Answer:
15 1-point and 38 2-point shots
Step-by-step explanation:
x: 1 point shots
y: 2 point shots
x + y = 53 (1)
1(x) + 2(y) = 91 (2)
From (1), x = 53 - y
In (2),
(53 - y) + 2y = 91
53 + y = 91
y = 91 - 53 = 38
x = 53 - 38 = 15
Subtract the sum of the known sides from the perimeter to find the length of the missing side.
<span>Changing the y-coordinates will make all coordinates negative and give us an image, or reflection, in the third quadrantSwitching the coordinates will flip the figure back to the right orientationEach coordinate (x,y) is changed to (-y,-x)This is our general formula for rotating the figure 270 degrees about the origin</span> .Changing the y-coordinates will give us an image in the third quadrantIn other words, it will be a reflection of the figure in the second quadrant<span><span> Switching the coordinates will flip the figure back to the right orientation</span><span> <span>Each coordinate (x,y) is changed to (-y,-x)<span>This is our general formula for rotating the figure 270 degrees about the origin</span></span></span></span>
Plug the y value in for y and plug the x value in for x
> less than
<u>></u> less than or equal to
Example:
(4,5)
y > 5y <u>></u> x
5 > 5x5 <u>></u> 4 = 5 > 25 <u>></u> 4 = false
they all should be false
if one had to be correct, I would say (0, 0)
The Lagrangian for this function and the given constraints is

which has partial derivatives (set equal to 0) satisfying

This is a fairly standard linear system. Solving yields Lagrange multipliers of

and

, and at the same time we find only one critical point at

.
Check the Hessian for

, given by


is positive definite, since

for any vector

, which means

attains a minimum value of

at

. There is no maximum over the given constraints.