Tickets for a certain show cost $17, $21, or, for VIP seats, $40. If ten times as many $17 tickets were sold as VIP tic
1 answer:
Answer:
Tickets sold:
VIP
$17 tickets
$21 tickets
Step-by-step explanation:
Let x be the number of VIP tickets.
If ten times as many $17 tickets were sold as VIP tickets, then the number of $17 tickets is
If the number of $17 tickets sold was 57 more than the sum of the number of $21 tickets and VIP tickets, then and the number y of $21 tickets is
Amounts earned:
VIP tickets
$17 tickets
$21 tickets
Total
The sales of all three kinds of tickets would total $51,471, so
Tickets sold:
VIP
$17 tickets
$21 tickets
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Answer:
- 108 cm^2
- 211.2 cm^2
- 308.8 mm^2
- 560 yd^2
Step-by-step explanation:
In each case, you can use the given formula to find the surface area. The area of the triangular base (B) is ...
A = 1/2bh
where b is the base of the triangle, and h is the height of the triangle perpendicular to that base.
You will notice that B is multiplied by 2 in the area formula, because there is a triangular base at either end of the prism. That means we can save some work by not multiplying by 1/2, and then by 2.
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For figures 1, 3, 4, the triangle is a right triangle, so the base and height make up two of the three sides of it. The perimeter is finished by adding the length of the hypotenuse. That sum is then multiplied by the "height" of the prism (distance between bases) to find the lateral area as part of the area formula (Ph).
In figure 3, the triangle is equilateral, so the perimeter is not the sum of the base and height and a third side. In the attached spreadsheet, we have used a value "rest of perimeter" to make the sum be the right value for use in computing the value of Ph. For figure 3, that is 6+6-5.2=6.8. Then the sum 6 +5.2 +6.8 is 18, the proper perimeter for that figure.
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The idea here is to let a spreadsheet do the tedious work of applying the same formula to different sets of numbers. The areas are ...
- 108 cm^2
- 211.2 cm^2
- 308.8 mm^2
- 560 yd^2
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By way of example, we can "show work" for problem 1:
1. S = Ph +2B
S = (4 +3 +5)(8) +2(1/2)(4)(3) = 12(8) +12 = 96 +12 = 108 . . . cm^2
