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.
Answer:
Step-by-step explanation:
From the information given,
Let the two digits that Chen writes down to be p and q
where,
q will be in the unit place and p will be in the tens place.
So, the value of the digit = 10p + q
So, if he swapped the number, he will have 10q + p
However,
the new number determined is thrice more than the 1/3 pf the original number.
i.e
the 1/3rd of the original number = 
=
thrice more than that will be = 
∴
multiply through by 3, we have :
10p+q + 9 = 30q + 3p
collecting the like terms, we have:
10p - 3p +q -30q +9 = 0
7p - 29q +9 = 0
7p - 29q = -9
Therefore, p,q lie between 0 and 9
Therefore, the possibility of the original number is p = 7 and q = 2
One pound is about 0.5, so pretty much divide it by half
Answer:
Step-by-step explanation:
7
21
+63 =91
Answer:
5
Step-by-step explanation:
a minus times by another minus makes a positive, so it is basically 1 x 5
