dierdurst

Hi Guest, I think it is better if you look up your question online. Depending on your actual equation, there will be examples that might help. 

- Daisy

\( 3x - 7≤5x + 9\) is our equation, and we want to move all the variables to one side. We can simplify the equation to  \( -2x ≤ 16\). Then, we need to divide each side by \(-2\). Since we are dividing/multiplying the equation by a negative number, we need to flip the sign. By doing this, we get \(x ≥ -8\). Since the problem is asking for an interval, we can get \([-8, +∞]\). Please correct me if I made a mistake!

- Daisy

We have \({a}^{2} - {b}^{2} = 8\), which we can square both sides to get \(a^4 + b^4 - 2a^2b^2 = 8^2\). Since \(ab = 2\), we can square both sides again to get \(a^2b^2 = 2^2\). Then, we can subsitute that value into the equation; \(a^4 + b^4 - 2(4) = 8^2\) -> \(a^4 + b^4 - 8 = 64\) -> \(a^4 + b^4 = 72\).

- Daisy

First we can expand \(-3(-x + 5)\) and \(-10(x-3)\). By doing this, we get \(3x - 15 + 20 = -10x + 30 + 4\). Then, we can get \(3x +5 = -10x + 34\). After this, we need to isolate the variable; \(13x = 29\). From here, we can get \(x = \frac{29}{13}\) or \(x = 2\frac{3}{13}\)​.

- Daisy

The slope of this line is \(-5\). In order for two lines to be perpendicular, their slope's must have a product of \(-1\). So \(-5x = -1\), solving this we can get \(x = \frac{1}{5}\). \(\frac{1}{5}\) is your slope.

- Daisy 

The question states that the price, \(x\) is not less than \(100\), which means it has to be greater than \(99\). But, it also did not say that it had to be greater than \(100\), so \(x ≥ 100\).

- Daisy

I got that also, hopefully we are both correct rather than both incorrect... Haha.

- Daisy

Since in this case \(x = -2\), then we can subsitute \(-2\) in for all the \(x\)​'s. We can get \(4{(-2)}^{3} - 4{(-2)}^{2} + 10\), which equals \(-32 - 16 + 10\), which equals \(-38\).

- Daisy

Thank you!

- Daisy

Our profit per package delivered is \($2.70 - $1.70 = $1\). Since we need to make \($15\), we can do \(\frac{15}{1} = 15\). So we would need \(15\) packages to be delivered.

- Daisy