Answer:
-67x + 10
Step-by-step explanation:
3x + 10(1 - 7x)
(use distributive property)
3x + 10 - 70x
(simplify)
3x - 70x + 10
-67x + 10
Answer:
80
Step-by-step explanation:
5(1+3)^2
Due to PENDAS, you will first need to do the root
5(4)^2
5(16)
80
Hope it helped!
Answer: x(t) = 5cm*cos(t*pi/2s)
Step-by-step explanation:
This is a sinusoidal equation, so we can write this as:
x(t) = A*cos(c*t + p) + B
where B is the axis around the movement, as the resting position is x = 0, we have B = 0
so x(t) = A*cos(c*t + p)
A is the amplitude of the oscilation, c is the frequency and p is a phase.
We know that when t = 0s, we have x(2s) = 5cm
if this is the maximum displacement, then knowing that the maximum of the cosine is cos(0) = 1
then we must have that p = 0
x(0s) = A*cos(0) = 5cm
then we have A = 5cm
Now, when t = 2s, we have:
x(2s) = 5cm*cos(2s*c) = -5cm
then 2s*c is the minimum of the cos(x) function, this is:
cos(pi) = -1
then 2s*c = pi
c = pi/2s.
then our function is:
x(t) = 5cm*cos(t*pi/2s)
Answer:
3 < x < 27
Step-by-step explanation:
We can't tell what "must ne greater" means, so we'll tell you the limits on the side length and you can choose the one that is relevant.
The third side of a triangle must have a length that lies between the difference and sum of the two lengths you know.
15 -12 = 3
15 +12 = 27
The value of x must be between 3 and 27:
3 < x < 27
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If you allow the triangle to have zero area, then x can be 3 or 27. Many authors claim such a "triangle" is not allowed, so don't allow those cases.
Slope (m) = 1/4
slope-intercept format is: y = mx + b
point-slope format is: y-k = m (x-h), where the point is at (h, k)
So we plug in for that using the point (8, 3):
y-3 = 1/4(x-8)
y-3 = 1/4x - 2 --> solve for y:
y-3+3 = 1/4x -2 +3
y = 1/4x + 1 --> now it's in slope-intercept format where the b is the y-intercept, which is +1
