<h3>
Answer: n = -11</h3>
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Explanation:
Since x-2 is a factor of f(x), this means f(2) = 0.
More generally, if x-k is a factor of p(x), then p(k) = 0. This is a special case of the remainder theorem.
So if we plugged x = 2 into f(x), we'd get
f(x) = x^3+x^2+nx+10
f(2) = 2^3+2^2+n(2)+10
f(2) = 8+4+2n+10
f(2) = 2n+22
Set this equal to 0 and solve for n
2n+22 = 0
2n = -22
n = -22/2
n = -11 is the answer
Therefore, x-2 is a factor of f(x) = x^3+x^2-11x+10
Plug x = 2 into that updated f(x) function to find....
f(x) = x^3+x^2-11x+10
f(2) = 2^3+2^2-11(2)+10
f(2) = 8+4-22+10
f(2) = 0
Which confirms our answer.
Answer:
option B is correct
Step-by-step explanation:
We have 5 spaces in the license plate:
_ _ _ _ _
we have 26 available letters, and 10 available numbers.
starting with letters:
- how many choices do i have to place the 1st letter? 26.
26 _ _ _ _
- how many choices do i have to place the 2nd letter? 26 (since we're allowed to repeat letters)
26 26 _ _ _
- how many choices do i have to place the 3rd letter? 26
26 26 26 _ _
we've used all the places for letters, (note: the exact position of the letters doesn't matter here, the first letter could've been placed anywhere in _ _ _ _ _, but the amount of possible choices for letters would always be 26).
let's move on to numbers.
- how many choices do i have to place the 1st number? 10
26 26 26 10 _
- how many choices do i have to place the 2nd number? 10
26 26 26 10 10
we've completed our number plate. Next we'll simply multiply all these numbers to get all the possible arrangements in which numbers and letters can be displayed on a license place.
option B is correct
Answer:
In this graph, the y-intercept of the line is -2, if the coordinates are needed, its (0,-2). The equation of the line is y= x-2 ( slope intercept form ).
Step-by-step explanation: I am not sure how to use the multiplication system below to write the equation, so sorry I couldn't help!
Answer:
The answer is 65,-4
Step-by-step explanation:
x coordinates is 65 while the Y coordinates is -4
35+25=60
y=60
If you add the opposite side values of the triangle (not the one touching the y), you get the value of y). 35+25=y
This works because y+x= 180 and the three angles of a triangle add to 180.
