Answer:
20
Step-by-step explanation:
10- 10, <u>20</u>, 30, 40 ,50
4- 4, 8, 12, 16, <u>20</u>
Answer: x = 8
(the correct answer was not provided as an option)
<u>Step-by-step explanation:</u>
![log_2(x-6)+log_2(x-4)=log_2(x)\\\\log_2[(x-6)(x-4)]=log_2(x)\\\\(x-6)(x-4)=x\\\\x^2-10x+24=x\\\\x^2-11x+24=0\\\\(x-3)(x-8)=0\\\\x=3\qquad x=8\\\\\\\text{The term after the log symbol (inside the parenthesis) must be greater than 0!}\\\\Check:\\3-6>0\ \text{FALSE --- so 3 is not a valid solution}\\\\8-6>0\ \text{TRUE}\\8-4>0\ \text{TRUE}\\8>0\ \text{TRUE --- 8 is a valid solution because it is true for all}](https://tex.z-dn.net/?f=log_2%28x-6%29%2Blog_2%28x-4%29%3Dlog_2%28x%29%5C%5C%5C%5Clog_2%5B%28x-6%29%28x-4%29%5D%3Dlog_2%28x%29%5C%5C%5C%5C%28x-6%29%28x-4%29%3Dx%5C%5C%5C%5Cx%5E2-10x%2B24%3Dx%5C%5C%5C%5Cx%5E2-11x%2B24%3D0%5C%5C%5C%5C%28x-3%29%28x-8%29%3D0%5C%5C%5C%5Cx%3D3%5Cqquad%20x%3D8%5C%5C%5C%5C%5C%5C%5Ctext%7BThe%20term%20after%20the%20log%20symbol%20%20%28inside%20the%20parenthesis%29%20must%20be%20greater%20than%200%21%7D%5C%5C%5C%5CCheck%3A%5C%5C3-6%3E0%5C%20%5Ctext%7BFALSE%20---%20so%203%20is%20not%20a%20valid%20solution%7D%5C%5C%5C%5C8-6%3E0%5C%20%5Ctext%7BTRUE%7D%5C%5C8-4%3E0%5C%20%5Ctext%7BTRUE%7D%5C%5C8%3E0%5C%20%5Ctext%7BTRUE%20---%208%20is%20a%20valid%20solution%20because%20it%20is%20true%20for%20all%7D)
Answer:
1). angle 3= 48° [by vertically opposite angle]
2). angle 4 = 132° [by linear pair]
3). angle 5 = 50° [angle 6 and angle 5 are complementary angles]
4). angle 8 =36° [angle 7 and angle 8 are complementary angles]
5). angle 6 = 31° [sum of angle on straight line is 180°]
6). angle 8=33° [sum of angles on straight line is 180°]
7). angle 9=40° [sum of angles of triangle is 180°]
8). angle 3= 30°[angle 9 and 12 are linear pair and 9 is part of the triangle. so, sum of all angle of triangle is 180° ]
9). angle 15= 80° [sum of angles of triangle is 180°]
10). angle 8=35° [sum of angles of triangle is 180°]
11). angle 7=66°[sum of angles of triangle is 180°]
12). angle 14=105° [Sum of angles of triangle is 180°]
13). angle 12=130°[by sum of angle is 180°we'll find 9 then by linear pair angle 12= 130°]
14). angle 8=55° [ angle 14 and 16 are equal by vertically opposite angles and angle 14+angle 8+angle 3=180°]
15). angle 15=90°[first find 7 and 9 by sum of 90°and sum 180° then sum of angles of triangle is180°]
16). angle 16=95°[angle 7 and 8 are complementary angles and angle 1 and 3 are equal by vertically opposite angles now we have our two angles of the triangle so we can find third angle because sum of angle of triangle is 180°]
She should us the coupon for $5 because with 10% she only gets 1 dollar of!
have a nice day!<3
