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2 years ago

What is the equation, in slope-intercept form, that relates the cost compared to the miles traveled for a Green Cab?

Mathematics

1 answer:

levacccp [35]2 years ago

6 0

Step-by-step explanation:

the general slope intercept form is

y = ax + b

a is the slope. it is expressed as ratio of y change / x change when going from one point to another.

b is the y-intercept (the point, where the line crosses the y-axis, meaning the y value when x=0).

we get b by using the point coordinates in the equation and solve for b.

we see costs is on the y axis, and miles is on the x axis.

so what points do we identify on the chart for the green taxi ?

there is right on the y-axis (0, 5). which is already our y-intercept.

and then let's pick e.g. the point where both lines intercept : (3, 8).

for the slope we look at the coordinate changes :

x changes by +3 (from 0 to 3).

y changes by +3 (from 5 to 8).

so, the slope is 3/3 = 1.

and again, the y- intercept is +5.

therefore, the line equation is

y = x + 5

meaning the cost of a fare is the number of miles plus 5.

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3 years ago

Do you agree with the statement that " cubic functions must have at least 1 x-intercept but not more than 3, whereas quadratic f

vladimir2022 [97]

Answer:

Yes, I agree

Step-by-step explanation:

For the cubic function

A cubic function is represented as:

$f(x)=ax^3+bx^2+cx+d$

A cubic function may have 1, 2 or 3 x intercepts. This is shown below

For 3 x intercepts

$y = x^3 - x$

Equate y to 0

$x^3 - x = 0$

Expand

$x(x^2 - 1) = 0$

Express $x^2 - 1$ as difference of two squares

$x(x - 1)(x +1 ) = 0$

x = 0 or 1 or -1

For 2 x intercepts

$y = x^3 - x$

$y =(x-5)^2)(x+7)$

Equate y to 0

$(x-5)^2(x+7) = 0$

Expand

$(x-5)(x-5)(x+7) = 0$

x= 5 or x = -7

For 1 x intercept

$y = x^3$

Equate y to 0

$x^3 = 0$

Take cube roots of both sides

$x = 0$

It has been shown above that a cubic function may have 1, 2 or 3.

So, I agree to the statement

For the quadratic function

A quadratic function will not have any x intercept when the function can not be factorized;

E.g.

$y = x^2 + x + 17$

The above function has no x intercept.

A quadratic function will have at least 1 x intercept when the function can be factorized;

E.g.

$y = x^2- 6x + 9$

Equate y to 0

$x^2- 6x + 9 = 0$

Expand

$x^2 - 3x - 3x + 9 = 0$

$(x - 3)(x-3) = 0$

$x = 3$

We've shown that a quadratic may have no x intercept, and it may also have x intercept(s)

Hence, I agree to both statement

3 0

2 years ago