To solve the equation, we can start by distributing 0.4 to the terms inside the parentheses:
0.4(x-0.5) = 0.2(x+3)
0.4x - 0.4(0.5) = 0.2x + 0.2(3)
Simplifying both sides of the equation gives us:
0.4x - 0.2 = 0.2x + 0.6
Next, let's combine the like terms on each side of the equation:
0.4x - 0.2x = 0.6 + 0.2
0.2x = 0.8
Now, we can solve for x by dividing both sides of the equation by 0.2:
0.2x/0.2 = 0.8/0.2
x = 4
Therefore, the solution to the equation 0.4(x-0.5)=0.2(x+3) is x = 4.
What is the solution to the equation below?
0.4(x-0.5)=0.2(x+3)
11 answers
The amount of pressure on a diver as she descends into the sea can be modeled by the equation y=1/10x+1, where x is her depth in meters and y is the amount of pressure in atmospheres (atm). Which of these statements are correct according to the model? Select TWO that apply.
A.
For every 1 meter that the diver descends, the amount of pressure on her decreases by 10 atms.
B.
For every 1 meter that the diver descends, the amount of pressure on her increases by 10 atms.
C.
For every 10 meters that the diver descends, the amount of pressure on her decreases by 1 atm.
D.
For every 10 meters that the diver descends, the amount of pressure on her increases by 1 atm.
E.
At sea level, the amount of pressure on the diver is
atm.
A.
For every 1 meter that the diver descends, the amount of pressure on her decreases by 10 atms.
B.
For every 1 meter that the diver descends, the amount of pressure on her increases by 10 atms.
C.
For every 10 meters that the diver descends, the amount of pressure on her decreases by 1 atm.
D.
For every 10 meters that the diver descends, the amount of pressure on her increases by 1 atm.
E.
At sea level, the amount of pressure on the diver is
atm.
To determine which statements are correct according to the model y = (1/10)x + 1, we can analyze the equation and the relationship between x (depth) and y (pressure).
A. For every 1 meter that the diver descends, the amount of pressure on her decreases by 10 atms.
This statement is incorrect. According to the equation, for every 1 meter the diver descends (x increases by 1), the pressure (y) decreases by 1/10 (0.1 atm).
B. For every 1 meter that the diver descends, the amount of pressure on her increases by 10 atms.
This statement is incorrect. As explained above, for every 1 meter the diver descends, the pressure increases by 0.1 atm, not by 10 atm.
C. For every 10 meters that the diver descends, the amount of pressure on her decreases by 1 atm.
This statement is incorrect. According to the equation, for every 1 meter the diver descends (x increases by 1), the pressure decreases by 0.1 atm. Therefore, for every 10 meters (x increases by 10), the pressure decreases by 1 atm.
D. For every 10 meters that the diver descends, the amount of pressure on her increases by 1 atm.
This statement is also incorrect. According to the equation, for every 1 meter the diver descends, the pressure increases by 0.1 atm. Therefore, for every 10 meters, the pressure would increase by 1 atm, not decrease.
E. At sea level, the amount of pressure on the diver is 1 atm.
This statement is correct. When x (depth) is 0 (sea level), the equation becomes y = (1/10)(0) + 1, which simplifies to y = 1. This means that at sea level, the amount of pressure on the diver is 1 atm.
Therefore, the two correct statements are:
- For every 1 meter that the diver descends, the amount of pressure on her increases by 0.1 atm.
- At sea level, the amount of pressure on the diver is 1 atm.
A. For every 1 meter that the diver descends, the amount of pressure on her decreases by 10 atms.
This statement is incorrect. According to the equation, for every 1 meter the diver descends (x increases by 1), the pressure (y) decreases by 1/10 (0.1 atm).
B. For every 1 meter that the diver descends, the amount of pressure on her increases by 10 atms.
This statement is incorrect. As explained above, for every 1 meter the diver descends, the pressure increases by 0.1 atm, not by 10 atm.
C. For every 10 meters that the diver descends, the amount of pressure on her decreases by 1 atm.
This statement is incorrect. According to the equation, for every 1 meter the diver descends (x increases by 1), the pressure decreases by 0.1 atm. Therefore, for every 10 meters (x increases by 10), the pressure decreases by 1 atm.
D. For every 10 meters that the diver descends, the amount of pressure on her increases by 1 atm.
This statement is also incorrect. According to the equation, for every 1 meter the diver descends, the pressure increases by 0.1 atm. Therefore, for every 10 meters, the pressure would increase by 1 atm, not decrease.
E. At sea level, the amount of pressure on the diver is 1 atm.
This statement is correct. When x (depth) is 0 (sea level), the equation becomes y = (1/10)(0) + 1, which simplifies to y = 1. This means that at sea level, the amount of pressure on the diver is 1 atm.
Therefore, the two correct statements are:
- For every 1 meter that the diver descends, the amount of pressure on her increases by 0.1 atm.
- At sea level, the amount of pressure on the diver is 1 atm.
