ChallengeThe price of Stock A at 9 AM Was $15.11. Since then, the price has been increasing at the rate of $0.12 each hour. At noon the price of Stock B was $15.86. It begins to decrease at the rate of
$0.11 each hour. If the two rates continue, in how many hours will the prices of the two stocks be the
same?
In about hours, the prices of the two stocks will be the same.
(Round to the nearest tenth as needed

Step-by-step explanation:

The information gives the Slope and y intercept of the line for stock A. At 9am, time = 0, the stock price is $15.11, the y intercept or b. The Slope of the line is 12 cents per hour, it is a positive Slope so it will rise from left to right.

The line in Slope form is

y= 0.12x+15.11

Stock B at noon, so 3 hours later, is $15.86 and is decreasing at a rate of 11 cents per hour.

We know the Slope is -0.11 and we know a point on its line is (3,15.86). From this we can solve for the y intercept by substituting the x and y values from the coordinate into the Slope equation.

15.86 = -0.11(3) + b

15.86 = -0.33 + b

Add 0.33 to both sides

16.19 = b so the equation of the line of stock B is y= - 0.11x + 16.19

Since we have two equations solved for y, we can set them equal to each other and solve for x

0.12x + 15.11 = - 0.11x + 16.19 add 0.11x - 15.11 to both sides

0.23x = 1.08 divide both sides by 0.23 to solve

x = 4.69565 to the nearest tenth 4.7 hours after 9am the two stocks will be the same price.

  21.3

step-by-step explanation:

multiplying the given equation by c/sin(25°), we get

  c = 9/sin(25°) ≈ 21.2958 ≈ 21.3

we assume "c" is the length of ab, the side opposite angle c in triangle abc.

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