PR and PS are two sides of a square. PS and PT are two sides of a regular pentagon. PR and PT are two sides of a regular polygon with sides. Work out the value of pie .

∠RPT = 18°, ∠PRT = ∠PTR = 81°

Step-by-step explanation:

First we would find the draw the diagram obtained from the given information. Then we would work out the angles of RPT, PRT and PTR.

Given:

PR and PS are two sides of a square

PR = PS (all the sides of a square are equal)

PS and PT are two sides of a regular pentagon

PS = PT (all sides of a pentagon are equal)

PR and PT are two sides of both polygons

Sum of interior angles = 180(n-2)

Pentagon has 5 sides, n = 5

180(5-2) = 540°

Each interior angles = 540/5 = 108°

∠SPT = ∠SPR + ∠RPT

∠SPT = 108°, ∠SPR = 90°

108 = 90+ ∠RPT

∠RPT = 108-90 = 18°

PT = PR (the side of the square has the same length as the side of

the regular pentagon)

This makes ∆RPT an isosceles

Let = ∠PRT = ∠PTR =x

2x + ∠RPT = 180° (sum of angles in a triangle)

2x = 180-18 = 162

x = 162/2 = 81°

∠PRT = 81°

∠PTR = 81°

since your problem is x^4 = 81, what you have to undeo is the "to the fourth power" part.

the inverse (opposite operation) of "to the fourth power" is "to the fourth root".

  (x^4) ^ ¼   = 81 ^ ¼  

  81 = 3^4     so (3 ^ 4) ^ ¼   =   3 ^ 1   = 3

by hand: (3 ^ 4) ^ ¼   =   3 ^ (4 x ¼) = 3 ^ 1   = 3   (when you take a power to a power, multiply the exponents.)

or, do it by calculator. one way of finding the fourth root is to use ^ (1/4)

step-by-step explanation:

d

step-by-step explanation:

hello and welcome!

so, when we see the words "proportional" along with a table, we need to know that we're looking numbers that divide by the same thing.

looking at this table, we simply have to do a trial and error, and divide to see which numbers have the same quotient. if you look at choice a & c, they both have equal quotients for three of the numbers, with one exception, so those can't be the answer. looking at b, there is no similarity, so that can't be it. then, we see d; if you divide all the numbers in the table, you'll see that they all divide by two, which is a proportional relationship, and our answer!

also, always remember that the x will always be the number that goes into y, and somewhere behind this table, is a formula. for this specific table, the formula would be:

since our x-value is being divided by two to get the y-value. and if they were to ask for more numbers in the series, this is the formula you would use to find them.