All categories

3 years ago

How to determine whether the pair of lines is parallel perpendicular or neither?

1 answer:

6 0

If the slopes of the 2 lines are equal then they are parallel.

If m1m2 = -1 (where m1 and m2 are the slopes of the 2 lines) then they are perpendicular.

If the 2 slopes do not match either the first or second conditions then they are neither parallel or perpendicular.

You might be interested in

A group of friends wants to go to the amusement park. They have no more than $505

liq [111]

Answer:

505>15+29x

Step-by-step explanation:

4 0

3 years ago

A direct variation includes the points (21,7) and (27,Y. Find value of y.

rjkz [21]

Answer:

Step-by-step explanation:

5 has been added by the 21 to make 27 to leave with adding 5 to old y and leaving the new variable y 13

3 0

3 years ago

2. Convert 9% to a fraction and a decimal.

Furkat [3]

Answer:

0.09 decimal 9/100 fraction

Step-by-step explanation:

4 0

4 years ago

PLEASE HELP!!!! Which of these pair of functions are inverse functions?

Mamont248 [21]

Answer:

Option B and C are correct.

Step-by-step explanation:

Inverse function: If both the domain and the range are R for a function f(x), and if f(x) has an inverse g(x) then:

$f(g(x)) = g(f(x)) = x$ for every x∈R.

Let $f(x) = \frac{1}{2}(\ln(\frac{x}{2}) -1)$ and $g(x) = 2e^{2x+1}$

Use logarithmic rules:

$ln e^a = a$

$e^{lnx} = x$

$\ln a^b = b\ln a$

then, by definition;

$f(g(x)) = f(2e^{2x+1}) =\frac{1}{2}(\ln(\frac{2e^{2x+1}}{2})-1)$ = $\frac{1}{2}(\ln(e^{2x+1}}){-1) = \frac{1}{2} (2x+1-1) =\frac{1}{2}(2x) = x$

$g(f(x)) = g(\frac{1}{2}(\ln(\frac{x}{2}) -1)) = 2e^{2({\frac{1}{2}(\ln(\frac{x}{2}) -1})+1$ $2e^{(\ln(\frac{x}{2}) -1+1}=2e^{\ln(\frac{x}{2})} =2\cdot \frac{x}{2} = x$

Similarly;

for $f(x) = \frac{4 \ln(x^2)}{e^2}$ and $g(x) = e^{\frac{e^2 \cdot x}{8} }$

then, by definition;

$f(g(x)) = f(e^{\frac{e^2 \cdot x}{8}}) =\frac{4 \ln {(\frac{e^2 \cdot x}{8})^2}}{e^2}$ = $\frac{8 \ln {(\frac{e^2 \cdot x}{8})}}{e^2} =\frac{8\frac{e^2\cdot x}{8} }{e^2}=\frac{8e^2 \cdot x}{8e^2}=x$