The lines are
i) y=-x+6
ii) y=2x-3
The solution of the system of equations is found by equalizing the 2 equations:
-x+6=2x-3
-2x-x=-6-3
-3x=-9
x=-9/(-3)=3
substitute x=3 in either i) or ii):
i) y=-3+6=3
ii) y=2(3)-3=6-3=3
(the result is the same, so checking one is enough)
This means that the point (3, 3) is a point which is in both lines, so a solution to the system.
In graphs, this means that the lines intersect at (3, 3) ONLY
Answer: The graph where the lines intersect at (3, 3)
Divide by 2.5: 2.5(12.75x+24.50)/2.5 = 188.75/2.5 .
simplify: 12.75x + 24.50=75.5 .
subtract 24.50 from both sides
simplify: 12.75x = 51 .
x= 4.
Answer:
900 front row seats
Step-by-step explanation:
Tickets for front row seat = 220 dollars (y)
Cost of remaining seats ticket = 50 dollars (z)
Number of front row seats = x
Number of remaining seats = 2050 (w)
Total amount earned when stadium is full = 300,500 dollars (T)
so if we formulate this using our variables y,z,x,w and T problem it becomes:
y*x + z*w = T, which says the
Tickets for front row seat times Number of front row seats plus Cost of remaining seats ticket times Number of remaining seats gives us Total amount earned by the stadium.
220*x + 2050*50 = 300500
220*x = 300500-102500
220*x = 198000
divide both side by 220
x = 900
If Rosie is trying to figure out the amount that she needs to pay for her total yoga classes.
First, we need to establish what we know, and what we do not know.
We know that Rosie knows how many yoga classes she has.
We know that she knows how many yoga classes she bought.
She does not know how much each yoga class costs.
So, that cancels out A, B, and C because she doesn't know how much one yoga class costs.
It can only be D, because D tells us that she knows the total is $30, but not the amount each class costs.
Answer:
x = 3/2
Step-by-step explanation:
Solve for x over the real numbers:
(5 x^2 - 4 x + 6) (3 - 2 x) = 0
Split into two equations:
3 - 2 x = 0 or 5 x^2 - 4 x + 6 = 0
Multiply both sides by -1:
2 x - 3 = 0 or 5 x^2 - 4 x + 6 = 0
Add 3 to both sides:
2 x = 3 or 5 x^2 - 4 x + 6 = 0
Divide both sides by 2:
x = 3/2 or 5 x^2 - 4 x + 6 = 0
Divide both sides by 5:
x = 3/2 or x^2 - (4 x)/5 + 6/5 = 0
Subtract 6/5 from both sides:
x = 3/2 or x^2 - (4 x)/5 = -6/5
Add 4/25 to both sides:
x = 3/2 or x^2 - (4 x)/5 + 4/25 = -26/25
Write the left hand side as a square:
x = 3/2 or (x - 2/5)^2 = -26/25
(x - 2/5)^2 = -26/25 has no solution since for all x on the real line, (x - 2/5)^2 >=0 and -26/25<0:
Answer: x = 3/2
