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Your truck: $T$

Neighbor: $t$

$T\ge t+600$

$T\le \frac{4t}{3}$

Solve the inequality chain.

Write everything in terms of powers of $2$. Then use that $2^n<2^N$ if and only if $n

$\frac{1}{6}$ for first and $\frac{1}{6}$ for second. Multiply the probabilities.

The parallel condition implies that it has slope $-\frac{1}{3}$. What can you determine about $A$ and $B$ given this? Now substitute $-7A+2B=3$ with your first equation to explicitly find $A,B$ and in turn find $B-A$.

$a^3+b^3+c^3=(a+b+c)(a^2+b^2+c^2-ab-bc-ac)+3abc=3abc=54$ since the first term is negligible as $a+b+c=0$.

cleannnn

I'm a bit confused with your work. 

First of all, find the equation in the $xy$ plane then substitute the $r\sin\theta$ and $r\cos\theta$ eqns

Question is incomplete

If $2,3,5,7,19|a$ then $lcm(2,3,5,7,19)=3990|a$. So just $3990*1$ and $3990*2$. 

Use the fact that $dist=2a\sqrt{1-\frac{b^2}{a^2}}$ and $a,b$ are given in the equation.

Wow nice.

$f(-2)+g(-2)=4+\frac{1}{4}=\frac{17}{4}$

$f(2)+g(2)=4+4=8$

By definition, $f(2)=f(-2)$ & $g(-2)=-g(2)$. So sub $f(2)=f(-2)=x$ and $g(-2)=-g(2)=y$.

Then $x+y=\frac{17}{4}$ and $x-y=8$. Adding the two, $2x=\frac{49}{4}$ hence $x=f(2)=\frac{49}{8}$. 

It's super easy once you use the divisibility rule for 11 and note that the digits must all be relatively high ($\frac{40}{5}=8$ is the average)

It's a depressed cubic equation. I would recommend multiplying both sides by 1000 and either using rational root theorem or using cardano's formula.

wolframalpha.com is also helpful 

You set it equal to zero and factor:

$$\left(\frac{x-3}{5}-\frac{y+1}{2}\right)\left(\frac{x-3}{5}+\frac{y+1}{2}\right)=0$$

So one or the other is zero. Solve both of them then pick the one with positive slope w.r.t x

There are 42,860 different short bingo cards.

(a,b,c) = (14,-2,5).

You just plug! Here's a start: $g(5)=5+8=13$ and $f(5)=5^2+2\cdot 5+5=25+10+5=40$.

2. The minimum value is 144.

3. f(2) = 7/3.

$5n+24+4n+30=180\implies 9n+54=180\implies n=14$

you can finish

At $x=-8.4$ in the second equation, $y=14+4.2=18.2$. Then plug this into the first equation along with $x$ to find $k$.

$62910=351261_7=172676_8$

Take the entire thing mod $10$.

It's then just $9(1^{2009}+...+9^{2009})\pmod{10}$.

And $1^{2009}=(-9)^{2009}=-9^{2009}\pmod{10}$.

Similarly, $2^{2009}=-8^{2009}\pmod{10}$, etc.

So everything cancels and it becomes $9\cdot 5^{2009}\pmod{10}$. Note that $5^n$ is always $5$ modulo $10$. Then the answer is $9\cdot 5=5\pmod{10}$.

(mod 10 is just the remainder when divided by 10)

7x+5 = 9x-5

10 = 2x

x = 5      PT = 7x+5   = 40 units

It says "figure to the right"

From P to Q    x goes from 5 to 6     from  Q to T will need to go the same amount    6  to  7       x = 7

                       y goes to  3 to -3          distance = -6                                                   -3 -6          y = -9

that was it