10. from the question; the circle theorem obeyed is "angled formed by semi-circle"
The angle formed in a semicircle is 90 degrees, hence
![m\angle XYZ=90^{\circ}](https://tex.z-dn.net/?f=m%5Cangle%20XYZ%3D90%5E%7B%5Ccirc%7D)
This gives
![m\angle YXZ\text{ + m}\angle YZX\text{ = 90}](https://tex.z-dn.net/?f=m%5Cangle%20YXZ%5Ctext%7B%20%2B%20m%7D%5Cangle%20YZX%5Ctext%7B%20%3D%2090%7D)
But
![\begin{gathered} m\angle YXZ\text{ = 2x + 8} \\ m\angle YZX\text{ = 5X - 2} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20m%5Cangle%20YXZ%5Ctext%7B%20%3D%202x%20%2B%208%7D%20%5C%5C%20m%5Cangle%20YZX%5Ctext%7B%20%3D%205X%20-%202%7D%20%5Cend%7Bgathered%7D)
Substituting values we get
![\begin{gathered} 2x\text{ + 8 + 5x - 2 = 90} \\ 2x\text{ + 5x + 8 - 2 = 90} \\ 7x\text{ + 6 = 90} \\ 7x\text{ = 90 -6} \\ 7x\text{ = 84} \\ \text{divide both sides by 7} \\ x\text{ = }\frac{84}{7} \\ x\text{ = 12} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%202x%5Ctext%7B%20%2B%208%20%2B%205x%20-%202%20%3D%2090%7D%20%5C%5C%202x%5Ctext%7B%20%2B%205x%20%2B%208%20-%202%20%3D%2090%7D%20%5C%5C%207x%5Ctext%7B%20%2B%206%20%3D%2090%7D%20%5C%5C%207x%5Ctext%7B%20%3D%2090%20-6%7D%20%5C%5C%207x%5Ctext%7B%20%3D%2084%7D%20%5C%5C%20%5Ctext%7Bdivide%20both%20sides%20by%207%7D%20%5C%5C%20x%5Ctext%7B%20%3D%20%7D%5Cfrac%7B84%7D%7B7%7D%20%5C%5C%20x%5Ctext%7B%20%3D%2012%7D%20%5Cend%7Bgathered%7D)
hence, x =12
Answer:
80
Step-by-step explanation:
Answer:
Step-by-step explanation:
slope is 3/4.
I'm pretty sure, cuz it's rise/run
Hey there :)
0.043
The first 0 before the decimal point is not significant since it is used for cosmetic purpose
The 0 after the decimal is not significant as the 0 is used to locate the decimal point
The 4 is the first nonzero integer and it counts as a significant figure
Therefore, 0.04 will be your answer rounded to 1 s.f
Answer:
The total members in the Spanish Club = 50
Step-by-step explanation:
Let the total members in the Spanish Club = x
Now, number of girls in the club = 30
Three-fifths of the members are girls.
⇒
of total members x = 30
or, ![(\frac{3}{5}) \times x = 30\\](https://tex.z-dn.net/?f=%28%5Cfrac%7B3%7D%7B5%7D%29%20%20%5Ctimes%20%20x%20%3D%20%2030%5C%5C)
Now, solving for x, we get:
![x = 30 \times\frac{5}{3} = 50](https://tex.z-dn.net/?f=x%20%3D%2030%20%5Ctimes%5Cfrac%7B5%7D%7B3%7D%20%20%20%3D%2050)
or, x = 50
Hence,the total members in the Spanish Club = 50