If you solve for x you get:
x=(<span><span><span>5/2)</span>y</span>+<span>10
</span></span>
If you solve for y you get:
y=(<span><span><span>2/5)</span>x</span>−<span>4</span></span>
3. 28 Quarters and 5 dimes.
The intersecting secant theorem states the relationship between the two intersecting secants of the same circle. The given problems can be solved using the intersecting secant theorem.
<h3>What is Intersecting Secant Theorem?</h3>
When two line secants of a circle intersect each other outside the circle, the circle divides the secants into two segments such that the product of the outside segment and the length of the secant are equal to the product of the outside segment other secant and its length.
a(a+b)=c(c+d)
1.)
6(x+6) = 5(5+x+3)
6x + 36 = 25 + 5x + 15
x = 4
2.)
4(2x+4)=5(5+x)
8x + 16 = 25 + 5x
3x = 9
x = 3
3.)
8x(6x+8x) = 7(9+7)
8x(14x) = 112
112x² = 112
x = 1
4.)
(x+3)² = 16(x-3)
x² + 9 + 6x = 16x - 48
x² - 10x - 57 = 0
x = 14.0554
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Step-by-step explanation:
With reference to the regular hexagon, from the image above we can see that it is formed by six triangles whose sides are two circle's radii and the hexagon's side. The angle of each of these triangles' vertex that is in the circle center is equal to 360∘6=60∘ and so must be the two other angles formed with the triangle's base to each one of the radii: so these triangles are equilateral.
The apothem divides equally each one of the equilateral triangles in two right triangles whose sides are circle's radius, apothem and half of the hexagon's side. Since the apothem forms a right angle with the hexagon's side and since the hexagon's side forms 60∘ with a circle's radius with an endpoint in common with the hexagon's side, we can determine the side in this fashion:
tan60∘=opposed cathetusadjacent cathetus => √3=Apothemside2 => side=(2√3)Apothem
As already mentioned the area of the regular hexagon is formed by the area of 6 equilateral triangles (for each of these triangle's the base is a hexagon's side and the apothem functions as height) or:
Shexagon=6⋅S△=6(base)(height)2=3(2√3)Apothem⋅Apothem=(6√3)(Apothem)2
=> Shexagon=6×62√3=216
The statement third "Betty wrote an indirect proof using contradiction' and statement fourth "Ken wrote direct proof using deductive evidence" are correct.
<h3>What is an angle?</h3>
When two lines or rays converge at the same point, the measurement between them is called a "Angle."
We have Ken's statements are shown in the table:
Angle AOC = Angle BOD (given)
Angle AOB + Angle BOC = Angle BOC + Angle COD (angle addition postulate)
Angle AOB = ANgle COD (subtraction property of equality)
Ken wrote direct proof using deductive evidence.
As we can in betty's proof:
Betty wrote an indirect proof using contradiction.
Thus, the statement third "Betty wrote an indirect proof using contradiction' and statement fourth "Ken wrote direct proof using deductive evidence" are correct.
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