Step-by-step explanation: We are given two lines 'h' and 'k' which are parallel to each other. Also, there is another line 'j' that is perpendicular to line 'h'.

We are to prove that line 'j' is perpendicular to line 'k'.

Let, m, n and p be the slopes of lines 'h', 'k' and 'j' respectively.

Now, since line 'h' and 'k' are parallel, so their slopes will be equal. i.e., m = n.

Also, lines 'h' and 'j' are perpendicular, so the product of their slopes is -1. i.e.,

m×p = -1.

Hence, we can write from the above two relations

n×p = -1.

Thus, the line 'j' is perpendicular to line 'k'.

Proved.

8 0

4 years ago

Find (f • g) when f(x) = x^2 + 5x + 6 and g(x) = 1/x+3

Nikitich [7]

Answer:

option D

Step-by-step explanation:

$f(x) = x^2 + 5x + 6$

$g(x)= \frac{1}{x+3}$

(fog)(x) = f(g(x))

Plug in g(x) in f(x)

We plug in 1/x+3 in the place of x in f(x)

$f(g(x))= f(\frac{1}{x+3})= (\frac{1}{x+3})^2 + 5(\frac{1}{x+3}) + 6$

To simplify it we take LCD

LCD is (x+3)(x+3)

$\frac{1}{(x+3)(x+3)}+5\frac{1*(x+3)}{(x+3)(x+3)}+\frac{6(x+3)(x+3)}{(x+3)(x+3)}$

$\frac{1}{x^2+6x+9}+\frac{(5x+15)}{x^2+6x+9}+\frac{6x^2+36x+54}{x^2+6x+9}$

All the denominators are same so we combine the numerators

$\frac{1+5x+15+6x^2+36x+54}{x^2+6x+9}$

$\frac{6x^2+41x+70}{x^2+6x+9}$

Option D is correct

8 0

3 years ago

Read 2 more answers

Look at the graph and tell me why it is proportional or nonproportional and why?

andreyandreev [35.5K]

Answer:

I think it is not proportional because the line is supposed to go thro the middle of each dot, and some of the dots don't have a line thro the middle only on the side or not even on the dot.

Hope this helps!

Step-by-step explanation:

please mark me brainliest...

8 0

3 years ago