Answer:
33 ft
Step-by-step explanation:
The image in a mirror is as far behind the reflecting surface as the actual object is in front. When working reflection problems such as this one, it is convenient to mirror the geometry in the line of reflection. This puts the target point at the same distance from the left edge of the room, but 8 feet beyond the reflecting wall. A straight line from the source to the target image will intersect the wall at the appropriate point.
Essentially, we want to know where a line between a point at coordinates (6, 12) and a point at coordinates (45, 38) will intersect the wall at y=30.
The 2-point form of the equation for the line is ...
y = (y2 -y1)/(x2 -x1)(x -x1) +y1
For the points listed above, this is ...
y = (38 -12)/(45 -6)(x -6) +12 = 26/39(x -6) +12
y = 2/3x +8
The value of x that gives y=30 is ...
30 = 2/3x +8 . . . . . substitute 30 for y
22 = 2/3x . . . . . . . . subtract 8
(3/2)·22 = x = 33 . . . . multiply by 3/2
Zack should shoot at a point 33 feet along the wall in order to hit Patrick.
_____
In short, Zack should aim at Patrick's reflection in the wall.
Answer:
(1) The slope intercept should be y=1/2x-5
So the table should be
x y point
-2 -6 (-2,-6)
0 -5 (0,-5)
2 -4 (2,-4)
(2) The slope -5/4
Step-by-step explanation:
(1) The reason why when she graphed the points is incorrect is because she needs to graph it in point slope form not in standard form and when she used the equation.
To find the slope intercept form you need to get the y on one side by itself:
x-2y=10
Subtract x on both sides:
-2y=-x+10
Divide by -2 on both sides:
y=1/2x-5
(2)The formula for the slope is y2-y1/x2-x1
-2-3/5-1
Which is -5/4
Thus the slope is -5/4
Hope this helps!
Answer:
Width=20 feet
Since Length=Width=20 feet, the rectangle is a Square.
Step-by-step explanation:
Area, ![A=40w - w^2](https://tex.z-dn.net/?f=A%3D40w%20-%20w%5E2)
To determine the width of the rectangle that gives the maximum area, we take the derivative of A and solve for its critical point.
![A'=40 - 2w\\$When A'=0\\40-2w=0\\40=2w\\w=20 feet](https://tex.z-dn.net/?f=A%27%3D40%20-%202w%5C%5C%24When%20A%27%3D0%5C%5C40-2w%3D0%5C%5C40%3D2w%5C%5Cw%3D20%20feet)
The width of the rectangle that gives the maximum area =20 feet.
Perimeter of a rectangle=2(l+w)
Perimeter of the rectangle=80 feet
2(l+w)=80
2l+2(20)=80
2l=80-40
2l=40
l=20 feet
Since the length and width are equal, the special type of rectangle that produces this maximum area is a Square.
Answer:
C
Step-by-step explanation:
2 x pi x r = circumfrence
2 x 7 x pi = 43.96
Answer:
932/1000
Step-by-step explanation:
To write .932 as a fraction you have to write .932 as numerator and put 1 as the denominator. Now you multiply numerator and denominator by 10 as long as you get in numerator the whole number.
.932 = .932/1 = 9.32/10 = 93.2/100 = 932/1000
And finally we have:
.932 as a fraction equals 932/1000