Answer:
-2, -1, -1, 1/3
Step-by-step explanation:
A graphing calculator can find the real roots of a polynomial pretty easily. The attached graph of this function shows its zeros to be ...
-2, -1, -1, 1/3
__
The rational root theorem tells you that rational roots will be from the set ...
{±1/3, ±2/3, ±1, ±2}
Descarte's rule of signs tells you there will be 1 positive real root. The sum of coefficients is 24 (a relatively large positive number), so it is certain the positive root will be less than 1.
The sum of coefficients of odd-degree terms (11+1) is equal to the sum of coefficients of even-degree terms (3+11-2), telling you that -1 is a root. Synthetic division gives the cubic factor as 3x³ +8x² +3x -2, which has the same characteristics as the original quartic. That is, there is one positive real root, and -1 is a root of the cubic (hence a double root of f(x)).
Another round of synthetic division reveals the quadratic factor to be 3x² +5x -2, which can be factored as (x +2)(3x -1) to reveal the remaining roots.
Answer:
Step-by-step Explanation:
Extend the sides AD and BP. This creates 2 congruent triangles using ASA. Triangles CBP and adjacent triangle are also congruent bc of ASA. This makes 3 congruent triangles (transitivity). That means just finding the area of the constructed large triangle, you find the area of the parallelogram. Since point P is the midpoint of B_, P_ also equals 9. Using the formula for the area of a triangle, and Pythagorean theorem (9-12-15), 12*18/2=108, which is the area of the parallelogram.
Basically, you are just adding 1,000,101 to 1,100,001. This is because 'one million, one hundred thousand, one' translates to 1,100,001. From there, you just add the two numbers, which totals to be 2,100,102. You would read this number by saying 'two million, one hundred thousand, one hundred two.'
Hope this helped!
------------------------------------------------------
Option A
------------------------------------------------------
------------------------------------------------------
Check if slope = 2
------------------------------------------------------
y + 2 = 2(x + 3)
y + 1 = 2x + 6
y = 2x + 6 - 1
y = 2x + 5
Slope = 2
Answer: Yes, Slope is 2
------------------------------------------------------
Check if it passed through (2, 3)
------------------------------------------------------
When x = 2
y = 2(2) + 5
y = 9
Answer: No, it does not passed through (2, 3)
------------------------------------------------------
Option B
------------------------------------------------------
------------------------------------------------------
Check if Slope is 2
------------------------------------------------------
y - 3 = 2(x - 2)
y - 3 = 2x - 4
y = 2x - 4 + 3
y = 2x - 1
Slope = 2
Ans : Yes, slope is 2.
------------------------------------------------------
Check if it passed through (2, 3)
------------------------------------------------------
when x = 2
y = 2(2) - 1
y = 4 - 1
y = 3
Answer : Yes, it passed through (2, 3)
------------------------------------------------------
Answer: (B) <span>y – 3 = 2(x – 2)
</span>------------------------------------------------------