17) A spider has taken up residence in a small cardboard box which measures 8 inches by 5 inches by 4 inches.
The spider travels from the lower right front corner of
the box to the upper left back corner of the box.
What is the length, in inches, that the spider travels?
Show your work and use mathematical vocabulary
to explain your reasoning.
4
8

10.2 in.

Step-by-step explanation:

You need to use the Pythagorean theorem twice.

First, draw a diagonal of the base of the box going from the front right side to the back left side.

That diagonal is the hypotenuse of a right triangle with legs measuring 8 in. and 5 in.

For this right triangle, I will use a and b for the legs and c for the hypotenuse.

c^2 = a^2 + b^2

c^2 = (8 in.)^2 + (5 in.)^2

c^2 = 89 in.^2

Now use the diagonal and the back left edge of the box as legs, and the path of the spider as a hypotenuse in a new right triangle.

For this right triangle, I will use A and B for the legs, and C for the hypotenuse. Notice that leg A of this case is hypotenuse c of the previous right triangle.

C^2 = A^2 + B^2

C^2 = 89 in.^2 + (4 in.)^2

C^2 = 105 in^2

C = 10.2 in.

The length is 10.2 in.

so firstly, we need to isolate the y variables to be able to solve these inequalities. firstly, add 0.5x on both sides of the first inequality and subtract 1.5x on both sides of the second inequality:

now since the slope is positive for the first inequality, this means that the line going upwards belongs to the first inequality, and the line going downwards belongs to the second inequality.

next, since y ≥ in the first inequality, this means that the shaded region will be above the first inequality's line, thus shading regions a and b.

next, since y ≤ in the second inequality, this means that the shaded region is going to be below this line, thus shading regions a and c.

since both lines shade region a, this means that region a is the solution.

step-by-step explanation:

mark brainliest!

step-by-step explanation: