Answer:
a = 1
Step-by-step explanation:
The important point here is that both lines are <em>horizontal reflections</em> of each other. If we treat the line x = a as a kind of "mirror" for these lines, every point at the same y value on each line is going to be an equal horizontal distance from that "mirror". If that's confusing, think about how, as you pull your hand away from a mirror, your hand's reflection seems to go deeper into it. As you bring it closer, your reflection gets closer too. And when you're touching the mirror, it seems like your hand and its reflection are touching!
We want to find that "touching" point for the two lines, the <em>intersection</em>, because it'll tell us exactly where our "mirror" - more commonly called the <em>axis of symmetry</em> - is. The point of intersection of any two lines is the point where their equations are exactly equal to each other.
Our equations are y = 3x - 5 and y = 1 - 3x, so setting those two equal to each other and solving for x:
This tells us that the two lines intersect at x = 1, which is exactly our axis of symmetry, so a = 1!
Answer:
Este acontecimento se repetirá 300 dias depois.
Step-by-step explanation:
Quando os eventos se repetirão no mesmo dia?
Cada evento tem uma frequência.
Eles ocorrem simultaneamente a cada x dias, e x é dado pelo MMC(Mínimo Múltiplico Comum) entre as frequência.
Neste problema:
A cada 15 dias o avô visita.
A cada 100 dias o tio visita.
A cada 12 dias vai à praia.
Quantos dias depois este acontecimento se repetirá?
Os três no mesmo dia vão se repetir após x dias, em que x é dado pelo MMC de 15, 100 e 12
MMC de 15, 100 e 12
Fatorando simultâneamente estes valores:
15 - 100 - 12|2
15 - 50 - 6|2
15 - 25 - 3|3
5 - 25 - 1|5
1 - 5 - 1|5
1 - 1 - 1
Então:
mmc(15,100,12) = 2*2*3*5*5 = 300
Este acontecimento se repetirá 300 dias depois.
You would be 26 im pretty sure
9514 1404 393
Answer:
Step-by-step explanation:
Let a and s represent the prices of adult and student tickets, respectively.
13a +12s = 211 . . . . . . ticket sales the first day
5a +3s = 65 . . . . . . . ticket sales the second day
Subtracting the first equation from 4 times the second gives ...
4(5a +3s) -(13a +12s) = 4(65) -(211)
7a = 49 . . . . . . . simplify
a = 7 . . . . . . . divide by 7
5(7) +3s = 65 . . . . substitute into the second equation
3s = 30 . . . . . . . subtract 35
s = 10 . . . . . . . divide by 3
The price of one adult ticket is $7; the price of one student ticket is $10.
