Answer:
Step-by-step explanation:
Each ticket is $15. The number of tickets is what we are trying to solve for. The class spends a certain amount of money to prepare for the formal. They hope that the money they make in ticket sales is MORE than what they spend. The expression that represents the number of tickets at $15 each is 15x, where x is the number of tickets. They hope that the sales are greater than what they spend, so what we have so far is
15x >
Greater than what, though? What do they spend? They spend 600 for the food, so
15x > 600...
but they also have to print a certain, unknown number of tickets at .50 each. The expression that represents the printing of each ticket is .5x (we can drop the 0; it doesn't change the answer or make it wrong if we drop it off). So the cost for this affair is the food + the printing.
15x > 600 + .5x
Solve this inequality for x. Begin by subtracting .5 from both sides to get
14.5x > 600 so
x > 41.3
Because we are not selling (or printing) .3 of a ticket, it's safe to say (and also correct!) that they need to sell (and print) 41 tickets. If they sell 41 tickets, the profit is found by
15(41) > 600 + .5(41)
615 > 600
This means that at 41 tickets, they make a profit. At 40 tickets, the inequality looks like this:
15(40) > 600 + .5(40) and
600 > 620. This is not true, so 40 tickets isn't enough.
Answer:
20 units
Step-by-step explanation:
This implies that the square can be divided into four equal L-shaped regions. These regions with respect to transformation forms a square.
Perimeter of the square is 40 units. Since a square has equal length of sides, thus each side of the square is 10 units.
Thus, each L-shape region has dimensions; 8 units, 5 units, 5 units and 2 units.
Perimeter of each L-shape region = the addition of the length of each side of the shape
Perimeter of each L-shape region = 8 + 5 + 5 + 2
= 20 units
V=(1/3)hπr^2 where h=height and r=radius
given
radius=3
height=2a
r=3
h=2a
v=(1/3)hπr^2
v=(1/3)(2a)π(3)^2
v=(1/3)2aπ9
v=6aπ
so the expression would be some variaant of v=6aπ
<h3>
Answer: Check out the diagram below.</h3>
Explanation:
Use your straightedge to extend segment AB into ray AB. This means you'll have it start at A and go on forever through B. Repeat these steps to turn segment AC into ray AC.
The two rays join at the vertex angle A. Point A is the center of the universe so to speak because it's the center of dilation. We consider it an invariant point that doesn't move. Everything else will move. In this case, everything will move twice as much compared to as before.
Use your compass to measure the width of AB. We don't need the actual number. We just need the compass to be as wide from A to B. Keep your compass at this width and move the non-pencil part to point B. Then mark a small arc along ray AB. What we've just done is constructed a congruent copy of segment AB. In other words, we've just double AB into AB'. This means the arc marking places point B' as the diagram indicates.
The same set of steps will have us construct point C' as well. AC doubles to AC'
Once we determine the locations of B' and C', we can then form triangle A'B'C' which is an enlarged copy of triangle ABC. Each side of the larger triangle has side lengths twice as long.
Note: Points A and A' occupy the same exact location. As mentioned earlier, point A doesn't move.
Line RS is where they intersect
