helperid1839321

So, TIP is a triangle with side lengths 5, 7, and x, an array of values the missing side lengths could be. Since TIP is a isosceles triangle, I know that the third side length is 5 or 7. Therefore, the answer to your problem is 12, since the sum of x is 5 + 7.

I'm assuming f^{-1} is a way of switching the input and output values, which works for this function. Therefore f^{-1}(f(f^{-1(19))) --> f^{-1} = 19, so f(x) = 19. I substituted the equation in and got x^3-8 = 19. I added 8 to each side to get x^3 = 27. To get x without an exponent, I took the cube root of each side, getting x = 3. Either way, f^{-1}(f(f^{-1(19))) = f^{-1}(19) = f(3)

First, Jennifer's weekly pay is $575 ($1,150 / 2 = $575)

Add that to Jim's, and you get $1,275/week

Since there is a little over 364 days in a year, we can round this number to make it easier to manage:

Family's income/year: $1,275/week * 52 weeks/year = $66,300/year

Now, convert all of the expenses to years to make it easier to manage:

Mortgage + taxes= $1320/month * 12 months = $15,840/year

Food: 150/week * 52 weeks/year = $7,800/year

Clothing: $2,000/year

Utilities: $500/month * 12 months/year = $6,000/year

Charity: $100/month * 12 months/year = $1,200/year

Entertainment: $250/month * 12 months/year = $3,000/year

Loan payments: $200/month * 12 months/year = $2,400/year

Savings: $100/week * 52 weeks/year = $5,200/year

Vacation Fund: $100/month * 12 months/year = $1,200/year

Transportation: $250 bi-weekly / 2 = $125/week --> $125/week * 52 weeks/year = $6500/year

Gifts: $1,200/year

Spending money: $120/week * 52 weeks/year = $3,640/year

Day care: $150/week * 52 weeks/year = $7,800/year

Total expenses: $7,800 + $3,640 + $1,200 + $6,500 + $1,200 + $5,200 + $2,400 + $3,000 + $1,200 + $6,000 + $2,000 + $7,800 + $15,840 = $63,780

They are making a surplus of $2,520. If they needed to cut something, they could try taking out the charity, entertainment, and vacation fund categories. I would, as of now, recommend putting more into the savings category.

You must have input it wrong, the calculator comes up with no solution.

The book is correct. 16-2x²/2 does equal x² - 8. What you found equates to the exact same thing. My solution: Both of you are right.

Updated it so the first 2 have 90^o rotation symmetry, and it has reflection symmetry over y=x and y=-x. Hope it looks even better!

Note: May cause some lag. Best to use on a modern laptop or a desktop.

Tip: Try enabling the first 2 only!

Good to know, but why is that a bad thing?

f(x) basically is a 0-input function from what I can see. The output is always 2, so no matter what x is, the result will be 2. Therefore f(x + 2) = 2.