Because two horizontal lines never intersect.
It will be a parabola withe line of symmetry = y axis and will open downwards. The coefficient of x^2 will be -1.
As it will have a maximum and y intercept of y = 4 the function will be
f(x) = -x^2 + 4
Explanation: First rewrite the ratio 3 : 12 as the fraction 3/12.
Next, we can find an equal ratio by
simply writing this fraction in lowest terms.
If we divide both the numerator and the denominator of 3/12
by their greatest common factor of 3, we get the equal ratio 1/4.
Now we can use 1/4 to find another equal ratio.
If we multiply both the numerator and denominator
of 1/4 by 2, we get the equal ratio 2/8.
So 3 : 12 is equal to 1 : 4 and 2 : 8.
Make sure to write your final answers as the same
form in the original problem.
Answer:
-3.98 (nearest hundredth)
Step-by-step explanation:
The average rate of change of function f(x) over the interval a ≤ x ≤ b is given by:
![\dfrac{f(b)-f(a)}{b-a}](https://tex.z-dn.net/?f=%5Cdfrac%7Bf%28b%29-f%28a%29%7D%7Bb-a%7D)
Given interval: -2 ≤ x ≤ 2
![\implies a = -2](https://tex.z-dn.net/?f=%5Cimplies%20a%20%3D%20-2)
![\implies b = 2](https://tex.z-dn.net/?f=%5Cimplies%20b%20%3D%202)
![\implies f(a) = f(-2)=16](https://tex.z-dn.net/?f=%5Cimplies%20f%28a%29%20%3D%20f%28-2%29%3D16)
![\implies f(b) =f(2)= \dfrac{1}{16}](https://tex.z-dn.net/?f=%5Cimplies%20f%28b%29%20%3Df%282%29%3D%20%5Cdfrac%7B1%7D%7B16%7D)
Substituting the values into the equation:
![\begin{aligned}\implies \textsf{rate of change} & =\dfrac{\frac{1}{16}-16}{2-(-2)}\\\\ & = \dfrac{-\frac{255}{16}}{4}\\\\ & = -\dfrac{255}{64}\\\\ & = -3.98\: \sf (nearest\:hundredth)\end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7D%5Cimplies%20%5Ctextsf%7Brate%20of%20change%7D%20%26%20%3D%5Cdfrac%7B%5Cfrac%7B1%7D%7B16%7D-16%7D%7B2-%28-2%29%7D%5C%5C%5C%5C%20%26%20%3D%20%5Cdfrac%7B-%5Cfrac%7B255%7D%7B16%7D%7D%7B4%7D%5C%5C%5C%5C%20%26%20%3D%20-%5Cdfrac%7B255%7D%7B64%7D%5C%5C%5C%5C%20%26%20%3D%20-3.98%5C%3A%20%5Csf%20%28nearest%5C%3Ahundredth%29%5Cend%7Baligned%7D)
Answer:
B
Step-by-step explanation:
multiply both sides by 2 to eliminate the fraction
- x > 12
multiply both sides by - 1
Remembering to reverse the inequality symbol as a consequence
x < - 12 ← reverse symbol
⇒ { x | x ∈ R, x < - 12 } → B