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.
Regina has enough money to buy all the items she needs
3 cans of dog food = 1.50*3 = 4.50
1 gallon of milk = 4.00*1 = 400
5 pounds of chicken = 1.55*5 = 7.75
1 box of cereal = 2.75*1 = 2.75
6 rolls of paper towels = .99*6 = 5.94
If you add all those together it equals 24.94 leaving 6 cents in change
4.50 + 4.00 + 7.75 + 2.75 + 5.94 = 24.94$
9514 1404 393
Answer:
(a) $133.88
Step-by-step explanation:
The addition of tax multiplies the purchase price by 1+6.45% = 1.0645. The payment of the down payment means the loan amount will be only 1-10% = 0.90 times the amount with tax. So, the loan amount is ...
$22,359(1.0645)(0.90) = $21,420.08
The loan is a secured loan (secured by the vehicle). So, the interest charged is that for a poor credit rating: 7.5%.
One month's interest is ...
I = Prt . . . . . interest on principal P at rate r for t years (1 mo = 1/12 yr)
I = $21,420.08(0.075)(1/12) = $133.88
Answer:
120°
Step-by-step explanation:
