Ask question

Ask question

All categories

3 years ago

11

Are parallel lines inconsistent

1 answer:

Gelneren [198K]3 years ago

5 0

If a consistent system has an infinite number of solutions, it is dependent. When you graph the equations, both equations represent the same line. <span>If a system has no solution, it is said to be </span>inconsistent. <span>The graphs of the </span>lines<span> do not intersect, so the graphs </span>are parallel<span> and there is no solution.</span>

You might be interested in

If a,b,c and d are positive real numbers such that logab=8/9, logbc=-3/4, logcd=2, find the value of logd(abc)

Eva8 [605]

We can expand the logarithm of a product as a sum of logarithms:

$\log_dabc=\log_da+\log_db+\log_dc$

Then using the change of base formula, we can derive the relationship

$\log_xy=\dfrac{\ln y}{\ln x}=\dfrac1{\frac{\ln x}{\ln y}}=\dfrac1{\log_yx}$

This immediately tells us that

$\log_dc=\dfrac1{\log_cd}=\dfrac12$

Notice that none of $a,b,c,d$ can be equal to 1. This is because

$\log_1x=y\implies1^{\log_1x}=1^y\implies x=1$

for any choice of $y$ . This means we can safely do the following without worrying about division by 0.

$\log_db=\dfrac{\ln b}{\ln d}=\dfrac{\frac{\ln b}{\ln c}}{\frac{\ln d}{\ln c}}=\dfrac{\log_cb}{\log_cd}=\dfrac1{\log_bc\log_cd}$

so that

$\log_db=\dfrac1{-\frac34\cdot2}=-\dfrac23$

Similarly,

$\log_da=\dfrac{\ln a}{\ln d}=\dfrac{\frac{\ln a}{\ln b}}{\frac{\ln d}{\ln b}}=\dfrac{\log_ba}{\log_bd}=\dfrac{\log_db}{\log_ab}$

so that

$\log_da=\dfrac{-\frac23}{\frac89}=-\dfrac34$

So we end up with

$\log_dabc=-\dfrac34-\dfrac23+\dfrac12=-\dfrac{11}{12}$

###

Another way to do this:

$\log_ab=\dfrac89\implies a^{8/9}=b\implies a=b^{9/8}$

$\log_bc=-\dfrac34\implies b^{-3/4}=c\implies b=c^{-4/3}$

$\log_cd=2\implies c^2=d\implies\log_dc^2=1\implies\log_dc=\dfrac12$

Then

$abc=(c^{-4/3})^{9/8}c^{-4/3}c=c^{-11/6}$

So we have

$\log_dabc=\log_dc^{-11/6}=-\dfrac{11}6\log_dc=-\dfrac{11}6\cdot\dfrac12=-\dfrac{11}{12}$

4 0

2 years ago

What is the value of the expression below? ( 9.5-3x1 1/2 ) / 0.5<br>PLEASE HURRY!!

GuDViN [60]

The answer would be 10!

7 0

3 years ago

Mr.Willams' physical education class lasts 7/8 hours. How many minutes are spent warming up and cooling down?

Ray Of Light [21]

7/8 of an hour is 52.5 minutes. 3/10 of 52.5 minutes is 15.75 minutes. They spent 15.75 minutes warming up and cooling down.

6 0

2 years ago

Val walks 2 3/5 miles each day.bill runs 10 once every 4 days.in 4 days.who covers the greater distance?

Mkey [24]

Answer: Val walks the greater distance. She walks 2/5 miles more than Bill. Hope this helps!

Step-by-step explanation:

6 0

2 years ago

The coefficient of -x is 1

juin [17]

Answer:

it -1

Step-by-step explanation:

3 0

3 years ago