Mikel wants to hire a carpenter to remodel a bathroom. Both carpenters interviewed charge a flat fee for setting up,
plus an hourly wage. Bonzo Bathrooms charges $50 to set
up and $27 per hour. Wonder Waterclosets charges $35 to
set up and $30 per hour. For how many hours of work
would the two bathroom carpenters charge exactly the same
amount?

c.   x=2.4cm

step-by-step explanation:

similar triangles are triangles which have the same shape but not the same size. this means their angle measures are equal but their side lengths are not instead they are proportional. to solve, we will set up a proportion and solve.

a proportion is two equal ratios set equal to each other. we form the ratios by finding corresponding sides (sides which match to each other on both triangles by their position). out ratios will be one side of the small triangle over the corresponding side on the big triangle as shown below:

.

to solve the proportion, we'll cross multiply by multiplying numerator with denominator across the equal sign.

isaiah walks 3 miles due north, turns and then 5 miles due east. how far is he from his starting point?

a^2 + b^2 = c^2

let c = distance from starting point.

(3)^2 + (5)^2 = c^2

9 + 25 = c^2

34 = c^2

sqrt{34} = sqrt{c^2}

sqrt{34} = c

a reflection across the x axis and a 90 degree rotation left and right.