Answer:
10 and 15
Step-by-step explanation:
Let 'x' and 'y' are the numbers we need to find.
x + y = 25 (two numbers whose sum is 25)
(1/x) + (1/y) = 1/6 (the sum of whose reciprocals is 1/6)
The solutions of the this system of equations are the numbers we need to find.
x = 25 - y
1/(25 - y) + 1/y = 1/6 multiply both sides by 6(25-y)y
6y + 6(25-y) = (25-y)y
6y + 150 - 6y = 25y - (y^2)
y^2 - 25y + 150 = 0 quadratic equation has 2 solutions
y1 = 15
y2 = 10
Thus we have
:
First solution: for y = 15, x = 25 - 15 = 10
Second solution: for y = 10, x = 25 - 10 = 15
The first and the second solution are in fact the same one solution we are looking for: the two numbers are 10 and 15 (since the combination 10 and 15 is the same as 15 and 10).
If u work it out and both sides don't equal, then there is no solution.
Example :
2x + 4 = 2x + 6
2x - 2x = 6 - 4
0 = 2....this is incorrect...therefore, there is no solution
Answer:
D
Step-by-step explanation:
Yes it's D. Answered by Gauthmath
Answer:
D - The elevator traveled upward at a rate of 2(2/5) feet per second.
Step-by-step explanation:
Okay, this is almost like kinematics, which deals with physics.
Here are your given values:
Position 1 = 70ft [down]
Position 2 = 10ft [down]
Change in time (Δt - time - scalar) = 25 seconds
The equation for displacement is d₂-d₁. This would be the change of position of the elevator during the 25 seconds.
So, we can use this equation to figure out the change in position.
Δd = d₂-d₁ = 10ft [down] - 70 ft [down] = 60ft [up]
The equation for velocity is Δd/Δt. This would be the rate of which the elevator travels. Velocity is simply speed but with a direction.
So, we can use this equation to solve.
v = Δd / Δt = 60 feet [up] / 25 seconds = 2.4 ft / second [up].
Now, we need to change 2.4 ft / second [up] into a fraction.
2.4 -> 2 (4/10) -> 2 (2/5)
All I am simply doing is figuring out the distance the elevator traveled and determined the direction of which the elevator traveled. Then, I divided that by the time the elevator traveled to determine its speed and the direction the elevator traveled.
Based on the problem statement you can write two equations for the cost of tables (t) and chairs (c).
.. 6c +2t = 20
.. 3c +5t = 35
You can solve these by your favorite method to find the costs are
.. chairs cost $1.25
.. tables cost $6.25
_____
My favorite method is to use the graphing calculator at Desmos [dot] com. Many graphing calculators will solve equations like these either directly, graphically, or indirectly using matrix functions. If you want to solve them by "elimination," you can double the second equation and subtract the first to get
.. 8t = 50
