Algebra 1 mauro has 140 ft of rope. he will cut it into two pieces so that the length of the longer piece is 3 times the length of the shorter piece. what will the length of the longer piece be?

The ratio of the lengths of the pieces of rope is 1 : 3. Then the longer piece is 3/(1+3) = 3/4 of the total length.

(3/4)×(140 ft) = 105 ft

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step-by-step explanation:

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p ÷ r = tan(x)

step-by-step explanation:

given that there is a figure below shows a right triangle: a right triangle is shown with hypotenuse equal to q units and the length of the legs equal to p units and r units.

graph is missing so i will create the graph as per given information.

the angle between the legs having lengths p units and q units is y degrees. the angle between the legs having lengths r units and q units is x degrees.

now we need to find about what is p ÷ r equal to.

so we can use trigonometric ratio tan(x)=[altitude]/[base] to find the value of p ÷ r, because p is the altitude and r is the base.

p ÷ r=tan(x)

hence final answer is p ÷ r=tan(x).