Complete the square for the given equation
x² - 2x + ____ + y² - 2y + _____ = 98
x² - 2x + (1) + y² - 2y + (1) = 98 + (1) + (1)
(x - 1)² + (x - 1)² = 100
(x - 1)² + (x - 1)² = 10²
Now the equation is in the form (x - h)² + (y - k)² = r²
Radius = 10
Answer:
∠STU = 69°
Step-by-step explanation:
The angle with vertex T is called an "inscribed angle." It intercepts arc SU. The relationship you are asked to remember is that the measure of the inscribed angle (T) is half the measure of the arc SU.
Point V is taken to be the center of the circle. The angle with vertex V is called a "central angle." It also intercepts arc SU. The relationship you are asked to remember is that the measure of the central angle (V) is equal to the measure of arc SU.
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Using these two relationships together, we realize angle V is twice the measure of angle T:
∠SVU = 2×∠STU
18x +12° = 2(18x -57°) . . . . . . relationship between the marked angles
18x +12° = 36x -114° . . . . . eliminate parentheses
126° = 18x . . . . . . . . . . . add 114°-18x
∠STU = 18x -57° = 126° -57°
∠STU = 69°
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<em>Additional comment</em>
You may notice we did not solve for x. We only needed to know the value of 18x, so we stopped when we found that value. (Actually, we only need the value of 18x-57°. See below.)
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<em>Alternate solution</em>:
(18x +12°) -(18x -57°) = 18x -57° . . . . . . . subtract 18x -57° from both sides of the first equation.
69° = 18x -57° . . . . . simplify. This is the answer to the problem.
<span>You run 0.5 miles every 3 minutes => 1 mile every 6 minutes. Your friend runs 2 miles every 14 minutes => 1 mile every 7 minutes. You run a whole number of miles every number of minutes that is a multiple of 6. Your freind runs a whole number of miles every number of minutes that is a multiple of 7 Then the least possible number of miles that you both run to end at the same time is the least common factor of 7 and 6 minutes. This is 7 * 6 = 42 minutes. You will have run 42 min / (6 miles/min) = 7 miles, and your friend will have run 42 min / (7 miles/min) = 6 miles</span>
Answer:
coinciding
Step-by-step explanation:
If you divide the second equation by 3, you get the first equation. They describe the same line, so the lines are <em>coinciding</em>.
