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3 years ago

How do you do this problem? Please show your work

Mathematics

1 answer:

NemiM [27]3 years ago

4 0

Answer:

-400

Step-by-step explanation:

-12

-------- is a fraction or expression,

0.03

Our job here is to simplify (reduce) the fraction as much as possible.

Get rid of the fraction in the denominator by multiplying both numerator and denominator by 100:

-1200

---------

Now reduce this using division. The correct result is -400.

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Paul went on a bike ride of 30 miles. He realized that if he had gone 8 mph faster, he would have arrived 12 hours sooner. How f

lara [203]

Answer: He actually rode 2 miles per hour on his trip

Step-by-step explanation: Maybe unconventional, but express the time it took, then figure the speed.

Time = distance /speed t will represent time, s is the speed: t = 30/s Use the rime it would have taken at the higher speed to create an equation:

t-12 = 30/s+8 replace the y with the 30/s

30/s -12 = 30/s+8

(s)(30/s -12 ) = (s)(30/s+8 ) Cross multiply to cancel denominators

(s-8)(30 -12s) = (s-8)(30s/s+8 ) ==> 30s +240 -12s² -96s =30s Simplify:

(-1)(-12s² -96s +240 ) =0 ==> 12s² +96s -240 divide all by 12

s² + 8s -20 = 0 Factor and solve for s

(s +10)(s -2) =0 s-2=0 S= 2

Proof:

30/2 = 15 hours for original trip at 2mph,

increase speed by 8mph 2 + 8 = 10mph

30 miles at 10mph takes 3 hours; that is 12 hours less than his actual trip.

(Brainilest, please :-)

4 0

3 years ago

*Asymptotes*<br> g(x) =2x+1/x-3 <br><br> Give the domain and x and y intercepts

Nataly [62]

Answer: Assuming the function is $g(x)=\frac{2x+1}{x-3}$ :

The x-intercept is $(\frac{-1}{2},0)$ .

The y-intercept is $(0,\frac{-1}{3})$ .

The horizontal asymptote is $y=2$ .

The vertical asymptote is $x=3$ .

Step-by-step explanation:

I'm going to assume the function is: $g(x)=\frac{2x+1}{x-3}$ and not $g(x)=2x+\frac{1}{x}-3$ .

So we are looking at $g(x)=\frac{2x+1}{x-3}$ .

The x-intercept is when y is 0 (when g(x) is 0).

Replace g(x) with 0.

$0=\frac{2x+1}{x-3}$

A fraction is only 0 when it's numerator is 0. You are really just solving:

$0=2x+1$

Subtract 1 on both sides:

$-1=2x$

Divide both sides by 2:

$\frac{-1}{2}=x$

The x-intercept is $(\frac{-1}{2},0)$ .

The y-intercept is when x is 0.

Replace x with 0.

$g(0)=\frac{2(0)+1}{0-3}$

$y=\frac{2(0)+1}{0-3}$

$y=\frac{0+1}{-3}$

$y=\frac{1}{-3}$

$y=-\frac{1}{3}$ .

The y-intercept is $(0,\frac{-1}{3})$ .

The vertical asymptote is when the denominator is 0 without making the top 0 also.

So the deliminator is 0 when x-3=0.

Solve x-3=0.

Add 3 on both sides:

x=3

Plugging 3 into the top gives 2(3)+1=6+1=7.

So we have a vertical asymptote at x=3.

Now let's look at the horizontal asymptote.

I could tell you if the degrees match that the horizontal asymptote is just the leading coefficient of the top over the leading coefficient of the bottom which means are horizontal asymptote is $y=\frac{2}{1}$ . After simplifying you could just say the horizontal asymptote is $y=2$ .