Answer:If the digit of 0 is allowed, then:
1/(10*9*8)= 1/720
If it is not permitted, then:
1/(9*8*7)= 1/504
I hope this helps you!
Step-by-step explanation:
<u>In a parallelogram,</u>
⇒the angles adjacent to each other
⇒ are of the same measure
⇒so
∠A = ∠C
∠B = ∠D
<u>Let's solve</u>:
![7z +5 = 8z - 10\\5+10=8z-7z\\8z-7z=5+10\\z = 15](https://tex.z-dn.net/?f=7z%20%2B5%20%3D%208z%20-%2010%5C%5C5%2B10%3D8z-7z%5C%5C8z-7z%3D5%2B10%5C%5Cz%20%3D%2015)
![5w-30=3w+10\\5w-3w=30+10\\2w = 40\\w=20](https://tex.z-dn.net/?f=5w-30%3D3w%2B10%5C%5C5w-3w%3D30%2B10%5C%5C2w%20%3D%2040%5C%5Cw%3D20)
<u>Let's check</u>:
⇒ for all quadrilaterals like a parallelogram
⇒all the angle measures added up to 360, so:
![(7z+5)+(8z-10)+(5w-30)+(3w+10)=360\\(7(15)+5)+(8(15)-10)+(5(20)-30)+(3(20)+10)=360\\(105+5)+(120-10)+(100-30)+(60+10)=360\\110+110+70+70=360\\220+140=360\\360=360](https://tex.z-dn.net/?f=%287z%2B5%29%2B%288z-10%29%2B%285w-30%29%2B%283w%2B10%29%3D360%5C%5C%287%2815%29%2B5%29%2B%288%2815%29-10%29%2B%285%2820%29-30%29%2B%283%2820%29%2B10%29%3D360%5C%5C%28105%2B5%29%2B%28120-10%29%2B%28100-30%29%2B%2860%2B10%29%3D360%5C%5C110%2B110%2B70%2B70%3D360%5C%5C220%2B140%3D360%5C%5C360%3D360)
<u>Thus</u>:
<u>Answer: w = 20 and z = 15</u>
Hope that helps!
Answer:
Step-by-step explanation:
The direction of movement of Jordan on his birthday forms a right angle triangle. His movement from his house to his parents due south represents the opposite side of the right angle triangle. His movement due west represents the adjacent side and the movement back home along the straight line, d represents the hypotenuse. To determine d, we would apply the Pythagorean theorem. Thus
d² = 6² + 4² = 52
d = √52 = 7.2 km
The total distance that he drove on his birthday is
6 + 4 + 7.2 = 17.2 km
Answer:
![y = \sin( \frac{2\pi}{3} x)](https://tex.z-dn.net/?f=y%20%3D%20%20%5Csin%28%20%5Cfrac%7B2%5Cpi%7D%7B3%7D%20x%29%20)
Step-by-step explanation:
The equation of a sine function is y = a sin(bx), where a = amplitude (aka height) and b equals period (aka time). I'm assuming there isn't any information other than the graph shown, so let's assume that our amplitude is 1 and our period is 2pi/3. Plugging these values into the equation, we get:
![y = (1) \sin(( \frac{2\pi}{3})x ) = \sin(\frac{2{\pi} }{3}x )](https://tex.z-dn.net/?f=y%20%3D%20%281%29%20%5Csin%28%28%20%5Cfrac%7B2%5Cpi%7D%7B3%7D%29x%20%29%20%20%3D%20%20%5Csin%28%5Cfrac%7B2%7B%5Cpi%7D%20%7D%7B3%7Dx%20%29)