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!