Answer:
The distance between the two train stations is 1728 km
Step-by-step explanation:
The speed of the bus = 54 km/h
The speed of the truck = 48 km/h
When the bus and truck meet again, the distance covered by the bus = 216 km more than he distance traveled by the truck
Let the distance between the two train stations = x
Let the location where they first meet be y from station A we have;
The location where they meet again = y - 216 km
Therefore, we have;
Location where they
The time for the truck and the bus to meet again = t
Therefore, 54 × t - 48 × t = 216 km
6·t = 216 km
t = 36 hours
Therefore, the time for the bus to travel x + 216 km = 36 hours
54 × 36 = 1944 = x + 216
x = 1944 - 216 = 1728 km
The distance between the two train stations = 1728 km.

The vertex is at (0,-5), therefore the range goes from (-infinity, - 5]
Answer:
Option b. Two solutions
Step-by-step explanation:
In order to find how many real number solutions the equation has we have to solve it
Given equation: -4x² + 10x + 6 = 0
taking 2 common from the equation
2(-2x² + 5x + 3) = 0
-2x² + 5x + 3 = 0
taking minus sign common from the above equation
2x² - 5x - 3 = 0
We will solve this equation by factorization in such a way that the sum of two factors is equal to -5x and the product is -6x²
2x² - 6x + x - 3 = 0
taking common above
2x(x-3) + 1(x-3) = 0
taking (x-3) common
(2x+1)(x-3) = 0
2x + 1 = 0
2x = -1
x = 
x - 3 = 0; x = 3
the solutions are

Both values are real numbers, therefore correct option is b
Answer:
33333
Step-by-step explanation:
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If Ali has x cards, then Belinda has 2x cards.
If Ali has x cards, then Charlie has x+5 cards.
2x (Belinda) + x+5 (Charlie) + x (Ali) = 33 (total)
2x + x+5 + x = 33
Now simplify the equation... x+x+5 can be simplified as 2x+5.
2x+5 plus 2x can become 4x+5.
So their total number is 4x+5.
So 4x+5=33.
You want to isolate the variables and numbers.
To remove the 5 from the left side, subtract 5 from both sides.
4x+5-5=4x - 33-5=28
So the equation now is 4x=28
To remove the 4, divide each side by 4.
4x÷4=x - 28÷4=7
So x equals 7, Ali has 7 cards.
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