Answer:
Step-by-step explanation:
The perimeter of a polygon is equal to the sum of all the sides of the polygon. Quadrilateral PTOS consists of sides TP, SP, TO, and SO.
Since TO and SO are both radii of the circle, they must be equal. Thus, since TO is given as 10 cm, SO will also be 10 cm.
To find TP and SP, we can use the Pythagorean Theorem. Since they are tangents, they intersect the circle at a 
, creating right triangles 
and 
.
The Pythagorean Theorem states that the following is true for any right triangle:
, where 
is the hypotenuse, or the longest side, of the triangle
Thus, we have:
Since both TP and SP are tangents of the circle and extend to the same point P, they will be equal.
What we know:
Thus, the perimeter of the quadrilateral PTOS is equal to 
Answer:
It lost 22 feathers.
Step-by-step explanation:
To complete this problem, this expression will be used: 2x/100.
2(1100)/100 {Multiply 2 by 1100}
2200/100 {Simplify by cancelling out 100}
22/1 {Divide}
22 feathers were lost.
Answer:
3. r = -8
4. x = -5
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
Equality Properties
Step-by-step explanation:
<u>Step 1: Define equation</u>
2(-5r + 2) = 84
<u>Step 2: Solve for </u><em><u>r</u></em>
- Divide 2 on both sides: -5r + 2 = 42
- Subtract 2 on both sides: -5r = 40
- Divide -5 on both sides: r = -8
<u>Step 3: Check</u>
<em>Plug in r into the original equation to verify it's a solution.</em>
- Substitute in <em>r</em>: 2(-5(-8) + 2) = 84
- Multiply: 2(40 + 2) = 84
- Add: 2(42) = 84
- Multiply: 84 = 84
Here we see that 84 does indeed equal 84.
∴ r = -8 is a solution of the equation.
<u>Step 4: Define equation</u>
264 = -8(-8 + 5x)
<u>Step 5: Solve for </u><em><u>x</u></em>
- Divide both sides by -8: -33 = -8 + 5x
- Add 8 to both sides: -25 = 5x
- Divide 5 on both sides: -5 = x
- Rewrite: x = -5
<u>Step 6: Check</u>
<em>Plug in x into the original equation to verify it's a solution.</em>
- Substitute in<em> x</em>: 264 = -8(-8 + 5(-5))
- Multiply: 264 = -8(-8 - 25)
- Subtract: 264 = -8(-33)
- Multiply: 264 = 264
Here we see that 264 does indeed equal 264.
∴ x = -5 is a solution of the equation.
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