Answer:
Lines a and b are parallel to each other! ... The same-side interior angle theorem states that when two lines that are parallel are intersected by a transversal line, the same-side interior angles that are formed are supplementary, or add up to 180 degrees.
Step-by-step explanation:
Study.com
Solve for x:x/5 - 2 = x/2 + 3
Put each term in x/5 - 2 over the common denominator 5: x/5 - 2 = x/5 - (10)/5:x/5 - (10)/5 = x/2 + 3
x/5 - (10)/5 = (x - 10)/5:(x - 10)/5 = x/2 + 3
Put each term in x/2 + 3 over the common denominator 2: x/2 + 3 = x/2 + 6/2:(x - 10)/5 = x/2 + 6/2
x/2 + 6/2 = (x + 6)/2:(x - 10)/5 = (x + 6)/2
Multiply both sides by 10:(10 (x - 10))/5 = (10 (x + 6))/2
10/5 = (5×2)/5 = 2:2 (x - 10) = (10 (x + 6))/2
10/2 = (2×5)/2 = 5:2 (x - 10) = 5 (x + 6)
Expand out terms of the left hand side:2 x - 20 = 5 (x + 6)
Expand out terms of the right hand side:2 x - 20 = 5 x + 30
Subtract 5 x from both sides:(2 x - 5 x) - 20 = (5 x - 5 x) + 30
2 x - 5 x = -3 x:-3 x - 20 = (5 x - 5 x) + 30
5 x - 5 x = 0:-3 x - 20 = 30
Add 20 to both sides:(20 - 20) - 3 x = 20 + 30
20 - 20 = 0:-3 x = 30 + 20
30 + 20 = 50:-3 x = 50
Divide both sides of -3 x = 50 by -3:(-3 x)/(-3) = 50/(-3)
(-3)/(-3) = 1:x = 50/(-3)
Multiply numerator and denominator of 50/(-3) by -1:Answer: x = (-50)/3
Answer:
(a) 680 km
(b) 680000 m
Step-by-step explanation:
(a) Distance run by hunter every day = 6.8 km
Total number of days under consideration = 100
So the total distance covered by the hunter = ![\[6.8 * 100\] ](https://tex.z-dn.net/?f=%5C%5B6.8%20%2A%20100%5C%5D%0A)
= 680 km
The hunter ran 680 km in the last 100 days.
(b) Converting this value to meters:
1 km = 1000 m
=> 680 km = 680 * 1000 m
= 680000 m
The equivalent distance run by the hunter when converted to meters is 680000 meters.
Answer:
Step-by-step explanation:
Given
Points (−5,−2) and (−3,0)
Required
Find a linear function that passes through the given points
The question implies that we solve for the equation for the line;
First, the slope of the line must be calculated;
This is calculated as thus:
Where 
So, becomes
The equation of the line can then be calculated using any of the given points;
Using
We have
Multiply both sides by x + 5
Subtract 2 from both sides
Replace y with f(x)
Hence, from the list of given options; Option B is correct
