Find the equation of the line connecting (0, 5) and (-2, 0).
As we go from the first point to the second, x decreases by 2 and y decreases by 5. Thus, the slope of this line is m = rise / run = -5/(-2), or 5/2.
Starting with the general equation of a line in slope-intercept form, y = mx + b, substitute the knowns as appropriate to determine the value of b:
y= mx + b => 5 = (5/2)(0) + b. Then b = 5, and the desired equation is
y = (5/2)x + 5.
Check this! If we subst. the coordinates of (-2,0) into this equation, is the equation true?
0 = (5/2)(-2) + 5
Yes. So, y = (5/2)x + 5 is the desired equation.
Answer:
(3x -1) (3x+1)
Step-by-step explanation:
9x^2 - 1
Rewriting
(3x)^2 -1^2
This is the difference of squares a^2 -b^2 = (a+b) (a-b)
(3x -1) (3x+1)
Answer:
60%
Step-by-step explanation:
You can solve this problem by setting up a system of equations.
Let's say that the number of tickets bought by students in the first year is x, and the number bought by continuing students is y. From there, you can set it up like this:
0.4x+0.2y=160
x+y=500
Now, you can multiply the first equation by 5 on both sides to get:
2x+y=800
Subtracting the second equation from the first equation now yields:
x=300
y=200
Since 300 of the 500 tickets bought were from the first year students, and 300/500 is 0.6, 60% of the students who bought the ticket were first year students. Hope this helps!
