Logarhythm

-5p + 20 - 5p + 20

= -5(p - 4 + p - 4)

= -5(2p - 8)

I understand it now. The question was just poorly written. 

              \(b^2 - 4ac = 7\)

\(b^2 - 4(1)(b + 3) = 7\) 
       \(b^2 - 4b - 12 = 7\)
       \(b^2 - 4b - 19 = 0\) 
                            \(b = {-(-4) \pm \sqrt{(-4)^2-4(1)(-19)} \over 2(1)}\) 

                            \(b = {4 \pm \sqrt{16+ 76} \over 2}\)

                            \(b = {4 \pm 2\sqrt{23} \over 2}\)

                            \(b = 2\pm\sqrt{23}\)

                            \(b>0 \)

                        \(\therefore b = 2 + \sqrt{23}\)

                                      \(25x^2 + 40x - 10 = 0\)
\(25x^2 + 40x + (\frac{40\div2}{5})^2 - (\frac{40\div2}{5})^2 - 10 = 0\)

                   \(25x^2 + 40x + 16 - 16 - 10 = 0\)

                                \((5x + 4)^2 - 16 - 10 = 0 \)

                                                    \((5x + 4)^2 = 26\)

therefore the value of a + b + c is 5 + 4 + 26, which equals 35. 

the value of the 7 in 735208 is "700000"
the value of the 7 in 137342 is "7000"

7000 x 10 ≠ 700000

therefore this isn't correct. 

you can approach this question multiple ways. 
start by finding the equation of this graph. you can do this in vertex or factored form for ease:

y = a(x + 1)² - 1    or    y = a(x)(x + 2)

now pick a point and substitute it in to find the dilation factor, a. 

(1, 3)  
3 = a(1 + 1)² - 1    or    3 = a(1)(1 + 2)
3 = 4a - 1                     3 = 3a
4 = 4a                          a = 1
a = 1

y = 1(x + 1)² - 1            y = 1x(x + 2)
y = (x + 1)² - 1              y = x(x + 2)

now you just convert the equation into standard form by expanding: 

y = (x + 1)² - 1       or    y = x(x + 2)
y = x² + 2x + 1 - 1         y = x² + 2x
y = x² + 2x

therefore a + b + c = 1 + 2 + 0
                               = 3. 

as said, start by isolating y: 
5x + y = 31
        y = 31 - 5x

then substituting that into the second equation: 
3x + 4y = -37
3x + 4(31 - 5x) = -37
3x + 124 - 20x = -37
        124 - 17x = -37
               - 17x = -161
                     x = \(9\frac{8}{17}\)

now you can substitute the x value back into the first equation to find y: 
y = 31 - 5x 
   = 31 - 5( \(9\frac{8}{17}\) )
   = 31 - \(47\frac{6}{17}\)
   = \(-16\frac{6}{17}\)

so your answer would be \((9\frac{8}{17}, -16\frac{6}{17})\). 

hope this helps and tell me if I did anything wrong :) 

  (2x + 7)(x - 5) = -43 + jx + x²
    2x² - 3x - 35 = -43 + jx + x²
 x² - 3x - jx + 8 = 0
x² - (3 + j)x + 8 = 0

when there is only one real solution, by the quadratic equation:
                b² - 4ac = 0
(-(3 + j))² - 4(1)(8) = 0
              (-(3 + j))² = 32
                  -(3 + j) = \(±\sqrt{32}\)
                     3 + j = \(±4\sqrt{2}\)
                           j = \(±4\sqrt{2} - 3\)

\(4\sqrt{2} - 3 ≈ 2.66\)
\(-4\sqrt{2} - 3 ≈ -8.66\)

which then your answer is -8.66, 2.66

please tell me if I did anything wrong. hope this helps

f(x) = x² - 2x + 5

g(x) = x + 8

f(g(5)) - g(f(5))
= [(g(5))² - 2(g(5)) + 5] - [(f(5)) + 8]
= [((5) + 8)² - 2((5)) + 5] - [((5)² - 2(5) + 5) + 8]
= [169 - 10 + 5] - [25 - 10 + 5 + 8]
= 164 - 28
= 136

 

we know the point of intersection is (-4, -7), so k has to be 0 since the y intercept of the equation y = kx - 7 is (0, -7), it follows that the line is horizontal therefore it has a slope of 0.