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dusya [7]
3 years ago
5

Billie and toni are driving from chicago to phoenix. the first day they drove 420 miles. they want to drive at 65 miles per hour

for the rest for the rest of their trip. answer
Mathematics
1 answer:
Ronch [10]3 years ago
7 0

Let x represents the numbers of hours that Billie and Toni are driving after first day and ‘Y’ represent the distance they have passed distance  

Y=420+65

And, first day they traveled : 410 mi  

2nd day they traveled =65.8=520 mi

3rd day they traveled =65.8=520

By the end of the third they traveled= 420+520=520

1460 mi


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Answer:

y=2x-5

Step-by-step explanation:

First simplify: y-1=2x-6

y-1=2(x-3)

First simplify and distribute everything.

<u>y-1=2x-6</u>

So, x equals 2 because it got distributed into the numbers inside the parenthesis.  Same with the 2 and -3.  They multiplied to become -6.

Since it's y-1=2x-6, you can simplify it even more so the -1 goes to the other side and turns into positive 1.

<u>y - 1 (+ 1) = 2x -6 (+ 1)</u>

-1(+1)=0 which leaves just the variable y on the <em><u>left side</u></em>.

-6(+1)=-5 which leaves 2x-5 on the <em><u>right side</u></em>.

This results in y=2x-5.  Hope this helped ;)

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Find the vertical and horizontal asymptotes, domain, range, and roots of f (x) = -1 / x-3 +2.
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Answer:

Vertical asymptote: x=3

Horizontal asymptote: f(x) =2

Domain of f(x) is all real numbers except 3.

Range of f(x) is all real numbers except 2.

Step-by-step explanation:

Given:

Function:

f (x) = -\dfrac{1 }{ x-3} +2

One root, x = 3.5

To find:

Vertical and horizontal asymptote, domain, range and roots of f(x).

Solution:

First of all, let us find the roots of f(x).

<em>Roots of f(x) means the value of x where f(x) = 0</em>

0= -\dfrac{1 }{ x-3} +2\\\Rightarrow 2= \dfrac{1 }{ x-3}\\\Rightarrow 2x-2 \times 3=1\\\Rightarrow 2x=7\\\Rightarrow x = 3.5

One root, x = 3.5

Domain of f(x) i.e. the values that we give as input to the function and there is a value of f(x) defined for it.

For x = 3, the value of f(x) \rightarrow \infty

For all, other values of x , f(x) is defined.

Hence, Domain of f(x) is all real numbers except 3.

Range of f(x) i.e. the values that are possible output of the function.

f(x) = 2 is not possible in this case because something is subtracted from 2. That something is \frac{1}{x-3}.

Hence, Range of f(x) is all real numbers except 2.

Vertical Asymptote is the value of x, where value of f(x) \rightarrow \infty.

-\dfrac{1 }{ x-3} +2 \rightarrow \infty

It is possible only when

x-3=0\\\Rightarrow x=3

\therefore vertical asymptote: x=3

Horizontal Asymptote is the value of f(x) , where value of x \rightarrow \infty.

x\rightarrow \infty \Rightarrow \dfrac{1 }{ x-3} \rightarrow 0\\\therefore f(x) =-0+2 \\\Rightarrow f(x) =2

\therefore Horizontal asymptote: f(x) =2

Please refer to the graph of given function as shown in the attached image.

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3 years ago
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