The vector pointing from (2, 1) to (1, 3) points in the same direction as the vector . The derivative of at (2, 1) in the direction of is
We have
Then
The vector pointing from (2, 1) to (5, 5) has the same direction as the vector . The derivative of at (2, 1) in the direction of is
so that
Solving the remaining system gives and .
Multiply out <span>f(x)=(x-8)(x-2): f(x) = x^2 - 8x - 2x + 16, or f(x) = 1x^2 - 10x + 16.
Thus, a=1, b= -10 and c=16.
One of several ways to find the vertex involves "completing the square."
x^2 - 10x + 16 = x^2 - 10x + 25 - 25 + 16, or y = (x-5)^2 -9, or y+9=(x-5)^2.
Compare this result to y-k = a(x-h)^2. We see that h=5 and k=-9.
Thus, the vertex is at (h,k) = (5, -9). </span>
Answer:
CBD = 63 degrees
Step-by-step explanation:
To find CBD, we must first find the value of x. To do so, we use this equation since CBD and ABC equal 96 degrees:
(6x+27) + (7x-9) = 96
13x+18 = 96
13x+18-18 = 96-18
13x = 78
13x/13 = 78/13
x = 6
Now that we know the value of x, we factor it in to CBD to find its true value:
6x+27
6(6)+27
36+27
= 63 degrees
To check if this answer is correct, we can also find the value of ABC and see if the two values equal 96:
7x-9
7(6)-9
42-9
= 33 degrees
63 + 33 = 96
The answer is correct. CBD = 63 degrees and ABC = 33 degrees.
Answer:
We can conclude that only option B is correct.
Step-by-step explanation:
A. The equation 3(3x - 2) - 4 = 5x has a solution.
Solving it we get,
3(3x - 2) - 4 = 5x
⇒ 9x - 6 - 4 = 5x
⇒ 4x = 10
⇒ x = 2.5
B. The equation 4(2x - 3) - 5 = 4x has exactly one solution.
Solving it we get,
4(2x - 3) - 5 = 4x
⇒ 8x - 12 - 5 = 4x
⇒ 4x = 17
⇒ x = 4.25
C. The equation 5(3x - 2) - 2 = 3x also has exactly one solution.
Solving it we get,
5(3x - 2) - 2 = 3x
⇒ 15x - 10 - 2 = 3x
⇒ 12x = 12
⇒ x = 1
D. The equation 6(2x - 3) - 3 = 2x also has exactly one solution.
Solving it we get,
6(2x - 3) - 3 = 2x
⇒ 12x - 18 - 3 = 2x
⇒ 10x = 21
⇒ x = 2.1
Therefore, we can conclude that only option B is correct. (Answer)