A movie theater sends out a coupon for 65% off the price of a ticket. Write an equation for the situation, where y is the pric
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Answer:
b=0.5 in
b=2 in
Step-by-step explanation:
we know that
The perimeter of triangle is equal to
Solve for a
-----> equation A
Applying the Triangle Inequality Theorem
a+a > b
2a > b -----> inequality B
<u>Verify each case</u>
case 1) b=-2 in
This value not make sense, the length side cannot be a negative number
case 2) b=0 in
This value not make sense
case 3) b=0.5 in
substitute the value of b in the equation A and solve for a
substitute the values of b and a in the inequality B
2a > b
2(7.25) > 0.5
14.50 > 0.5 -----> is true
therefore
b=0.5 in make sense for possible values of b
case 4) b=2 in
substitute the value of b in the equation A and solve for a
substitute the values of b and a in the inequality B
2a > b
2(6.5) > 2
13 > 2 -----> is true
therefore
b=2 in make sense for possible values of b
case 5) b=7.9 in
substitute the value of b in the equation A and solve for a
substitute the values of b and a in the inequality B
2a > b
2(3.55) >7.9
7.1 > 7.9 -----> is not true
therefore
b=7.9 in not make sense for possible values of b
Direct variation means that the line goes through the origin of the graph, so you know that the line must go through point (0,0). Using that along with the given point, you can find the slope of the line.
m =
m =
m =
m = 6
Now that you know the slope of the line you are looking for is 6, you can plug that into a point-slope form equation and find the equation of your line.
y - y_1 = m (x - x_1) Plug in either set of coordinate. I chose (3, 18).
y - 18 = 6 (x - 3) Use he Distributive Property
y - 18 = 6x - 18 Add 18 to both sides
y = 6x
The equation of a direct variation line that includes the point (3, 18) is y = 6x.
m =
m =
m =
m = 6
Now that you know the slope of the line you are looking for is 6, you can plug that into a point-slope form equation and find the equation of your line.
y - y_1 = m (x - x_1) Plug in either set of coordinate. I chose (3, 18).
y - 18 = 6 (x - 3) Use he Distributive Property
y - 18 = 6x - 18 Add 18 to both sides
y = 6x
The equation of a direct variation line that includes the point (3, 18) is y = 6x.