The range of possible values is all numbers less than or equal to -2.5
Answer:
Point (1,8)
Step-by-step explanation:
We will use segment formula to find the coordinates of point that will partition our line segment PQ in a ratio 3:1.
When a point divides any segment internally in the ratio m:n, the formula is:
![[x=\frac{mx_2+nx_1}{m+n},y= \frac{my_2+ny_1}{m+n}]](https://tex.z-dn.net/?f=%5Bx%3D%5Cfrac%7Bmx_2%2Bnx_1%7D%7Bm%2Bn%7D%2Cy%3D%20%5Cfrac%7Bmy_2%2Bny_1%7D%7Bm%2Bn%7D%5D)
Let us substitute coordinates of point P and Q as:
,
![y_1=-4](https://tex.z-dn.net/?f=y_1%3D-4)
![x_2=4](https://tex.z-dn.net/?f=x_2%3D4)
![y_2=12](https://tex.z-dn.net/?f=y_2%3D12)
![m=3](https://tex.z-dn.net/?f=m%3D3)
![[x=\frac{4}{4},y=\frac{32}{4}]](https://tex.z-dn.net/?f=%5Bx%3D%5Cfrac%7B4%7D%7B4%7D%2Cy%3D%5Cfrac%7B32%7D%7B4%7D%5D)
Therefore, point (1,8) will partition the directed line segment PQ in a ratio 3:1.
Answer:
Mile = length
Cup = Volume
Pound= Mass
Centimeter = length
Liter = volume
Gram = mass
pint = volume
yard=length
kilogram=mass
teaspoon=volume
millimeter=length
Step-by-step explanation:
By "y = −9x2 − 2x" I assume you meant <span>y = −9x^2 − 2x (the "^" symbol represents exponentiation).
Let's find the first derivative of y with respect to x: dy/dx = -18x - 2. This is equivalent to the slope of the tangent line to the (parabolic) curve. Now let this derivative (slope) = 0 and solve for the critical value: -18x - 2 = 0, or
-18x = 2. Solving for x, x = -2/18, or x = -1/9.
When x = -1/9, y = -9(-1/9)^2 - 2(-1/9). This simplifies to y = -9/9 + 2/9, or
y = -7/9.
The only point at which the tangent to the curve is horiz. is (-1/9,-7/9).</span>
Answer:
There isn't much to say. Since the x repeats, and the y's are different, it wouldn't be a function.