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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Answer:
9 + (-8) = 1
Step-by-step explanation:
Answer:
Remember that the slope of perpendicular lines are negative reciprocals of each other.
Step-by-step explanation:
y = 1 - 2x the slope is -2 the value of the x term.
So the slope of the new line using point (- 1, 2) is 1/2.
Now use y = mx + b where y = -1, x = 2, and m = 1/2 .
y = mx + b
-1 = 1/2(2) + b solve for "b", the y-intersect
-1 = 1 + b
-2 = b
The line that is perpendicular to y = 1 - 2x is y = 1/2x - 2
Answer:
x = pi/2 + 2 pi n x = pi + 2 pi n where n is an integer
x = 5pi /3 + 2 pi n
Step-by-step explanation:
8 cos^2 x + 4 cos x-4 = 0
Divide by 4
2 cos^2 x + cos x-1 = 0
Let u = cos x
2 u^2 +u -1 =0
Factor
(2u -1) ( u+1) = 0
Using the zero product property
2u-1 =0 u+1 =0
u = 1/2 u = -1
Substitute cosx for u
cos x = 1/2 cos x = -1
Take the inverse cos on each side
cos ^-1(cos x) = cos ^-1(1/2) cos ^-1( cos x) =cos ^-1( -1)
x = pi/2 + 2 pi n x = pi + 2 pi n where n is an integer
x = 5pi /3 + 2 pi n
Answer:
12a + .5B
B= -6a
a=.042B
Step-by-step explanation:
1/2(6a+B)= 12a+.5B
1/2(6a+B)=0
-12a=.5B
-6a=B
12a=-.5B
a=.042B
