Which is the smallest ratio? 3 to 4, Two-thirds, 10:12, 2 to 1
3 to 4
Two-thirds
10:12
2 to 1

Each ratio can be rewritten as a fraction:

3 to 4 becomes 3/4

2/3 is already a fraction

10:12 becomes 10/12 which can be simplified to 5/6 by dividing both the numerator and the denominator by 2

2 to 1 is 2/1 or 2

2 to 1 is the greatest because it is the only whole number. Comparing the three remaining can be a little more difficult because they have different denominators (the number on the bottom of the fraction).

In order to compare them we can find equivalent(equal) fractions that have a common denominator.

In order to find equivalent fractions we first find the common denominator. Then we multiple the fraction by a unit of one (ex. 2/2, 3/3, 4/4).

3/4 ,2/3, 10/12 12 would be a common denominator because 4 x 3 =12 3 x 4=12 and 12 x 1=12

3 x 3 = 9 3/4=9/12

4 x 3 = 12 2/3=8/12

10/12= 10/12

2 x 4 = 8

3 x 4 =12

Now that they have the same denominator we can see that 8/12 or 2/3 is the smallest fraction.

So, 2/3 is the smallest ratio

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.

pentagon

step-by-step explanation:

the coordinates   a(5, -2), b(3,-1),c(-4,-4) d(-3,8) and e(-1,4) forms the vertices of the polygon when they are connected in order.

in order to classify that which polygon is it with the given coordinates, first count the number of vertices and then count the number of sides it can make with these vertices.

since, the given coordinates have five vertices, therefore, it will make five sides. moreover, pentagon is regular in nature therefore it will be convex.

now, a polygon with five sides is known as pentagon, therefore, the given polygon is the pentagon.