While browsing for the best deal, Fred finds a brand-new lawn mower on sale for 35% off the total price of $339 with an 8% sales tax. His neighbor had offered to sell him a similar lawn mower that he had just bought a month ago because he was moving and no longer needed it for $250.

a. We will use our composite functions, h(x) = (f + g)(x) to find the final price of the brand-new lawn mower. Use the equations f(x) = 0.65x, for the 35% off, and g(x) = .08(.65x), for the sales tax on the sales price of the lawn mower. What is the final price? Show your steps.

b. Which lawn mower should Fred buy? Circle one

The Lawn Mower on Sale or The Neighbor’s Lawn Mower

d

step-by-step explanation:

by observation, we can see that the the graph is simply the graph of y = |x| that has been shifted 4 units downwards and 3 units to the left.

we can recognize in choice d :

y = | x + 3 |   - 4 (rewriting in general form)

y = | x - (- 3) |   - 4

the "-4 " term means   that the graph has been shifted by 4 units in the negative y direction

the "-3 " term means   that the graph has been shifted by 3 units in the negative x direction

this matches our observation of the graph described above.

for the friend request.

when a figure, such as triangle (xyz) is reflected over the line y = x to create x'y'z' the x-coordinates and y-coordinates of the original image (pre-image) will be reversed for the image. (e.g., (x, y) > (y, x)) this means that the pre-image position of the x- and y-coordinates switch places which in turn provides a mirror like image of the original xyz.  

i notice that when i draw a line segment from x to x', that the points are parallel from each other -- they are exactly across from each other and do not intersect with any other points.  

yes, think i would see the same characteristic if you drew the line segment connecting y with the reflecting line and then y' with the reflecting line because of the essence of reflections. because it is a mirror image, each point was effected the same way which leads me to conclude that they same would apply to y and y'.

i think the amount would be $140.62