In triangle MNO, angle N is 5 times the measure of angle M, and angle O is 4 times the measure of angle M
1 answer:
Answer:
Step-by-step explanation:
In order to find the measure of each angle, it is important to remember that the sum of the interior angles of a triangle is 180 degrees. Knowing this, you can write the following equation:
[Equation 1]
Based on the information given in the exercise, you know that:
[Equation 2]
[Equation 3]
Then, you can substitute the Equations 2 and 3 into the Equation 1 and then solve for "M" in order to find the measure of the angle "M" in degrees:
Substituting this value into the Equations 2 and 3, you can find the measure of the angle "N" in degrees and the mesure of the angle "O" in degrees. These are:
Therefore:
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Answer:
YES
NO
NO
Step-by-step explanation:
The given polynomial is:
(x - a) is a factor of a polynomial iff x = a is a solution to the polynomial.
To check if (x - 5) is a factor of the polynomial f(x), we substitute x = 5 and check if it satisfies the equation.
∴ f(5) = 5³ + 4(5)² - 25(5) - 100
= 125 + 100 - 125 - 100
= 225 - 225
= 0
We see, x = 5 satisfies f(x). So, (x - 5) is a factor to the polynomial.
Now, to check (x + 2) is a factor.
i.e., to check x = - 2 satisfies f(x) or not.
f(-2) = (-2)³ + 4(-2)² - 25(-2) - 100
= -8 + 16 + 50 - 100
= -108 + 66
≠ 0
Therefore, (x + 2) is not a factor of f(x).
To check (x - 4) is a factor.
∴ f(4) = 4³ + 4(4)² - 25(4) - 100
= 64 + 64 - 100 - 100
= 128 - 200
≠ 0
Therefore, (x - 4) is not a factor of f(x).