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Oh, yeah! Thanks!

Use this formula to calculate your monthly payment:

PMT=FV / {[[1 + R]^N - 1]^/ R}

PMT =700,000 / {[1 + 0.04/12]^(35*12) - 1 / [0.04/12]}

PMT =700,000 / {[1.003333]^420 - 1 / [0.003333]}

PMT =700,000 /                       913.730937.........

PMT =$766.09 - Monthly payment that you need to deposit.

If (16x - 20) represents the perimeter, and we have a square,  then each side is  1/4 of this....

So.....an expression for the side is

(16x - 20)  * (1/4)  =

(4x  - 5 )   feet

\(6 \frac23 \cdot 3 \frac23 = \frac{20}3 \cdot \frac{11}3 = \frac{220}9=24 \frac49=24. \bar 4\)

The last three should all be acceptable answers depending on how you want it formatted. 

You can make it either one by selecting one of the bubbles in the bottom left corner. It should be in degrees by default. :)

Your answer is:

163499238157084246970890052651977815332245607254872681799888670100456398181905536269103756533156716633238933245476249210386222120009203192687752953715493389952614864728152938620316690140722215910002962984513038253533659992483501702257775023591263777382983344691261934931342007929269781293292322816

Here's the equation we need to solve

Regular Wage + Deliveries > 155

8(9)   +  6D  > 155

72 + 6D > 155      subtract 72 from both sides

6D >  83    divide both sides by 6

D > 13.83

So.....he needs to make at least 14 deliveries to meet his goal 

This one is a little difficult.....however.......note that x^2 + x + 3  is positive for all x

We can see this because this is a parabola that turns upward and the vertex is  (-1/2, 2.75)  .....which is above the x  axis......so this part of the function is never negative

So.....only the denominator can  make this function negative....and we have

 [ 2x^2 + x - 6 ] ≥ 0

Factor the denominator

(2x -3) ( x + 2)  ≥ 0

Setting each factor to  0 and solving for x, we have that   x = 3/2   and x =  -2

And we can see that when    -2 < x < 3/2   the denominator will be  negative

Then...the function will be   ≥ 0  on these intervals :

 (-infinity , -2) U (3/2, +infinity)

Notice that we have to exclude  -2 and 3/2  from the soution because these would make the denominator 0

See the graph here :   https://www.desmos.com/calculator/dztw4t5o0m

\(\frac{d-1}{5}=\frac{d-3}{3}\)

Cross-multiply.

\((3)(d-1)=(5)(d-3)\)

Distribute.

\(3d-3=5d-15\)

Subtract 3d from both sides.

\(-3=5d-3d-15\)

Add 15 to both sides.

\(-3+15=5d-3d \\~\\ 12=2d\)

Divide both sides by 2.

\(\frac{12}{2}=d \\~\\ 6=d\)

To solve for x:

\(\tan 60^{\circ}=\frac{35}{x} \\~\\ \frac{\sin60^{\circ}}{\cos60^{\circ}}=\frac{35}{x}\)

You can look at a unit circle to get exact values for sin60º and cos60º .

\(\frac{\frac{\sqrt3}{2}}{\frac12}=\frac{35}{x} \\~\\ \frac{\sqrt3}{2}*2=\frac{35}{x} \\~\\ \sqrt3=\frac{35}{x} \\~\\ x=\frac{35}{\sqrt3} \\~\\ x=\frac{35\sqrt3}{3}\)

what's e^(i*pi) + 1 =0

e^(i*pi) = -1 =sum_(n=0)^∞ (π i)^n/(n!) = -1

9x^2 + 18x + 7

If you know Calculus, you can find this quickly, but, if not, the x value that will minimize this is given by

-b / (2a)    where  b  = 18   and a  = 9 .......so

x =  -18 / ( 2 * 9)  =   -18 / 18   =  -1

And since this is a parabola that turns upward, this is the x value of the vertex, i.e., the x value that minimizes the function

No doctors

5..............

5 apples.