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:
<h3>
f(x) = -¹/₄(x + 2)² - 6</h3>
Step-by-step explanation:
The vertex form of an equation of the parabola:
f(x) = a(x - h)² + k
vertex is (-2, -6) so h = -2, k = -6
so:
f(x) = a(x - (-2))² + (-6)
f(x) = a(x + 2)² - 6
the parabola goes through the point (-4, -7) so for x=-4, f(x)=-7
-7 = a(-4+2)² - 6
-7 +6 = a(-2)² - 6 +6
- 1 = a(4)
a = -¹/₄
Therefore the equation of the parabola in vertex form:
f(x) = -¹/₄(x + 2)² - 6
Answer:
4x^2 + 9x + 4 = 0
Using the quadratic formula:
x = [-9 +- sqrt(81 - (-64)] / 2 * 4
x = [-9 +- sqrt (145)] / 8
So, the solution is your second answer:
negative 9 plus or minus the square root of 145 divided by 8.
Hello,
26r^3s+52r^5-39r²s^4
=13r²(4r^3+2rs-3s^4)
Answer:
Step-by-step explanation:
<u>Scale is:</u>
- 1 foot = 3/4 inch
- 1 inch = 1 : 3/4 foot = 4/3 foot
a. The length of the room
- 9 inches = 9*4/3 foot = 12 feet
b. The width of the room
- 6 3/4 inches = 27/4 inches = 27/4*4/3 = 9 feet
