Choose an appropriate scale and construct a scale drawing of each rectangular state to fit on a 4-by-6-inch index card. The state of Colorado is approximately 380 miles long (east to west) and 280 miles wide (north to south). The state of Wyoming is approximately 365 miles long (east to west) and 265 miles wide (north to south).

1:8,632,800

Step-by-step explanation:

we have a 4-by-6-inch index card on which the state of Colorado and Wyoming should be drawn, so we must add the areas of the two states and adapt them in scale , for this we must add the width of the two states (within 4 inches) and the length (within 6 inches) of them  

According graph:

380 miles+365 miles=745 miles (long)

265 miles+280 miles=545 miles (wide)

if 545 miles ≡ 4 inch

    x miles    ≡ 1 inch

1 inch ≡ 136.25 miles, but 1 mile ≡ 63,360 inch, so

1 inch (index card) ≡ (63,360 inch * 136.25 miles) = 8,632,800 inch in the reality, then 545 miles = 34,531,200 inch and 745 miles= 47,203,200, inch

This to say that:

34,531,200 inch / 8,632,800 inch/mile = 4 inch

47,203,200 / 8,632,800 inch/mile = 5.46 inch

finally,

the scale is 1:8,632,800  ≡ 1 inch in the index card = 8,632,800 in the reality or 1 inch in the index card = (8,632,800/63360) 136.25 miles in the reality

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.

594 square inches

step-by-step explanation:

vote !