Answer:
y = 65°
Step-by-step explanation:
z = 70° (corresponding angels are equal)
y + z = 135° (exterior angle theorem of a triangle)
y + 70 = 135 (substitution)
Subtract 70 from each side
y + 70 - 70 = 135 - 70
y = 65
Does it give you options? If so, what are they?
Answer:
![\large\boxed{4x^2-25=(2x-5)(2x+5)}](https://tex.z-dn.net/?f=%5Clarge%5Cboxed%7B4x%5E2-25%3D%282x-5%29%282x%2B5%29%7D)
Step-by-step explanation:
![a^2-b^2=(a-b)(a+b)\\\\4x^2-25=2^2x^2-5^2\qquad\text{use}\ (ab)^n=a^nb^n\\\\=(2x)^2-5^2=(2x-5)(2x+5)](https://tex.z-dn.net/?f=a%5E2-b%5E2%3D%28a-b%29%28a%2Bb%29%5C%5C%5C%5C4x%5E2-25%3D2%5E2x%5E2-5%5E2%5Cqquad%5Ctext%7Buse%7D%5C%20%28ab%29%5En%3Da%5Enb%5En%5C%5C%5C%5C%3D%282x%29%5E2-5%5E2%3D%282x-5%29%282x%2B5%29)
Answer:
The first 4 guests can arrive in 32,760 ways.
Step-by-step explanation:
The order in which the guests arrive is important. For example, A,B,C,D is a different outcome to B,A,C,D. So we use the permutations formula to solve this question.
Permutations formula:
The number of possible permutations of x elements from a set of n elements is given by the following formula:
![P_{(n,x)} = \frac{n!}{(n-x)!}](https://tex.z-dn.net/?f=P_%7B%28n%2Cx%29%7D%20%3D%20%5Cfrac%7Bn%21%7D%7B%28n-x%29%21%7D)
In this question:
4 guests from a set of 15. So
![P_{(15,4)} = \frac{15!}{(15-4)!} = 32760](https://tex.z-dn.net/?f=P_%7B%2815%2C4%29%7D%20%3D%20%5Cfrac%7B15%21%7D%7B%2815-4%29%21%7D%20%3D%2032760)
The first 4 guests can arrive in 32,760 ways.