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lisabon 2012 [21]
3 years ago
12

Nathaniel purchases a one-year membership pass to an art museum. As a member, he receives a discounted entrance fee. The total c

ost for the year, f(x), after x visits to the art museum is shown on the graph below.
What is the discounted members entrance fee to the art museum, and what would be the total cost after 20 visits?

A. The discounted entrance fee to the art museum is $2.00. The total cost is $52.00 after 20 visits.
B. The discounted entrance fee to the art museum is $2.50. The total cost is $62.00 after 20 visits.
C. The discounted entrance fee to the art museum is $3.00. The total cost is $72.00 after 20 visits.
D. The discounted entrance fee to the art museum is $1.50. The total cost is $42.00 after 20 visits.

Mathematics
1 answer:
wolverine [178]3 years ago
5 0

It's a linear function with y-intercept = 12.

The slope-intercept form:

f(x)=mx+b\\\\m=\dfrac{y_2-y_1}{x_2-x_1}

Let's read the coordinates of two points on the graph:

(2, 15) and (4, 18)

Substitute to the formula of a slope:

m=\dfrac{18-15}{4-2}=\dfrac{3}{2}=1.5

We have the equation of a line:

\boxed{f(x)=1.5x+12}

We need calculate the value of function for x = 1 and x = 20.

Substitute:

f(1)=1.5(1)+12=13.5

f(20)=1.5(20)+12=30+12=42

$12 is the "Fixed Fee", therefore the discounted entrance fee to the art museum is

\$13.50-\$12.00=\$1.50

The total cost is $42.00 after 20 visits.

<h3>Answer D.</h3>
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The equation for the line passing through point A and perpendicular to AB will be y-0.5x=6, the gradient of line AB is -2, and the gradient of a line perpendicular to AB is 0.5.

<h3 /><h3>What is the slope or gradient?</h3>

A numerical assessment of a line's angle relative to the ground is known as the slope.

Given data;

m₁ is the slope of line AB

m₂ is the slope of a line perpendicular to AB

The coordinate points are,

A,(x₁,y₁)= (0, 6)

B,(x₂,y₂)=(3, 0).

The gradient of line AB;

\rm m_{{1} }= \frac{y_2-y_1}{x_2-x_1} \\\\ \rm m_{{1} }= \frac{0-6}{3-0} \\\\ m_{{1} }=-2

The slope of the lines has a perpendicular relation is -1;

m₁ × m₂ = -1

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m₂ = 1/2

m₂ = 0.5

The equation of the line passing through point A and perpendicular to AB;

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(y-6)=0.5(x-0)

y-6 = 0.5 x

y-0.5x=6

Hence, the gradient of line AB, the gradient of a line perpendicular to AB, and the equation of the line passing through point A and perpendicular to AB will be -2,0.5 and y-0.5x=6.

To learn more about the slope, refer to the link;

brainly.com/question/3605446

#SPJ1

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1 year ago
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