Answer: 115, 2645
(x= 115, y= 2645)
Step-by-step explanation:
There are two methods to this, which is using the graph with each x and y value, or substituting in values.
I would suggest looking at the graph first and then substituting values so you know the equation is being satisfied by the ordered pair.
In this case, one way to check it could look like this (substituting y value):
y = 23x
2645 = 23x
x = 2645÷23
x = 115
Answer:
`The answer is below
Step-by-step explanation:
P and q are points on the line y=2-4X. complete the coordinates of P and Q, P(0, ) Q( ,0)
Draw the line y= 2-4X for vales of x from -2 to 2
Solution:
The equation of a line is given by:
y = mx + b
Where y and x are variables, m is the slope of the line and b is the y intercept (that is value of y when x = 0).
The line of y = 2 - 4x is drawn by finding the corresponding values of y for x from -2 to 2 and plotting on a graph.
x: -2 -1 0 1 2
y: 10 6 2 -2 -6
The value P(0, ) Q( ,0)
The y coordinate of point P is gotten by substituting x = 0:
y = 2 - 4(0) = 2
P = (0, 2)
The x coordinate of point Q is gotten by substituting y = 0:
0 = 2 - 4x
4x = 2
x = 0.5
Q = (0.5, 0)
Answer:
92 attendees had activity cards
Step-by-step explanation:
Let x be the number of students with activity cards. Then 130-x is the number without, and the total revenue is ...
7x +10(130 -x) = 1024
7x +1300 -10x = 1024 . . . . eliminate parentheses
-3x = -276 . . . . . . . . . . . . . collect terms; subtract 1300
x = 92 . . . . . . divide by 3
92 students with activity cards attended the dance.
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<em>Comment on the solution</em>
Often, you will see such a problem solved using two equations. For example, they might be ...
Let 'a' represent the number with an activity card; 'w' the number without. Then ...
- a+w = 130 . . . . the total number of students
- 7a +10w = 1024 . . . . the revenue from ticket sales
The problem statement asks for the value of 'a', so you want to eliminate w from these equations. You can do that using substitution. Using the first equation to write an expression for w, you have ...
w = 130-a
and making the substitution into the second equation gives ...
7a +10(130 -a) = 1024
This should look a lot like the equation we used above. There, we skipped the extra variable and went straight to the single equation we needed to solve.
