Answer:
domain - (-infinity,infinity)
range - (-infinity, 2]
axis of sym - x=-1
y int - (0,-1)
at what value (row 1) - (-1,2)
Step-by-step explanation:
domain is side to side, it never ends bc of the arrows
range is top to bottom, there is no bottom bc of the arrow, but it has a top at 2 (the value on the y axis)
the axis of sym is basically the line that runs through the vertex, it's where you could fold it in half and it would still match up
I'll do problem 1 to get you started.
The vertical sides are 3 and x for the left and right figures.
The horizontal sides are 15 and 60 for the left and right figures.
The corresponding sides form fractions which are equal (due to the nature of the similar polygons)
3/x = 15/60
3*60 = x*15 ... cross multiply
180 = 15x
15x = 180
x = 180/15 .... divide both sides by 15
x = 12
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Another way you can see this is note how the jump from 15 to 60 is "times 4", so the jump from 3 to x must also be "times 4" to keep the same proportion
3 ---> x = 3*4 = 12
Or you could set up the proportion
60/15 = x/3
4 = x/3
x/3 = 4
x = 3*4
x = 12
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<h3>Final Answer: 12</h3>
Answer:
x = -5
Step-by-step explanation:
Since these two triangles are similar, the ratio between the corresponding lengths of each triangle will be the same.
This means the ratio between one side of each triangle (e.g. AD and DC) will be the same as the ratio between a different side of each triangle (e.g. BE and BC).
So, to create an equation for the sides which contain the unknown 'x', we must first find the ratio between the two sides by using a different set of sides.
On the right side we are given 9 for AD, and 18 for DC.
9/18 = 0.5
This means that the extra length of the larger triangle from the smaller one (AD) is half the length of the smaller triangle (DC). We can use this to make an equation for x:
If AD/DC = 0.5, then BE/EC will also = 0.5
BE = x+23
EC = x+41
Therefore:
![\frac{x+23}{x+41} = 0.5](https://tex.z-dn.net/?f=%5Cfrac%7Bx%2B23%7D%7Bx%2B41%7D%20%3D%200.5)
Now we can solve by multiplying both sides by x+41 to eliminate the fraction:
![x+23=0.5(x+41)](https://tex.z-dn.net/?f=x%2B23%3D0.5%28x%2B41%29)
Now we multiply out the brackets and move the terms to different sides:
![x+23=0.5x+20.5](https://tex.z-dn.net/?f=x%2B23%3D0.5x%2B20.5)
![0.5x = -2.5](https://tex.z-dn.net/?f=0.5x%20%3D%20-2.5)
![x = -5](https://tex.z-dn.net/?f=x%20%3D%20-5)
And if we substitute the -5 into the equations:
-5+23 = 18
-5 + 41 = 36
We will see that -5 does indeed give us the same ratio between the lengths:
18/36 = 0.5
Hope this helped!
Answer:
n=5
Step-by-step explanation: