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.
Assume that the rule connecting height of the candle to time is a linear one. If you do, then we have to find the equation of this line, and then use this equation to predict the height of the candle after 11 hours.
Two points on this line are (6,17.4) and (23, 7.2). The slope is thus
7.2-17.4 -6
m = --------------- = ----------- or -3/5.
23-6 10
Find the equation of the line. I'm going to use the slope-intercept formula:
y = mx + b => 7.2 = (-3/5)(23) + b. Solving for b, b = 21.
Now we know that y = (-3/5)x + 21
Let x=11 to predict the height of the candle at that time.
y = (-3/5)(11) + 21 = 14.4 inches (answer)
<span>$8.22h ≥ $623
Let's look at the options and see what works and what doesn't.
$8.22h > $623
* This inequality mostly works and it's true. But there may be a better choice later. So let's hold off on this one.
$8.22h ≤ $623
* That less than or equal has issues. Let's buy the bike if I have less money than what's needed? Nope, not gonna work. Although that equal portion does have an element of truth to it. But this is a bad choice.
$8.22h ≥ $623
* And this third option is better than the first. It simply says that you have to have enough or more money to buy the bike. The 1st equation basically said you have to have more money than the cost of the bike. So this is the correct choice.
$8.22h < $623
* This is worse than the 2nd option. In a nutshell, is says buy the bike when you don't have enough money. So bad choice.</span>
Answer: The polynomial is 92 - 46t
92,92,-46,46
Step-by-step explanation:
Answer:
13. (E) all of the above 14. (E) the diagonals bisect the angles at the vertices
Step-by-step explanation:
