Answer:
x=15
Step-by-step explanation:
the angle 7x+12 and 63 are on opposite sides of complimentary, meaning they add to 180.
180-63 = 117
117-12 = 105
105/7 = 15
Answer: 120 ways
Step-by-step explanation: In this problem, we're asked how many ways can 5 people be arranged in a line.
Let's start by drawing 5 blanks to represent the 5 different positions in the line.
Now, we know that 5 different people can fill the spot in the first position. However, once the first position is filled, only 4 people can fill the second spot and once the second spot is filled, only 3 people can fill the third spot and so on. So we have <u>5</u> <u>4</u> <u>3</u> <u>2</u> <u>1</u>.
Now, based on the counting principle, there are 5 x 4 x 3 x 2 x 1 ways for all 5 spots to be filled.
5 x 4 is 20, 20 x 3 is 60, 60 x 2 is 120, and 120 x 1 is 120.
So there are 120 ways for all 5 spots to be filled which means that there are 120 ways that 5 people can be arranged in a line.
I have also shown my work on the whiteboard in the image attached.
Answer:
SAS
Step-by-step explanation:
Triangles QRS and TRS share the same side which is congruent by the reflexive property and perpendicular angles. They also have another congruent leg as marked on the diagram. These forms side-angle-side or SAS.