Write this number in expanded form 4,508,227
2 answers:
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Answer:
The three points lie on a straight line
A line through the points passes through the origin
The graph shows a proportional relationship
Step-by-step explanation:
Given statements:
a) The three points do not lie on a straight line.
b) The three points lie on a straight line.
c) A line through the points passes through the origin.
d) A line through the points does not pass through the origin.
e) The graph shows a proportional relationship.
f) The graph does not show a proportional relationship.
For the first and second statements, we can see that the points are able to be connected with a straight, diagonal line (see attached graph). This makes statement a false, and statement b true.
a = false
b = true
For the third and fourth statements, we can see that on the attached (revised) graph on my answer, that the line can continue and pass through the origin, or (0,0). This means that statement c is true, and statement d is false.
c = true
d = false
For the fifth and sixth statements, we know that a relationship is proportional if it is a straight line and passes through the origin when graphed. We have already concluded above that both of these are true, so this means that the graph does represent a proportional relationship. This means that statement e is true, and statement f is false.
e = true
f = false
From the above work, we can conclude that the following statements are true:
b (The three points lie on a straight line)
c (A line through the points passes through the origin)
e (The graph shows a proportional relationship)
Hope this helps :)
We need to use rational root theorem to find out roots here.
The rational root theorem states that if p(x) is a polynomial with integer coefficients and if is a zero of p(x) then p is a factor of constant term and q is a factor of leasing term coefficient.
Here factors of constant term are 1,2,3,4,6,8,12,24,-1,-2,-3,-4,-6,-8,-12, and -24.
And factors of leading coefficient is -1,1.
Hence possible roots may be -1,1,-2,2,-3,3,-4,4,-6,6,-8,8,-12,12,-24 and 24.
Let us plugin these in f(x) to find zeroes.
Hence x=-1 is a zero which means x-(-1)=x+1 is a factor.
Let us use synthetic division to find quotient.
-1 | 1 10 35 50 24
<u>| 0 -1 -9 -26 -24</u>
<u> 1 9 26 24 0</u>
Hence quotient is
Since all coefficients are positive, root must be negative. Let's plugin all remaining negative numbers in the quotient.
Hence x+2 is another factor.
Let us find quotient again using synthetic division.
-2 | 1 9 26 24
<u>| 0 -2 -14 -24</u>
<u> 1 7 12 0</u>
Hence quotient is
Again we got quotient with all positive coefficients, let us plugin remaining negative numbers from rational root theorem.
Hence x+3 is also a factor.
Let us find quotient using synthetic division.
-3 | 1 7 12
<u>| 0 -3 -12</u>
<u> 1 4 0</u>
Hence quotient is x+4.
So,
Please have a look at the graph attached.
