We are given original equation:
We need to find the enter and radius of a circle using the completing the square method.
The steps are as following :
Step 1 [original equation]: x^2 − 10x + y^2 + 12y = 20 .
Step 2 [group like terms]: (x^2 − 10x) + (y^2 + 12y) = 20
Step 3 [complete the quadratics]: (x^2 − 10x + 25) + (y^2 + 12y + 36) = 20 + (25 + 36).
Step 4 [simplify the equation]: (x^2 − 10x + 25) + (y^2 + 12y + 36) = 64.
Step 5 [factor each quadratic]: (x − 5)^2 + (y + 6)^2 = 8^2
Step 6 [identify the center and radius]: Center = (5, −6) Radius = 8.
<h3>Step 6 is incorrect.</h3><h3>The center should be (5,-6).</h3><h3> Replace − 5 with + 5 and replace + 6 with − 6.</h3>
Answer:
Step-by-step explanation:
Linear equation:
A linear equation has the following format:
In which m is the slope and b is the y-intercept.
Finding the slope:
We have two points: (110, 73.5) and (760, 301).
The slope is given by the change in y divided by the change in x. So
Change in y: 301 - 73.5 = 227.5
Change in x: 760 - 110 = 650
Slope:
So
Finding the y-intercept:
(760, 301) means that when . So
So
Answer:
-3 and -15
Step-by-step explanation:
-3*-15=45
Answer:
Step-by-step explanation:
This can happen because of the timestamp on the toll card. When you pass through the initial entrance point the timestamp marks the exact moment you passed. When you pass through the exit toll point the individual subtracts the current time from the time you entered the initial toll entrance. From this, he can easily determine the average speed that you were driving at. If the average speed is higher than the speed limit, it means that at some point between the two toll booths you were speeding and therefore they can give you a speeding ticket.