Each year, votes are cast for the rookie of the year in a softball league. The voting results for the top three finishers are shown in the table below. How many points is a third-place vote worth?

A third place vote is worth 1 point

Step-by-step explanation:

Let the number of points for a first place vote be x, number of points for a second place vote be y and the number of points for a third place vote be z.

So, by multiplying the number of points by the number of what the point is worth and adding all together, we shall have the total points;

Hence, we have the following equation systems;

23x + 5y + z = 131

5x + 17y + 4z = 80

x + 5y + 15z = 35

These are the three equations we need to solve simultaneously to get the value of z

From equation 3, x = 35 -5y -15z

Insert this into the first two equations;

23 ( 35 -5y -15z) + 5y + z = 131

5(35-5y-15z) + 17y + 4z = 80

805 - 115y -345z + 5y + z = 131

805-131 = 115y + 345z -5y - z

674 = 110y + 344z ••••••••••(*)

The second equation now becomes the following;

5(35-5y-15z) + 17y + 4z = 80

175 -25y -75z + 17y + 4z = 80

175-80 = 25y + 75z -17y -4z

95 = 8y + 71z

8y + 71z = 95 •••••••••••(**)

So we have to solve x and xx simultaneously;

110y + 344z = 674

8y + 71z = 95

110/8 = 13.75 , so multiply equation xx by 13.75 and equation x by 1

110y + 344z = 674

110y + 976.25z = 1306.25

Subtract equation xx from x

(976.25z - 344z) = (1306.25 -674)

632.25z = 632.25

z = 632.25/632.25

z = 1

x=-2

infinite number of lines, so there is an infinite number of equations.

step-by-step explanation:

there are an infinite number of line that passes through the point (-2,5)

x=-2   is one line that passes through the point

y = 5 is another line that passes through the point

(these two lines are perpendicular to each other).

since the number of   numbers are infinite and the slope is the ratio of two numbers,(change in y over change in x) we can have an infinite number of slopes.     our only condition is that it passes through the point (-2,5)

the system of inequity is

step-by-step explanation:

from the given graph it is noticed that we have two related lines. one is solid and another is dashed.

if a line passing through two points, then the equation of line is

the solid line passing through the points (0,4) and (4,0).

the related equation of solid line is .

similarly, find the related equation of dashed line. the dashed liune passing through the points (0,0) and (3,1).

the related equation of dashed line is

from the given graph it is noticed that the point (0,1) lies on the shaded region, therefore the point (0,1) must be satisfied by the related equations.

check the related equations by the point (0,1).

this statement is true if the sign of inequality is < instead of equality. since it is an solid line therefore the sign of inequality will be . the required inequality is

similarly, check the second related equation.

it is a dashed line, so this statement is true if the sign of inequality is > . the required inequality is