Given:
A figure of a triangle.
To find:
The measure of angle A.
Solution:
Label the points in the figure as shown below.
In the below figure,
(Vertically opposite angles)
(Congregant angles)

Using exterior angle theorem in triangle ABC, we get




Isolate the variable term x.




Now, the measure of angle A is:




Therefore, the correct option is B.
2(x-2)(x+3) you have to factor
The domain of the function is the range of values of x that can be used to be replaced in the equation for it to become true. We are given that the value of f(x) should range only from -1 to 3. We evaluate each of the choices and see if the values of f(x) will fall within the range.
(a) -12; f(x) = 2^(-12) - 10 = -9.9999 (NOT AN ANSWER)
(b) -10; f(x) = 2^(-10) - 10 = -9.999 (NOT AN ANSWER)
(c) -9; f(x) = 2^(-9) - 10 = -9.999 (NOT AN ANSWER)
(d) -6; f(x) = 2^(-6) - 10 = -9.98 (NOT AN ANSWER)
(e) -2; f(x) = 2^(-2) - 10 = -9.75 (NOT AN ANSWER)
Hence, none of the choices will allow the value of f(x) to fall between -1 and 3.
Let's
simplify step-by-step.
3x2(x2−4x−4)+5x3+7x2+2x+11
Distribute:
=(3x2)(x2)+(3x2)(−4x)+(3x2)(−4)+5x3+7x2+2x+11
=3x4+−12x3+−12x2+5x3+7x2+2x+11
Combine
Like Terms:
=3x4+−12x3+−12x2+5x3+7x2+2x+11
=(3x4)+(−12x3+5x3)+(−12x2+7x2)+(2x)+(11)
=3x4+−7x3+−5x2+2x+11
Answer:
=3x4−7x3−5x2+2x+11
<span> </span>
Answer:
-20 < 4 - 2x (subtract 4 from both sides)
-24 < -2x (divide each side by -2)
12> x (when you divide by a negative number, the inequality flips)
x< 12 ( I always put it so x is first)
so the answer is C