Tutor profile: Lauren E.
What is the solution (both x and y) for the set of equations: 6x + 3y = 33 6x - y = 5
To begin solving for this problem, we must first set one variable in terms of the other. Let's use the second equation to set "y" in terms of "x." To do this, we want to isolate y on one side of the equation. We begin by subtracting "6x." - y = 5 - 6x We then divide by "-1" to get a positive "y" on the left side of the equation. y = (5/-1) - (6x/-1) y = -5 - (-6x) y = -5 + 6x Now that we know what "y" equals, we can plug this into "y" in the first equation. 6x + 3(-5 +6x) = 33 Now distribute the "3" by multiplying it by the equation is parentheses. 6x + (-15) + 18x = 33 6x - 15 + 18x = 33 Now combine "x" values on one side of the equation and non-variable number on the other side and solve. 6x + 18x = 33 + 15 24x = 48 x = 48/24 x = 2 Now that we know the value of "x," you can plug this value into "x" in either of the two original equations to solve for "y". We'll use the second one. 6(2) - y = 5 12 - y = 5 Isolate "y" on one side of the equation. - y = 5 - 12 y = (5/-1) - (12/-1) y = -5 - (-12) y = -5 + 12 y = 7
A beaker contains a solution of 85% water and 15% NaCl. Inside the beaker is a cell comprised of 90% water and 10% NaCl. Describe what will happen to the fluid flow in/out of the cell when it is placed in the beaker. Is the solution hypertonic, hypotonic, or isotonic and why?
If the cell is 10% NaCl, and the solution is 15% NaCl, then the solution has a higher solute concentration and will tend to draw in water. Therefore, water will leave the cell and enter the solution until both the cell and solution are balanced in solute concentration. The solution is hypertonic because the solution has a higher solute concentration than the cell.
The sum of four times a number and three less than that same number equals 27. Write an equation and solve to determine the number.
let "x" be the number we are trying to solve for. "four times a number" can be written as: 4x "three less than that same number" can be written as: (x-3) Therefore, "the sum of four times a number and three less than that same number equals 27" can be written as: 4x + (x-3) = 27 To solve for this equation, we group all "x" values on one side of the equation, and all non-variable numbers on the other side. To do this, we first add the two "x" values: 5x - 3 = 27 Then we move "-3" to the other side by adding it to 27: 5x = 27 + 3 5x = 30 Now solve for "x" by dividing by 5: x = 30/5 x = 6
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