Check the picture below.
assuming both hyperbolas at centered at the origin, the values for the numerator and denominator will switch, so that the slope of one is the reciprocal of the other's slope.
knowing the answer is between 3 & 4 plug those as x and see what you get for answers than adjust the number accordingly
3^3+2(3) = 33 so its higher than 3
4^3 + 2(4) = 72 so it is lower than 4
try the middle so try 3.5
3.5^3 + 2(3.5) = 49.875
question states use 1 decimal place so now try 3.6
3.6^3+2(3.6) = 53.856
3.5 is closest
The graph can be divided into two shapes. A rectangle and a right triangle.
The distance that the rover will cover if it completes one circuit can be computed using the Pythagorean theorem and adding the sides of the rectangle.
Rectangle:
Width = 4 - 2 = 2 meters
Length = 11 - 2 = 9 meters
Triangle = 16 - 2 = 14 ; 14 - 2 = 12 meters (this is the short leg)
long leg of the triangle = length of the rectangle = 9 meters.
12² + 9² = c²
144 + 81 = c²
225 = c²
√225 = √c²
15 = c
Point A to B = 4 - 2 = 2 meters
Point B to C = 15 meters
Point C to D = 16 - 2 = 14 meters
Point D to A = 11 - 2 = 9 meters
Total distance traveled = 2 + 15 + 14 + 9 = 40 meters.
the formula for area of a rectangle is
Area = length x width
since both the length and the width of the rectangle lie on the same x and y axis, we can find the distance between the width and the distance between the length by subtracting
(-4,9) (-4,-3)
these points lie on the same x axis, so they create a vertical line
9-(-3) = 12
12 units is the distance between them
(-4,-3) (-1,-3)
these points lie on the same y axis, so they create a horizontal line
-1-(-4) = 3
3 units is the distance between them
now that we have the length and the width, we can find the area
A = 12 x 3
A = 36 units²
we are given

Firstly , we can distribute

now, we can combine like terms


now, we can solve for x
and we get
...........Answer