Dimitristhym

$7𝑥 + 2𝑦 = 11$

$<=> 𝑦 =- \frac{7x}{2} + \frac{11}{2}$

We will call $λ=-7/2$ is the coefficient of x 

so every parallel line to AB will have $λ=-7/2$

lines have type : $y-y1=λ(x-x1)$ We want coordinates (-5, 25/2 ) 

so x1=-5 and y1=(25/2) 

$y-(\frac{25}{2})=-\frac{7}{2}(x-(-5))$

$y=-\frac{7}{2}(x+5))+\frac{25}{2}$

$y=-\frac{7}{2}x-\frac{35}{2}+\frac{25}{2}$

$y=-\frac{7}{2}x-\frac{10}{2}$

$7x+ 2y=-10$

"Given the line AB passes through the point (k, k+1) find the value of the constant k."

This means  x= k, y=k+1 verify the equation 7𝑥 + 2𝑦 = 11 

So 

$7k+2(k+1)=11$

$7k+2k+2=11$

$9k=9$

so $k=1$ 

Finally the point (k, k+1) is (1,2) 

Help its helps! 

Yesterday morning at 8 a.m. the temperature was -14˚F. At noon it was 10 degrees warmer

So at noon it was -14˚F + 10˚F = -4˚F 

The temperature increase between noon and and 4 p.m. was twice the temperature increase between 8 a.m. and noon

So the temperature increase between noon and and 4 p.m is 10 so $2 \times 10=20$

Finally -4˚F + 20˚F = 16˚F   The temperature at 4 p.m!

Hope it helps! 

 21 divisors:1 2 4 8 16 32 64 128 256 512 1024 2048 4096 8192 16384 32768 65536 131072 262144 524288 1048576

so the size of the number n = $21$

Hope it helps! 

Correct answer B

and  $f(x)=3x^2$

Hope it helps! 

$\frac{x}{x−1} − \frac{1}{ x−2} = \frac{2x−5 }{ x^2−3x+2}$ ,$x≠1,x≠2$ <=> $(x-2)\frac{x}{x−1(x-2)} − (x-1)\frac{1}{(x-1) x−2} = \frac{2x−5 }{ x^2−3x+2}$<=>$x^2-3x+1=2x-5$ <=> $x^2-5x+6=0$ <=>$(x-3)(x-2)=0$  

BUT  $x≠2$ SO 

$x=3$ 

So correct answer is B

Hope it helps! 

$f(-6) = (-6)^4 + 8(-6)^3 + 10(-6)^2 - 7(-6) + 40=1296 -1728 + 360 +42 +40 = 10$

so $f(-6)=10$

Thank you CPhill!

Just learn the theory how divide polyonyms.It's easy.If i just tell you the answer I'll not help you! 

Perfect will be a=b, because $\left |a-b \right |=> \left |a-a \right |=0$ so for $a=b$ we have:

$a^2 -6a + 5a - 373 =0$ <=> $a^2 -a - 373 =0$

$x = {-b \pm \sqrt{b^2-4ac} \over 2a}$=> $x = {1 \pm \sqrt{1-4(1)(-373)} \over 2}$=>$x = {1 \pm \sqrt{1493} \over 2}$=> $x = {1 \pm ~38.63 \over 2}$

$x1=\frac{39.63}{2} = 19.81$

$x2=\frac{-37.63}{2}=-18.81$ BUT because is negative rejected 

so $a=20$ so $20b-120+5b=373$ => b=19.72 its NOT integers so you try values until a,b  integers

Finaly the answer is a=44  and  b =13 like Guest says and can see it in this graph if you try values!