Enter the value for x that makes the equation 2(x-3)+21=-3 true.
To find the value of x that makes the equation 2(x-3) + 21 = -3 true, we can solve for x.
1. Start by simplifying the equation:
2(x-3) + 21 = -3
Distribute 2 to the terms inside the parentheses:
2x - 6 + 21 = -3
Combine like terms:
2x + 15 = -3
2. Next, isolate the variable x by subtracting 15 from both sides of the equation:
2x + 15 - 15 = -3 - 15
2x = -18
3. Finally, solve for x by dividing both sides of the equation by 2:
2x/2 = -18/2
x = -9
Therefore, the value of x that makes the equation 2(x-3) + 21 = -3 true is x = -9.
1. Start by simplifying the equation:
2(x-3) + 21 = -3
Distribute 2 to the terms inside the parentheses:
2x - 6 + 21 = -3
Combine like terms:
2x + 15 = -3
2. Next, isolate the variable x by subtracting 15 from both sides of the equation:
2x + 15 - 15 = -3 - 15
2x = -18
3. Finally, solve for x by dividing both sides of the equation by 2:
2x/2 = -18/2
x = -9
Therefore, the value of x that makes the equation 2(x-3) + 21 = -3 true is x = -9.
Solve:
2(3r+4)-3(r+1)=11
2(3r+4)-3(r+1)=11
To solve the equation 2(3r+4)-3(r+1)=11, we can follow these steps:
1. Distribute the 2 and the -3 to the terms inside the parentheses:
6r + 8 - 3r - 3 = 11
Simplify each side of the equation:
3r + 5 = 11
2. Next, isolate the variable r by subtracting 5 from both sides of the equation:
3r + 5 - 5 = 11 - 5
3r = 6
3. Finally, solve for r by dividing both sides of the equation by 3:
(3r) / 3 = 6 / 3
r = 2
Therefore, the solution to the equation 2(3r+4)-3(r+1)=11 is r = 2.
1. Distribute the 2 and the -3 to the terms inside the parentheses:
6r + 8 - 3r - 3 = 11
Simplify each side of the equation:
3r + 5 = 11
2. Next, isolate the variable r by subtracting 5 from both sides of the equation:
3r + 5 - 5 = 11 - 5
3r = 6
3. Finally, solve for r by dividing both sides of the equation by 3:
(3r) / 3 = 6 / 3
r = 2
Therefore, the solution to the equation 2(3r+4)-3(r+1)=11 is r = 2.
Solve for t.
t-3(4-t)=-24
t-3(4-t)=-24
To solve the equation t-3(4-t)=-24, we can follow these steps:
1. Distribute the -3 to the terms inside the parentheses:
t - 3 * 4 + 3 * t = -24
Simplify each side of the equation:
t - 12 + 3t = -24
2. Combine like terms on the left side of the equation:
t + 3t - 12 = -24
4t - 12 = -24
3. Move the constant term to the right side of the equation by adding 12 to both sides:
4t - 12 + 12 = -24 + 12
4t = -12
4. Finally, solve for t by dividing both sides of the equation by 4:
(4t) / 4 = -12 / 4
t = -3
Therefore, the solution to the equation t-3(4-t)=-24 is t = -3.
1. Distribute the -3 to the terms inside the parentheses:
t - 3 * 4 + 3 * t = -24
Simplify each side of the equation:
t - 12 + 3t = -24
2. Combine like terms on the left side of the equation:
t + 3t - 12 = -24
4t - 12 = -24
3. Move the constant term to the right side of the equation by adding 12 to both sides:
4t - 12 + 12 = -24 + 12
4t = -12
4. Finally, solve for t by dividing both sides of the equation by 4:
(4t) / 4 = -12 / 4
t = -3
Therefore, the solution to the equation t-3(4-t)=-24 is t = -3.
Solve for x.
3x + 2 = x + 8
3x + 2 = x + 8
To solve the equation 3x + 2 = x + 8, we can follow these steps:
1. First, let's simplify the equation by combining like terms:
3x + 2 = x + 8
Subtract x from both sides of the equation:
3x - x + 2 = x - x + 8
2x + 2 = 8
2. Next, isolate the variable x by subtracting 2 from both sides of the equation:
2x + 2 - 2 = 8 - 2
2x = 6
3. Finally, solve for x by dividing both sides of the equation by 2:
(2x) / 2 = 6 / 2
x = 3
Therefore, the solution to the equation 3x + 2 = x + 8 is x = 3.
1. First, let's simplify the equation by combining like terms:
3x + 2 = x + 8
Subtract x from both sides of the equation:
3x - x + 2 = x - x + 8
2x + 2 = 8
2. Next, isolate the variable x by subtracting 2 from both sides of the equation:
2x + 2 - 2 = 8 - 2
2x = 6
3. Finally, solve for x by dividing both sides of the equation by 2:
(2x) / 2 = 6 / 2
x = 3
Therefore, the solution to the equation 3x + 2 = x + 8 is x = 3.
1 answer