This does not make sense, Sorry.

Let h be the height of the pole and d be the distance from the building.

tan(28) = h/d   ...(1)

tan(14) = (h-60)/d  ...(2)

Rewrite (2) as tan(14) = h/d - 60/d   ...(3)

Use (1) in (3):     tan(14) = tan(28) - 60/d  ...(4)

Rearrange (4) to get d = 60/(tan(28)-tan(14))

$${\mathtt{d}} = {\frac{{\mathtt{60}}}{\left(\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{tan}}{\left({\mathtt{28}}^\circ\right)}{\mathtt{\,-\,}}\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{tan}}{\left({\mathtt{14}}^\circ\right)}\right)}} \Rightarrow {\mathtt{d}} = {\mathtt{212.478\: \!562\: \!245\: \!221\: \!509\: \!7}}$$

or d ≈ 212.5 ft

Well i think this is it but I am not really sure what your teacher is after 

$$\\2310 - 1293\\
\approx 2000-1000\\
\approx 1000\\\\\\
987-213\\
\aaprox 1000-200\\
\approx 800$$

There are 7 numbers which, when raised to the power of 7 result in -1.42.  However, all but one of them are complex.  Melody has identified the only real number solution.  Here are all the solutions:

lbs is pounds

what are you trying to do?

T=t^0-a(z-z^0)

I think I am being asked to make a the subject of the formula.

$$\\T=t^0-a(z-z^0)\\
T=1-a(z-1)\\
T=1-az+a\\
T-1=a-az\\
T-1=a(1-z)\\\\
\dfrac{T-1}{1-z}=a\\\\
a=\dfrac{T-1}{1-z}\\$$

(1/2) (4p+8)-(p+9)

$$\\(1/2) (4p+8)-(p+9)\\
=2p+4-(p+9)\\
=2p+4-p-9\\
=p-5$$

There is no formula

 (1.23)(3.46)/3.96

1.23 x 3.46 / 3.97

$${\frac{{\mathtt{1.23}}{\mathtt{\,\times\,}}{\mathtt{3.46}}}{{\mathtt{3.97}}}} = {\mathtt{1.071\: \!989\: \!924\: \!433\: \!249\: \!4}}$$

I think this is what you are being asked.

$44.64 to $38.08

$${\frac{{\mathtt{4\,464}}}{{\mathtt{3\,808}}}} = {\frac{{\mathtt{279}}}{{\mathtt{238}}}} = {\mathtt{1.172\: \!268\: \!907\: \!563\: \!025\: \!2}}$$

You just want the fraction answer in the middle.

Yes Rosala, I don't understand either!

the application of different theories to find an answer ot one problem is both time consuming and confusing. This is why some people might think maths is hard

(-1.42)^(1/7)

This is the web2 calculator ouput

$${\left(-{\mathtt{1.42}}\right)}^{\left({\frac{{\mathtt{1}}}{{\mathtt{7}}}}\right)} = \underset{{\tiny{\text{Error: not real}}}}{{{\left(-{\mathtt{1.42}}\right)}}^{{\mathtt{0.142\: \!857\: \!142\: \!857\: \!142\: \!9}}}}$$

However, this is the answer (approx because it is an irrational number)

$${\mathtt{\,-\,}}\left({\left({\mathtt{1.42}}\right)}^{\left({\frac{{\mathtt{1}}}{{\mathtt{7}}}}\right)}\right) = -{\mathtt{1.051\: \!369\: \!751\: \!024\: \!905\: \!2}}$$

check:

$${\left(-{\mathtt{1.051\: \!369\: \!751\: \!029\: \!052}}\right)}^{{\mathtt{7}}} = {\mathtt{\,-\,}}{\frac{{\mathtt{71}}}{{\mathtt{50}}}} = -{\mathtt{1.420\: \!000\: \!000\: \!039\: \!206\: \!4}}$$

I think that this can only work if the denominator of the power is an odd number.

Most calculators have a real problems with this - sometimes you really do have to use your own brain. 

I invite further comment on this one.   

This involves derivatives.

For example, if we had f(x) = 3x^2 + 2x + 3...

The 1st derivative would be f ' (x) = 6x + 2.

Note, when 6x + 2 = 0 --> 6x = -2 --> x = -2/6 = -1/3, the slope is 0 at that point on the graph of f(x).

If we had x = 1, our f ' (x) > 0, meaning we have a positive slope at point x = 1 on f(x).

If we had x = -1, our f ' (x) < 0, meaning we have a negative slope at point x= -1 on f(x).

In any case, anytime x < 0, f ' (x) will always be negative, meaning the slope will always be negative on the original f(x) graph.

When $$x \ge 0$$, f ' (x) will always be positive, meaning the slope will always be positive on the original f(x) graph.

Also, if we take the 2nd derivative, we would get f '' (x) = 6.

This means that no matter if the x value is positive, negative, or 0, the original f(x) graph will always be concave up.

Which combination would you choose, DS, if you had the money and could not eat or drink anything else for 4 hours?

There are 8 

Dragon stop being so slack and do some thinking for yourself !!!!!  

How many combinations are there?

Cross multiply:

26*5x = 57*849

130x = 48393

Divide both sides by 130:

x = 48393/130

x = 372.2538461538461538 = ~372.

Multiply both sides by 6:

24x + 2 = 6x - 15

Subtract 2 from both sides and subtract 6x from both sides as well:

18x = -17

x = -17/18.

3 waters, 1 juice.

2 waters, 2 juices.

2 waters, 1 popcorn.

2 waters, 1 trail mix.

1 water, 2 juices.

1 water, 1 popcorn.

1 water, 1 trail mix.

2 juices, 1 trail mix.

4 = x - 1

Add 1 to both sides:

5 = x

x = 5.

Distribute the 4 first:

4y^2 + 12 y + 4 + y^2 + 3y

Collect "like" terms:

5y^2 + 15 y + 4.

It is not reliable you do not have enough money!

This is some interesting homework...I have never done front-end estimation before...had to search it up!