Answer:
-3, 1, 4 are the x-intercepts
Step-by-step explanation:
The remainder theorem tells you that dividing a polynomial f(x) by (x-a) will result in a remainder that is the value of f(a). That remainder will be zero when (x-a) is a factor of f(x).
In terms of finding x-intercepts, this means we can reduce the degree of the polynomial by factoring out the factor (x-a) we found when we find a value of "a" that makes f(a) = 0.
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For the given polynomial, we notice that the sum of the coefficients is zero:
1 -2 -11 +12 = 0
This means that x=1 is a zero of the polynomial, and we have found the first x-intercept point we can plot on the given number line.
Using synthetic division to find the quotient (and remainder) from division by (x-1), we see that ...
f(x) = (x -1)(x² -x -12)
We know a couple of factors of 12 that differ by 1 are 3 and 4, so we suspect the quadratic factor above can be factored to give ...
f(x) = (x -1)(x -4)(x +3)
Synthetic division confirms that the remainder from division by (x -4) is zero, so x=4 is another x-intercept. The result of the synthetic division confirms that x=-3 is the remaining x-intercept.
The x-intercepts of f(x) are -3, 1, 4. These are the points you want to plot on your number line.
Answer:
the answer is 7/9
Step-by-step explanation:
Answer:
cot∅ = (-2√30)/7.
Step-by-step explanation:
Given the value of csc∅ = -13/7 and ∅ is in quad III.
We know y = r sin∅ and r > 0. So csc∅ = r/y = -13/7 = 13/(-7).
It means y = -7, r = 13.
We know x² + y² = r².
x² = r² - y²
x² = (13)² - (-7)² = 169 - 49 = 120.
x = √120 = 2√30.
we know cot∅ = x/y = (2√30)/(-7) = (-2√30)/7.
Hence, cot∅ = (-2√30)/7.
Answer:
C
Step-by-step explanation:
Since the triangles are congruent then corresponding angles are congruent
x is the angle between line with 3 strokes and 2 strokes
The corresponding angle is therefore ∠ C
∠ C = 180° - (63 + 29)° = 180° - 92° = 88°
Then x = 88 → C
Answer:
3, 5, 7
Step-by-step explanation:
1st number: (2k+1)
2nd number: (2k+3)
3rd number: (2k+5), k∈Z
3*[(2k+1) + (2k+3)] = 3 + 3*(2k+5)
3*(4k+4)=3+6k+15
12k+12=18+6k
6k=6
k=1
1st number: (2k+1) = 3
2nd number: (2k+3)=5
3rd number: (2k+5)=7