A boat leaves the dock and travels 5 miles due south, then 12 miles due west How far is the boat from the dock?

13 miles

Step-by-step explanation:

This problem can be represented as a right angle triangle (shown in the diagram).

The distance of the boat from the dock is the hypotenuse of the triangle, hence, we need to find the hypotenuse of the triangle. To do this, we apply Pythagoras theorem:

where opp = side opposite angle of consideration = 12 miles

adj = side adjacent angle of consideration = 5 miles

Hence:

The boat is therefore, 13 miles from the dock.

the ratio of balloons to tables is 5: 2 and the constant variation is 5.

the equation is y=5x

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!