k%20-%203%29%3B%20k%20%3D%204%5C%20to%5C%20l)
Required
What is l when S = 725
This can be solved using Sum of n terms of an AP;
![S_n = \frac{n}{2}(T_1 + T_n)](https://tex.z-dn.net/?f=S_n%20%3D%20%5Cfrac%7Bn%7D%7B2%7D%28T_1%20%2B%20T_n%29)
Where
![S_n = 725](https://tex.z-dn.net/?f=S_n%20%3D%20725)
![T_1 = first\ term](https://tex.z-dn.net/?f=T_1%20%3D%20first%5C%20term)
To get T1; we substitute 4 for k in 2k - 3
![T_1 = 2 * 4 - 3](https://tex.z-dn.net/?f=T_1%20%3D%202%20%2A%204%20-%203)
![T_1 = 8 - 3](https://tex.z-dn.net/?f=T_1%20%3D%208%20-%203)
![T_1 = 5](https://tex.z-dn.net/?f=T_1%20%3D%205)
![T_n = last\ term](https://tex.z-dn.net/?f=T_n%20%3D%20last%5C%20term)
To get Tn; we substitute l for k in 2k - 3
![T_n = 2 * l - 3](https://tex.z-dn.net/?f=T_n%20%3D%202%20%2A%20l%20-%203)
![T_n = 2l - 3](https://tex.z-dn.net/?f=T_n%20%3D%202l%20-%203)
n = the number of terms;
Since k = 4 to l, then
![n = l - 4 +1](https://tex.z-dn.net/?f=n%20%3D%20l%20-%204%20%2B1)
![n = l - 3](https://tex.z-dn.net/?f=n%20%3D%20l%20-%203)
Substitute these values in ![S_n = \frac{n}{2}(T_1 + T_n)](https://tex.z-dn.net/?f=S_n%20%3D%20%5Cfrac%7Bn%7D%7B2%7D%28T_1%20%2B%20T_n%29)
![725 = \frac{l-3}{2}(5 + 2l - 3)](https://tex.z-dn.net/?f=725%20%3D%20%5Cfrac%7Bl-3%7D%7B2%7D%285%20%2B%202l%20-%203%29)
Collect Like Terms
![725 = \frac{l-3}{2}(2l + 5- 3)](https://tex.z-dn.net/?f=725%20%3D%20%5Cfrac%7Bl-3%7D%7B2%7D%282l%20%2B%205-%203%29)
![725 = \frac{l-3}{2}(2l + 2)](https://tex.z-dn.net/?f=725%20%3D%20%5Cfrac%7Bl-3%7D%7B2%7D%282l%20%2B%202%29)
Open the bracket
![725 = \frac{l-3}{2} * 2l + \frac{l-3}{2} * 2](https://tex.z-dn.net/?f=725%20%3D%20%5Cfrac%7Bl-3%7D%7B2%7D%20%2A%202l%20%2B%20%5Cfrac%7Bl-3%7D%7B2%7D%20%2A%202)
![725 = (l-3) * l + (l-3)](https://tex.z-dn.net/?f=725%20%3D%20%28l-3%29%20%2A%20l%20%2B%20%28l-3%29)
![725 = l^2-3l + l-3](https://tex.z-dn.net/?f=725%20%3D%20l%5E2-3l%20%2B%20l-3)
![725 = l^2-2l -3](https://tex.z-dn.net/?f=725%20%3D%20l%5E2-2l%20-3)
Subtract 725 from both sides
![725 - 725 = l^2-2l -3 - 725](https://tex.z-dn.net/?f=725%20-%20725%20%3D%20l%5E2-2l%20-3%20-%20725)
![l^2-2l -3 - 725 = 0](https://tex.z-dn.net/?f=l%5E2-2l%20-3%20-%20725%20%3D%200)
![l^2-2l - 728 = 0](https://tex.z-dn.net/?f=l%5E2-2l%20-%20728%20%3D%200)
![l^2 + 26l - 28l - 728 = 0](https://tex.z-dn.net/?f=l%5E2%20%2B%2026l%20-%2028l%20-%20728%20%3D%200)
![l(l + 26) - 28(l + 26) = 0](https://tex.z-dn.net/?f=l%28l%20%2B%2026%29%20-%2028%28l%20%2B%2026%29%20%3D%200)
![(l - 28)(l + 26) = 0](https://tex.z-dn.net/?f=%28l%20-%2028%29%28l%20%2B%2026%29%20%3D%200)
or ![l + 26 = 0](https://tex.z-dn.net/?f=l%20%2B%2026%20%3D%200)
or ![l = -26](https://tex.z-dn.net/?f=l%20%3D%20-26)
But l must be positive;
Hence, ![l = 28](https://tex.z-dn.net/?f=l%20%3D%2028)
Answer:
1) 55°
2)45°
3)62°
4)23°
Step-by-step explanation:
Complementary angles are angles that add up to 90°.
1) 90°-35°=55°
2)90°-45°=45°
3)90°-28°=62°
4)90°-67°=23°
Answer: 10 baseballs
Step-by-step explanation:
71 divided by 7 equals 10, he would have a remainder of $1, I hope this is helpful :)
The area of the triangle should be 0.92.
The answer is A, it being squared.