Answer:
a) 62
b) 24
Step-by-step explanation:
For A, add the students who watched only one movie: 18+24+20=62
For B, look at how many students only watched Star Wars: 24
<u>Direct Variation:</u> ![\frac{y}{x} = k](https://tex.z-dn.net/?f=%5Cfrac%7By%7D%7Bx%7D%20%3D%20k)
![\frac{15}{2} = k](https://tex.z-dn.net/?f=%5Cfrac%7B15%7D%7B2%7D%20%3D%20k)
when y = 7: ![\frac{7}{x} = \frac{15}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B7%7D%7Bx%7D%20%3D%20%5Cfrac%7B15%7D%7B2%7D)
14 = 15x
![\frac{14}{15} = x](https://tex.z-dn.net/?f=%5Cfrac%7B14%7D%7B15%7D%20%3D%20x)
<u>Inverse variation:</u> y*x = k
15 * 2 = k
30 = k
when y = 7: 7 * x = 30
![x = \frac{30}{7}](https://tex.z-dn.net/?f=x%20%3D%20%5Cfrac%7B30%7D%7B7%7D%20)
![|6+9x|\le24](https://tex.z-dn.net/?f=%7C6%2B9x%7C%5Cle24)
this is the correct way to solve these types of exercises
then we will try to do the same where a is (6+9x) and b is 24
![|6+9x|\le24\longrightarrow-24\le6+9x\le24](https://tex.z-dn.net/?f=%7C6%2B9x%7C%5Cle24%5Clongrightarrow-24%5Cle6%2B9x%5Cle24)
and solve the right inequality for x
![-24\le6+9x\le24](https://tex.z-dn.net/?f=-24%5Cle6%2B9x%5Cle24)
subtract 6 for all expression
![\begin{gathered} -24-6\le6-6+9x\le24-6 \\ -30\le9x\le18 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20-24-6%5Cle6-6%2B9x%5Cle24-6%20%5C%5C%20-30%5Cle9x%5Cle18%20%5Cend%7Bgathered%7D)
now divide on 9
![\begin{gathered} -\frac{30}{9}\le\frac{9x}{9}\le\frac{18}{9} \\ \\ -\frac{10}{3}\le x\le2 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20-%5Cfrac%7B30%7D%7B9%7D%5Cle%5Cfrac%7B9x%7D%7B9%7D%5Cle%5Cfrac%7B18%7D%7B9%7D%20%5C%5C%20%20%5C%5C%20-%5Cfrac%7B10%7D%7B3%7D%5Cle%20x%5Cle2%20%5Cend%7Bgathered%7D)
ok, this means that the x values will be from -10/3 to 2 including these
Graph
solution is the red zone
Given:
![m \angle A B D=96^{\circ}](https://tex.z-dn.net/?f=m%20%5Cangle%20A%20B%20D%3D96%5E%7B%5Ccirc%7D)
![m \angle 2 =m \angle 1+ 26^{\circ}](https://tex.z-dn.net/?f=m%20%5Cangle%202%20%3Dm%20%5Cangle%201%2B%2026%5E%7B%5Ccirc%7D)
To find:
![m \angle 1](https://tex.z-dn.net/?f=m%20%5Cangle%201)
Solution:
![m \angle DBC+ m \angle CBA = m \angle ABD](https://tex.z-dn.net/?f=m%20%5Cangle%20DBC%2B%20m%20%5Cangle%20CBA%20%3D%20m%20%5Cangle%20ABD)
![m \angle 1+ m \angle 2 = m \angle ABD](https://tex.z-dn.net/?f=m%20%5Cangle%201%2B%20m%20%5Cangle%202%20%3D%20m%20%5Cangle%20ABD)
Substitute
.
![m \angle 1+ m \angle 1 + 26^\circ = 96^\circ](https://tex.z-dn.net/?f=m%20%5Cangle%201%2B%20m%20%5Cangle%201%20%2B%2026%5E%5Ccirc%20%3D%2096%5E%5Ccirc)
![2m \angle 1+ 26^\circ = 96^\circ](https://tex.z-dn.net/?f=2m%20%5Cangle%201%2B%2026%5E%5Ccirc%20%3D%2096%5E%5Ccirc)
Subtract 26° from both sides.
![2m \angle 1+ 26^\circ -26^\circ = 96^\circ -26^\circ](https://tex.z-dn.net/?f=2m%20%5Cangle%201%2B%2026%5E%5Ccirc%20-26%5E%5Ccirc%20%3D%2096%5E%5Ccirc%20-26%5E%5Ccirc)
![2m \angle 1 = 70^\circ](https://tex.z-dn.net/?f=2m%20%5Cangle%201%20%3D%2070%5E%5Ccirc)
Divide by 2 on both sides, we get
![m \angle 1=35^{\circ}](https://tex.z-dn.net/?f=m%20%5Cangle%201%3D35%5E%7B%5Ccirc%7D)
Therefore, m∠1 = 35°.