Hello again! I've got two questions I'm stuck on in an algebra worksheet.
1. Solve the equation:
2𝑦 + 5 = 1/2(4𝑦 + 8)
(I really don't know how to solve these correctly, I've tried everything.)
2. The density of an
object is calculated using
the formula 𝐷 = m/v, where
m is the object’s mass and
v is its volume. Gold has a
density of 19.3 g/cm3. What is the volume of an
amount of gold that has a
mass of 96.5 g?
(Please help me work this out!)
2𝑦 + 5 = 1/2(4𝑦 + 8)
multiply both sides by 2
4y + 10 = 4y + 8
10 = 8,
ahhh, I see your problem, the y's dropped out
ok, if your variables drop out, and you end up with a false statement, such as our 10=8,
then the equation has no solution.
If we end up with a true statement after the variable drops out, then you are dealing with an identity, and there would be an infinite number of solutions.
I see now, no wonder I couldn't get it! Thank you for helping me understand. Anything for question 2?
Hello! I'm here to help you with your algebra questions. Let's start with the first one.
1. Solve the equation:
2𝑦 + 5 = 1/2(4𝑦 + 8)
To solve this equation, we need to isolate the variable, which in this case is 𝑦. Here's how you can do it step by step:
Step 1: Distribute the 1/2 to the terms inside the parentheses on the right side of the equation.
2𝑦 + 5 = 1/2(4𝑦) + 1/2(8)
Simplifying the right side:
2𝑦 + 5 = 2𝑦 + 4
Step 2: Move all terms involving 𝑦 to one side of the equation.
Subtract 2𝑦 from both sides of the equation:
(2𝑦 - 2𝑦) + 5 = (2𝑦 - 2𝑦) + 4
Simplifying:
5 = 4
Step 3: Determine if the equation is true or false.
In this case, we can see that the equation simplifies to 5 = 4, which is not true. Therefore, there is no solution to this equation. Sometimes, you may encounter an equation that has no solution.
Now let's move on to your second question.
2. The density of an object is calculated using the formula 𝐷 = m/v, where m is the object’s mass and v is its volume. Gold has a density of 19.3 g/cm3. What is the volume of an amount of gold that has a mass of 96.5 g?
To find the volume, we can rearrange the density formula to solve for v:
𝐷 = m/v
Multiply both sides of the equation by v:
𝐷 * v = m
Divide both sides of the equation by 𝐷:
v = m / 𝐷
Now, plug in the given values:
v = 96.5 g / 19.3 g/cm3
To simplify, divide the mass by the density:
v = 5 cm3
Therefore, the volume of an amount of gold that has a mass of 96.5 g is 5 cm3.
I hope this helps! Let me know if there's anything else I can assist you with.