Write an equation to represent the situation. mrs. davis bought one pair of pants and two polo shirts for each of her three children. she had $3.09 left after purchasing the clothing items for her children. item : polo shirt pants sweater jacket price ($) : $9.99 $12.99 $15.99 $19.99 let m represent the amount of money mrs. davis initially had to spend on each of her three children.

3(m - 32.97) = 3.09

Step-by-step explanation:

She started with m money for each of the three children.

A pair of pants costs $12.99. Each polo shirt costs $9.99.

A pair of pants and 2 polo shirts cost

$12.99 + 2 * $9.99 = $12.99 + $19.98 = $32.97

For each child, she had m money and spent $32.97.

For each child, she had m - 32.97 money left.

For the three children, the amount of money left was 3(m - 32.97).

We are told that for the three children, the amount of money left is $3.09.

That means that 3(m - 32.97) must equal $3.09.

The equation is:

3(m - 32.97) = 3.09

step-by-step explanation:

we are given a graph for system of inequalities.

in order to write the system of inequalities for the given graph, we need to find the inequality for each of the line separately.

let us find the slope of dotted line first.

taking two coordinates on the graph.

let us say (0,0) and (3,1).

let us find the slope of the line now.

slope of the dotted line would be =.

y-intercept of dotted line is y=0 only.

plugging slope m= and b=0 in slope-intercept form y=mx+b, we get

.

the line is shaded up of that dotted line.

therefore, for shading up we would take greater than inequality symbol > .

and because it's a dotted line we would take only > symbol in place of = sign in above equation of line.

therefore, inequality for dotted line would be

let us take two points (3,1) and (0,4) on the solid line.

slope of the solid line would be =.

for the solid line we have y-intercept b= 4.

plugging slope m= -1 and b=4 in slope-intercept form y=mx+b, we get

y = -1x + 4.

the line is shaded down of that solid line.

therefore, for shading down we would take less than inequality symbol < .

and because it's a solid line we would take ≤ symbol in place of = sign in above equation of line.

therefore, inequality for solid line would be

answer: a video game has three difficulty levels: easy, medium, and expert. the game's scoring works in such a way that a player has to score a fixed number of points to advance to the next level, and then the scoring starts over. the total score needed to clear all three difficulty levels is 7,500. two times the number of points needed to clear the easy level is 500 more than the number of points needed to clear the medium level. twice the number of points needed to clear the medium difficulty level is 1,500 more than the number of points needed to clear the expert level. if x, y, and z represent the easy, medium, and expert levels, respectively, and a is the coefficient matrix of the system of equations modeling this situation, identify the inverse matrix, a-1, and the solution matrix, x, of the system of equations.

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step-by-step explanation: