Angelique had 20 tokens to use for games at the arcade. she lost some of them. her dad tripled the tokens she had left. angelique wrote the expression 3(20−t) to find the number of tokens she has now, where t is the number of tokens she lost. dante correctly wrote another expression, 60−3t, to find the number of tokens angelique has now. use the drop-down menus to explain what each part of angelique's and dante's expressions mean. angelique had 20 tokens to use for games at the arcade. she lost some of them. her dad tripled the tokens she had left. angelique wrote the expression 3(20−t) to find the number of tokens she has now, where t is the number of tokens she lost. dante correctly wrote another expression, 60−3t, to find the number of tokens angelique has now. use the drop-down menus to explain what each part of angelique's and dante's expressions mean.

 Both the expressions are exactly same . Both are representing the number of tokens she has now.

Step-by-step explanation:

Given: The total number of tokens Angelique has= 20

Since, she lost some of them, let the number of lost tokens be t.

Then, The remaining  tokens she has = 20-t

Then her father triples the tokens she has.

now, the number of token she has=....>Angelique's expression

By using distributive property,

The number of token she has=

⇒The number of token she has=...> Dante's expressions

Hence, both are the same expressions. Both are representing the number of tokens she has now.

the range of a function is the range of y-values for which it is defined, or exists. given that we are only looking at the y-values, we can already discount the first two answers as they deal with the domain of the function (range of x-values).

now, what we need to do is find the smallest and highest y-values for which the function is defined. if you'd like, you could take a ruler and start at the very bottom of the graph, find the lowest point, then move the ruler higher and higher until you reach the highest point. doing so either in your head or with an actual ruler, we can see that the lowest y-value is -5 and the highest y-value is -1.

the question now remains as to whether they are included in the range (fourth answer) or excluded (third answer). the key here is to recognise whether they are marked with an open or a closed circle. since both (-2, -5) and (2, -1) are marked with a closed circle, they are points that exist on the graph and are thus included in the range (note that if they were marked with an open circle like (4, -2) then that would signify that there is a break in the graph at that point).

thus, the fourth answer, (y | -5 ≤ y ≤ -1), is correct.

also note that usually it is good practice to scan your eye inbetween the highest and lowest point for any breaks in the graph - we do have one here at (4, -2), however -2 is still included in the range because there is another point that is included in the graph with the same y-value, ie. point (1, -2).

i hope that but if you require any further explanation don't hesitate to comment below.

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