Mathematics, 21.08.2019 11:30 owlgirl554

Agroup of 100 people, some students and some faculty, attended a museum opening. each student paid $10 per person for entrance to the museum and each of the faculty paid $25 per person for entrance. if the total paid, for all 100 people, was $1300, how many students attended the museum opening?

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Answer from: cool185635

STUDENTS X 10

FACULTY 100-X 25

10X + 25(100-X) = 1300

10X + 2500 -25X = 1300

10X - 25X = -2500 + 1300

-15X = -1200

15X = 1200

X = 1200/15

X = 80 STUDENTS <SOLUTION

Answer from: Quest

The coordinates of point a right now is (-3,-1) you have to multiply these coordinates by a factor of 2 to get (-6,-2)
If abcd is dilated by a factor of 2, the coordinate a would be:

If abcd is dilated by a factor of 2, the coordinate a would be:

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

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