Answer:
45
Step-by-step explanation:
AEF is a similar triangle to ABC. that means it has the same angles, and the sides (and all other lines in the triangle) are scaled from the ABC length to the AEF length by the same factor f.
now, what is f ?
we know this from the relation of AC to FA.
FA = 12 mm
AC = 12 + 28 = 40 mm
so, going from AC to FA we multiply AC by f so that
AC × f = FA
40 × f = 12
f = 12/40 = 3/10
all other sides, heights, ... if ABC translate to their smaller counterparts in AEF by that multiplication with f (= 3/10).
the area of a triangle is
baseline × height / 2
aABC = 500
and because of the similarity we don't need to calculate the side and height in absolute numbers. we can use the relative sizes by referring to the original dimensions and the scaling factor f.
baseline small = baseline large × f
height small = height large × f
we know that
baseline large × height large / 2 = 500
baseline large × height large = 1000
aAEF = baseline small × height small / 2 =
= baseline large × f × height large × f / 2 =
= baseline large × height large × f² / 2 =
= 1000 × f² / 2 = 500 × f² = 500 ×(3/10)² =
= 500 × 9/100 = 5 × 9 = 45 mm²
Answer:
Maximum speed of bird A is 
Maximum speed of bird B is 
Step-by-step explanation:
This is a problem with two unknowns: Max speed of bird A (we name that "A"), and max speed of bird B (we call that "B"). Now we can create two equations with these two unknowns, based on the info provided:
Equation 1): based on the phrase "bird A can travel six times as fast as bird B" we write:
Equation 2): based on the phrase; "the total speeds for these two birds is 224 miles per hour", we write:
Now, we use the first equation to substitute A in the second equation, ad then solve for the unknown B:
Now we can solve for the other unknown "A" using the substitution equation and the value of B we just found:
First, you would have to make the number of hours the x value and total cost the y value in the graph. Then, you would take however many hours to replace x, let’s say 5, and replace it for x in the equation y=8x+12, giving you y=8*5+12. You would then solve it by multiplying 8 and the x value, 5, giving you 40 in this example, and then adding 12, giving you 52 dollars for 5 hours.
To draw the line on the graph, you would start 0 hours with 12 dollars, 1 hour for 20 dollars, 2 hours for 28 dollars, and so on, adding 8 each time you add an hour.
Addition you would use first
The next answer is 85.
Counting by five is the same as adding 5 to the number he starts with.
Therefore, 80 + 5 = 85
