Mathematics, 29.10.2020 18:00 lalimares1038

A theater is tracking the number of adults and children in the audience at various shows. The table shows how the number of adults and children
are related
Select the equation that matches the relationship.

X+y = 1000

X-y1000

y-x= 1000

Y= 1000xc

Adults

Children

500
500
450
550
400
600
350
650 I Need help i dont understand

A theater is tracking the number of adults and children in the audience at

various shows. The tab

Answers: 1

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Answer from: CamFootball638

The correct option is;

x + y = 1000

Step-by-step explanation:

The data from the table can be presented as follows

Adults (x) Children (y)

500 500

450 550

400 600

350 650

Therefore, we have the rate of change of the children, y to the adults, x, which is also the slope of the graph of the data given as follows;

The slope, m = dy/dx = (650 - 500)/(350 - 500) = 150/(-150) = -1

m = -1

The function of the graph in point and slope form, using the first point, becomes;

y - 500 = -1 × (x - 500) = -x + 500

∴ y - 500 = -x + 500

y + x = 500 + 500 = 1,000

Which gives

y + x = 1,000

y + x = x + y = 1,000

A theater is tracking the number of adults and children in the audience at

various shows. The table

Answer from: Quest

the system of inequity is

$y\leq -x+4$

$3y> x$

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

$y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$

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

$y-4=\frac{0-4}{4-0}(x-0)$

$y=-x+4$

the related equation of solid line is $y=-x+4$ .

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

$y-0=\frac{0-1}{3-0}(x-0)$

$3y=x$

the related equation of dashed line is $3y=x$

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).

$1=-0+4$

$1=4$

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 $\leq$ . the required inequality is

$y\leq -x+4$

similarly, check the second related equation.

$3(1)=0$

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

$3y> x$

15 points write a system of inequalities to represent the shaded portion of the graph

Answer from: Quest

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