ANSWER
65
EXPLANATION
This will form a sequence with first term:
with constant difference d=6 and last term
The last term is a term in the sequence, therefore;
Simplify the LHS
Divide both sides by 6.
Therefore
Hence there are 65 multiples of 6.
What is x+x+x+x+x+x+x+x+x+x+b+b+b+b+3=
1 answer:
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The graph (by some miracle) has been uploaded for you. It is just about the first time I've done this sort of thing, and I've answered nearly 800 questions.
The first thing you have to do is study the graph. The two functions are
f(x) = 4^x That's the curved graph. (in red)
g(x) = x + 4. That's the straight line. (in blue)
You know that the first one is not a linear relationship because the x values go from integer values -2 to 2 (including 0). The y values are a bit different. They go from 1/16 to 16 with those integer values. So you could try y = 4^(-x). It doesn't work, but you could try it. It gives the table numbers for y in the reverse order that the table you are given goes. For x you get -2 -1 0 1 2 and for y you would get 16 4 1 1/4 1/16.
You could try y = (1/4)^x
For this try, you would get x = -2 -1 0 1 2 and for y = 16 4 0 1/4 and 1/16
but that doesn't work either.
You could try until you get y = 4^x which does work.
g(x) is a lot easier to deal with. It looks better behaved. as x goes up, so does y. You will find that the y values obey y = x + 4. You could try other lines, but that one works. Many times it's just a guess
The first thing you have to do is study the graph. The two functions are
f(x) = 4^x That's the curved graph. (in red)
g(x) = x + 4. That's the straight line. (in blue)
You know that the first one is not a linear relationship because the x values go from integer values -2 to 2 (including 0). The y values are a bit different. They go from 1/16 to 16 with those integer values. So you could try y = 4^(-x). It doesn't work, but you could try it. It gives the table numbers for y in the reverse order that the table you are given goes. For x you get -2 -1 0 1 2 and for y you would get 16 4 1 1/4 1/16.
You could try y = (1/4)^x
For this try, you would get x = -2 -1 0 1 2 and for y = 16 4 0 1/4 and 1/16
but that doesn't work either.
You could try until you get y = 4^x which does work.
g(x) is a lot easier to deal with. It looks better behaved. as x goes up, so does y. You will find that the y values obey y = x + 4. You could try other lines, but that one works. Many times it's just a guess
Answer:
<em>Proof below</em>
Step-by-step explanation:
<u>Right Triangles</u>
In any right triangle, i.e., where one of its internal angles is 90°, some interesting relations stand. One of the most-used is Pythagora's Theorem.
In a right triangle with shorter sides a and b, and longest side c, called the hypotenuse, the following equation is satisfied:
The image provided in the question shows a line passing through points A(0,4) and B(3,0) that forms a right triangle with both axes.
The origin is marked as C(0,0) and the point M is the midpoint of the segment AB. We have to prove.
First, find the coordinates of the midpoint M(xm,ym):
Thus, the midpoint is M( 1.5 , 2 )
Calculate the distance CM:
CM=2.5
Now find the distance AB:
AB=5
AB/2=2.5
It's proven CM is half of AB