Answer:
The length of PR is 54.
Step-by-step explanation:
![\frac{PT}{PS}=\frac{PQ}{PR}\\\frac{4}{4+23}=\frac{8}{8+QR}\\\frac{4}{27}=\frac{8}{8+QR}\\4(8+QR) = 8*27\\8+QR = 54\\QR = 46\\](https://tex.z-dn.net/?f=%5Cfrac%7BPT%7D%7BPS%7D%3D%5Cfrac%7BPQ%7D%7BPR%7D%5C%5C%5Cfrac%7B4%7D%7B4%2B23%7D%3D%5Cfrac%7B8%7D%7B8%2BQR%7D%5C%5C%5Cfrac%7B4%7D%7B27%7D%3D%5Cfrac%7B8%7D%7B8%2BQR%7D%5C%5C4%288%2BQR%29%20%3D%208%2A27%5C%5C8%2BQR%20%3D%2054%5C%5CQR%20%3D%2046%5C%5C)
So PR = 8+QR = 8+46=54
The value of y is equal to 2
Given:
The figure of a circle.
To find:
The measure of arc AD and measure of each arc.
Solution:
The measure of arc is equal to the central angle of that arc.
The central angle of arc AD is 105 degrees. So,
![m(arc(AD))=105^\circ](https://tex.z-dn.net/?f=m%28arc%28AD%29%29%3D105%5E%5Ccirc)
The central angle of arc BC is 35 degrees. So,
![m(arc(BC))=35^\circ](https://tex.z-dn.net/?f=m%28arc%28BC%29%29%3D35%5E%5Ccirc)
The central angle of arc CD is 50 degrees. So,
![m(arc(CD))=50^\circ](https://tex.z-dn.net/?f=m%28arc%28CD%29%29%3D50%5E%5Ccirc)
The central angle of a complete circle is 360 degrees. So,
![m(arc(AD))+m(arc(BC))+m(arc(CD))+m(arc(AB))=360^\circ](https://tex.z-dn.net/?f=m%28arc%28AD%29%29%2Bm%28arc%28BC%29%29%2Bm%28arc%28CD%29%29%2Bm%28arc%28AB%29%29%3D360%5E%5Ccirc)
![105^\circ+35^\circ+50^\circ+m(arc(AB))=360^\circ](https://tex.z-dn.net/?f=105%5E%5Ccirc%2B35%5E%5Ccirc%2B50%5E%5Ccirc%2Bm%28arc%28AB%29%29%3D360%5E%5Ccirc)
![190^\circ+m(arc(AB))=360^\circ](https://tex.z-dn.net/?f=190%5E%5Ccirc%2Bm%28arc%28AB%29%29%3D360%5E%5Ccirc)
![m(arc(AB))=360^\circ-190^\circ](https://tex.z-dn.net/?f=m%28arc%28AB%29%29%3D360%5E%5Ccirc-190%5E%5Ccirc)
![m(arc(AB))=170^\circ](https://tex.z-dn.net/?f=m%28arc%28AB%29%29%3D170%5E%5Ccirc)
Therefore, the measure of arc AD is 105°, the measure of arc BC is 35°, the measure of arc CD is 50° and the measure of arc AB is 170°
Answer:
(1,2) (3,2) ( 5,2)
Step-by-step explanation:
Each input value can only go to one output value
The only one that has each input only going to one output is (1,2) (3,2) ( 5,2)
Answer:
y = 2x - 3
Step-by-step explanation:
Since the equation for the line y = 2x + 5 is already in slope-intercept form (y = mx + b), the slope (m) is 2. A parallel line will have the same slope. Now use point-slope formula to find an equation for the parallel line including point (3,3). Point-slope formula is:
(y – y₁) = m(x – x₁), where m is the slope (2) and (x₁, y₁) is the point the line passes through (3,3).
Therefore:
(y – 3) = 2 (x – 3)
y – 3 = 2x – 6
y – 3 + 3 = 2x – 6 + 3
y = 2x - 3