Does this graph show a function? Explain how you know.
2 answers:
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Answer:
a) 5+13k where k is integer
b) 20+13k where k is integer
c)12+13k where k is integer
Step-by-step explanation:
(a)
.
8x-1=13k
Subtract 13k on both sides:
8x-13k-1=0
Add 1 on both sides:
8x-13k=1
I'm going to use Euclidean Algorithm.
13=8(1)+5
8=5(1)+3
5=3(1)+2
3=2(1)+1
Now backwards through the equations:
3-2=1
3-(5-3)=1
3-5+3=1
(8-5)-5+(8-5)=1
2(8)-3(5)=1
2(8)-3(13-8)=1
5(8)-3(13)=1
So compare this to:
8x-13k=1
We see that x is 5 while k is 3.
Anyways 5 is a solution or 5+13k is a solution where k is an integer.
b)
8x-4=13k
Subtract 13k on both sides:
8x-13k-4=0
Add 4 on both sides:
8x-13k=4
We got this from above:
5(8)-3(13)=1
If we multiply both sides by 4 we get:
8(20)-13(12)=4
So x=20 and 20+13k is also a solution where k is an integer.
c)
[tex]99x \equiv 5 (mod 13)[/tex
99x-5=13k
Subtract 13k on both sides:
99x-13k-5=0
Add 5 on both sides:
99x-13k=5
Using Euclidean Algorithm:
99=13(7)+8
13=8(1)+5
Go back through the equations:
13-8=5
13-(99-13(7))=5
8(13)-99=5
99(-1)+8(13)=5
Compare this to 99x-13k=5 and see that x=-1 or -1+13=12 or 12+13k is a solution where k is an integer.
We have that
y=-3x²<span>+5x+11
we know that
the equation of the parabola in standard form can be expressed in one of the following two ways
y=ax</span>²+bx+c
<span>the parabola opens up if a is positive and opens down if a is negative
and
x=ay</span>²+by+c
the parabola opens right if a is positive and opens left if a is negative
<span>
in this problem
the equation is of the form
</span>y=ax²+bx+c<span>
a=-3
so
the parabola opens down
using a graph tool
see the attached figure
the vertex of a parabola is a maximum
the answer is
</span>the parabola opens down
y=-3x²<span>+5x+11
we know that
the equation of the parabola in standard form can be expressed in one of the following two ways
y=ax</span>²+bx+c
<span>the parabola opens up if a is positive and opens down if a is negative
and
x=ay</span>²+by+c
the parabola opens right if a is positive and opens left if a is negative
<span>
in this problem
the equation is of the form
</span>y=ax²+bx+c<span>
a=-3
so
the parabola opens down
using a graph tool
see the attached figure
the vertex of a parabola is a maximum
the answer is
</span>the parabola opens down