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3 years ago

In the table below, x represents miles traveled and y represents the cost to travel by train.

Mathematics

2 answers:

Fiesta28 [93]3 years ago

8 0

Answer:

4.00

Step-by-step explanation:

Given

x: 2 , 5 , 8 , 12

y: 8.50, 15.25, 22.00. 31.00

Required

Determine the y intercept

First, we calculate the slope:

$m = \frac{y_2- y_1}{x_2 - x_1}$

Where

$(x_1,y_1) = (2,8,50)$

$(x_2,y_2) = (12,31.00)$

$m = \frac{31.00 - 8.50}{12 - 2}$

$m = \frac{22.5}{10}$

$m = 2.25$

Next, we calculate the equation:

$y - y_1 = m(x - x_1)$

Where:

$(x_1,y_1) = (2,8,50)$

$m = 2.25$

The equation becomes:

$y - 8.50 = 2.25(x - 2)$

$y - 8.50 = 2.25x -4.5$

Make y the subject

$y = 2.25x -4.5+8.50$

$y = 2.25x +4$

Take $x =0$ ; to get the y intercept

$y = 2.25*0 +4$

$y = 4$

Hence, the y intercept is 4.00

svet-max [94.6K]3 years ago

6 0

Answer:

The answer is B

Step-by-step explanation:

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3 years ago

What are the measurements of the sides of a pentagon that has the area of 32?

LenaWriter [7]

Answer:

4.31 units

Step-by-step explanation:

A pentagon is a polygon with five straight sides.

The formula to apply here will be finding area from side length, assuming that this is a regular pentagon with five sides of equal length.

Lets take each side length to be x units

Divide the pentagon into five triangles by joining a line from the center to any vertex of the pentagon.

Now you have five equal triangle.Take the base triangle and divide it into two(take a line from center of pentagon to hit the base at 90°)

This will divide the base triangle of length x unit into two equal triangles with base length x/2 units.

The angle at the pentagon center for the small formed triangle will be 36°. Here you have a triangle with base x/2 units and angle 36° at top center.

To get the height of the triangle you apply formula for tangent of an angle;

height, h=0.5x /tan 36°

Find area of the small triangle;

Area=1/2 *b*h

where b is base length=0.5x and h is height = 0.5x/tan 36°

Area=1/2*0.5x * (0.5x /tan 36°) Area for one small triangle.

However, you notice that you will have 10 small triangles for the whole pentagon, hence multiply this area by 10 which should be equal to the area of the pentagon given 32.

32=1/2 * 0.5x *(0.5x /tan 36°) *10

32=1.25x² /tan 36°

32*0.7265=1.25x²

18.60=x²

√18.60=x

4.31=x

Measurement of one side is 4.31 units

3 0

3 years ago

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mr_godi [17]

F(x) = (x + 1) (x - 3)

8 0

2 years ago

Hey can someone please help explain and answer this 1 question. There's a picture. Thank you!

g100num [7]

We'll first clear a few points.
1. A hyperbola with horizontal axis and centred on origin (i.e. foci are centred on the x-axis) has equation
x^2/a^2-y^2/b^2=1
(check: when y=0, x=+/- a, the vertices)
The corresponding hyperbola with vertical axis centred on origin has equation
y^2/a^2-x^2/b^2=1
(check: when x=0, y=+/- a, the vertices).

The co-vertex is the distance b in the above formula, such that
the distance of the foci from the origin, c satisfies c^2=a^2+b^2.
The rectangle with width a and height b has diagonals which are the asymptotes of the hyperbola.

We're given vertex = +/- 3, and covertex=+/- 5.
And since vertices are situated at (3,0), and (-3,0), they are along the x-axis.
So the equation must start with
x^2/3^2.

It will be good practice for you to sketch all four hyperbolas given in the choices to fully understand the basics of a hyperbola.

6 0

3 years ago

How many 2/5 are in 4?

Juliette [100K]

For this case what we must do is a division using the following relationship:
 $N = (total amount) / (partial amount)
$ Substituting values we have:
 $N = (4) / (2/5)
$
 Rewriting the fraction we have:
 $N = (20) / (2)
$
 Simplifying we have:
 $N = 10
$
 Answer:
The number of times repeated 2/5 for 4 is:
10

6 0

3 years ago