If <em>x</em> + 1 is a factor of <em>p(x)</em> = <em>x</em>³ + <em>k</em> <em>x</em>² + <em>x</em> + 6, then by the remainder theorem, we have
<em>p</em> (-1) = (-1)³ + <em>k</em> (-1)² + (-1) + 6 = 0 → <em>k</em> = -4
So we have
<em>p(x)</em> = <em>x</em>³ - 4<em>x</em>² + <em>x</em> + 6
Dividing <em>p(x)</em> by <em>x</em> + 1 (using whatever method you prefer) gives
<em>p(x)</em> / (<em>x</em> + 1) = <em>x</em>² - 5<em>x</em> + 6
Synthetic division, for instance, might go like this:
-1 | 1 -4 1 6
... | -1 5 -6
----------------------------
... | 1 -5 6 0
Next, we have
<em>x</em>² - 5<em>x</em> + 6 = (<em>x</em> - 3) (<em>x</em> - 2)
so that, in addition to <em>x</em> = -1, the other two zeros of <em>p(x)</em> are <em>x</em> = 3 and <em>x</em> = 2
Answer:
Therefore Marcus is incorrect.
Step-by-step explanation:
Total ticket that Marcus bought= 100%.
Marcus used 50% of ticket on rides.
and he used 
of the tickets on the video games.
The percentage form of any number x is
The percentage form of is
=25%
Therefore rest tickets are
=Total ticket-( ticket used in rides + ticket used in video games)
=100% - (50%+25%)
=100% - 75%
=25%
Therefore he used 25% of tickets in batting cage.
But he said that Marcus said that he used 24% of ticket in batting cage.
Therefore Marcus is incorrect.
Answer: The number of girls in the auditorium is represented by the algebraic expression y=(4x +72) /5
Step-by-step explanation:
Hi, to answer this question we have to analyze the information given:
- <em>Number of boys added: 18
</em>
- <em>Ratio of boys to girls: 5:4
</em>
So, the total number of boys is:
x + 18
Number of girls = y
Number of boys / number of girls = 5/4
(x+18) /y = 5/4
Solving for "y"
4 (x +18) =5 y
4x +72 = 5y
(4x +72) /5 = y
The number of girls in the auditorium is represented by the algebraic expression y=(4x +72) /5
Answer:
(h*h)(10) is the same as h(10)*h(10). Let's find the value of h(10) first. To do this, replace every x with 10 like so
Step-by-step explanation:
h(x) = 6-x
h(10) = 6-10
h(10) = -4
So,
h(10)*h(10) = (-4)*(-4)
h(10)*h(10) = 16
The final answer is 16
