Answer: 18 units
Step-by-step explanation:since its is a horizontal line x2 - x1
7 -1 = 6
line 2:
since this is a vertical line y2 - y1
7 - 3 = 4
line 3:
since this is a horizontal line x2 - x1
7 - 4 = 3
line 4:
for this we need to use the distance formula which allows us to find the distance making a third point to form a right angle triangle
point 1: (1,3)
point 2: (4,7)
point 3 (new point) : (4,3)
now we can apply the pythogorean thereum (C squared = B squared + A squared) with the following lines.
line 1: (1,3) - (4,7)
line 2: (1,3) - (4,3)
line 3: (4,3) - (4,7)
line 1 squared = line2 squared + line 3 squared
calculate length of line 2 and 3
line 1 squared = (4 - 1) squared + (7 - 3) squared
line 1 squared = 3 squared + 4 squared
line 1 squared = 9 + 16
line 1 squared = 25
root both sides
line 1 = 5
add all the liens together
6 + 4 + 3 + 5 = 18
The mean is 35/5=7
The variance is the average of the sum of squared differences of each element from the mean:
v=((7-7)^2+(5-7)^2+(11-7)^2+(1-7)^2+(11-7)^2)/5
v=(0+4+16+36+16)/5
v=14.4
1. Answer (D). By the law of sines, we have 
in any 
2. Answer (C). The law of cosines, 
accepts up to three sides and an angle as an input.
3. Answer (D). Although this triangle is right, we are not given enough information to uniquely determine its sides and angles - here, we need either one more side or one more angle.
4. Answer (D). Don't get tripped up by answer choice (C) - this is just a rearrangement of the statement of the law of cosines. In choice (D), the signs of 
and 
are reversed.
5. Answer (B). By the law of sines, we have 
Solving gives 
Note that this is the <em>ambiguous (SSA) case</em> of the law of sines, where the given measures could specify one triangle, two triangles, or none at all!
6. Answer (A). Since we know all three sides and none of the angles, starting with the law of sines will not help, so we begin with the law of cosines to find one angle; from there, we can use the law of sines to find the remaining angles.
1. all functions are relations.
2.
-7 + 3(-12) ÷ (-3)
-7 - 36 ÷ -3
-7 - (-12)
-7 + 12
5
3.
f(n) = n² - n f(-4)
f(-4) = -4² - (-4)
f(-4) = 16 - (-4)
f(-4) = 16 + 4
f(-4) = 20
hope this helped, God bless!
Step-by-step explanation:
That function is a line that goes through the origin (0,0).
You only need one more point to be able to draw it.
Take x=4,5 the corresponding value of y is exactly what you want to know, the number of miles the lava moved after 4,5 hours.
So y = 6 * 4,5 = 27
Your second point is (4,5 , 27).
Now you can draw your line.
