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3 years ago

The graph shows the cost of some taxi journeys work out a formula for c in terms of n

Mathematics

1 answer:

Vitek1552 [10]3 years ago

4 0

Answer:

$c=\frac{3}{5}(n)+2.5$

Step-by-step explanation:

see the attached figure to better understand the problem

Let

c -----> the cost of some taxi journeys

n ----> the number of miles

we know that

The graph is a line

The equation of a line in slope intercept form is

$c=m(n)+b$

where

m is the slope

b is the c-intercept (value of c when the value of n is equal to zero)

Observing the graph we have the points

(0,2.5), (5,5.5)

<em>Find the slope</em>

The formula to calculate the slope between two points is equal to

$m=\frac{c2-c1}{n2-n1}$

substitute the values

$m=\frac{5.5-2.5}{5-0}$

$m=\frac{3}{5}$

we have

$b=2.5$ -----> because the point (0,2.5) is the c-intercept

substitute in the equation of slope-intercept form

$c=\frac{3}{5}(n)+2.5$

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Answer:

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Step-by-step explanation:

Distribute:

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3 years ago

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The answer to the question below is 8/15 right?

ioda

When you have something like this, to simplify the exponent you multiply them together, so the exponent is 1/3 x 1/5.
1/3 x 1/5 is 1/15, so the simplified expression is:
$m^{ \frac{1}{15} }$
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3 years ago

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This graph represents a quadratic function. What is the function’s equation written in factored form and in vertex form?

creativ13 [48]

Answer:

Part a) The function’s equation written in vertex form is

$f(x)=2(x-2)^2-8$

Part b) The function’s equation written in factored form is equal to

$f(x)=2x(x-4)$

Step-by-step explanation:

Part a) What is the function’s equation written in vertex form?

we know that

The equation of a vertical parabola written in vertex form is equal to

$f(x)=a(x-h)^2+k$

where

a is a coefficient

(h,k) is the vertex

Looking at the graph

The vertex is the point (2,-8)

substitute

$f(x)=a(x-2)^2-8$

Find the value of the coefficient a

take one point from the graph

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substitute in the equation

$0=a(0-2)^2-8\\0=4a-8\\4a=8\\a=2$

therefore

The function’s equation written in vertex form is

$f(x)=2(x-2)^2-8$

Part b) What is the function’s equation written in factored form?

we know that

The equation of a vertical parabola written in factored form is equal to

$f(x)=a(x-x_1)(x-x_2)$

where

a is a coefficient

x_1 and x_2 are the zeros or x-intercepts of the function

Remember that the x-intercept is the value of x when the value of the function is equal to zero

Looking at the graph

The zeros or x-intercepts of the function are

x=0 and x=4

$f(x)=a(x-0)(x-4)$

$f(x)=ax(x-4)$

Find the value of the coefficient a

take one point from the graph

(2,-8)

substitute

$-8=a(2)(2-4)\\-8=-4a\\a=2$

therefore

The function’s equation written in factored form is equal to

$f(x)=2x(x-4)$

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KonstantinChe [14]

Answer:

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Step-by-step explanation:

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Answer:

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