Jamie is buying tickets to a movie. How many $6 tickets can he buy if he wants to spend less than $36

Mathematics

1 answer:

Margaret [11]3 years ago

8 0

Jamie can only buy 5 tickets priced at $30 total because if he buys one more he is no longer spending less than $36

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Each side of a square calendar is 19 inches long. What is the calendar's perimeter?

liberstina [14]

Answer:

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3 years ago

Read 2 more answers

100 POINTS

Shkiper50 [21]

Answer:

6√3 ±3 ≈ {7.392, 13.392}

Step-by-step explanation:

The length of AB is the long side of a right triangle with hypotenuse CD and short side (AC -BD). The desired radius values will be half the length of EF, with AE added or subtracted.

<h3>length of AB</h3>

Radii AC and BD are perpendicular to the points of tangency at A and B. They differ in length by AC -BD = 12 -9 = 3 units.

A right triangle can be drawn as in the attached figure, where it is shaded and labeled with vertices A, B, C. Its long leg (AB in the attachment) is the long leg of the right triangle with hypotenuse 21 and short leg 3. The length of that leg is found from the Pythagorean theorem to be ...

AB = √(21² -3²) = √432 = 12√3

<h3>tangent circle radii</h3>

This is the same as the distance EF. Half this length, 6√3, is the distance from the midpoint of EF to E or F. The radii of the tangent circles to circles E and F will be (EF/2 ±3). Those values are ...

6√3 ±3 ≈ {7.392, 13.392}