Answer:
Option D In step 4 Keith should have subtracted 5 from each side
Step-by-step explanation:
step 1
we have
f(x)=7x+5 -----> given
step 1 is correct
step 2
Change f(x) to y
y=7x+5
so
step 2 is correct
step 3
Exchange x for y and y for x
x=7y+5
so
step 3 is correct
step 4
Subtract 5 each side
x-5=7y+5-5
x-5=7y
<u><em>step 4 is not correct</em></u>
step 5
Divide by 7 each side
(x-5)/7=y
step 6
Change y to g(x)
(x-5)/7=g(x)
step 7
switch sides of the equation
g(x)=(x-5)/7
therefore
In step 4 Keith should have subtracted 5 from each side
Yes, a point of inflection exists where f''(x) = DNE.
We know that the point of inflection, also known as the inflection point, is where the function's concavity changes. Changing the function from concave down to concave up, or vice versa, means that. In other words, an inflection point is a location at which the rate of slope change from an increasing to a decreasing manner, or vice versa, occurs. There is no doubt that those points are neither local maxima nor minima. They are called stationary points.
Let's take an example ![f(x) = x^{\frac{1}{3} }](https://tex.z-dn.net/?f=f%28x%29%20%3D%20x%5E%7B%5Cfrac%7B1%7D%7B3%7D%20%7D)
Here, ![f'(x)=\frac{1}{3x^{\frac{2}{3} } }](https://tex.z-dn.net/?f=f%27%28x%29%3D%5Cfrac%7B1%7D%7B3x%5E%7B%5Cfrac%7B2%7D%7B3%7D%20%7D%20%7D)
and ![f''(x)=-\frac{2}{9x^{\frac{5}{3} } }](https://tex.z-dn.net/?f=f%27%27%28x%29%3D-%5Cfrac%7B2%7D%7B9x%5E%7B%5Cfrac%7B5%7D%7B3%7D%20%7D%20%7D)
Clearly f''(x) = DNE at x = 0. We are going to check if x = 0 is a point of inflection or not.
At x = -1, (left side of 0),
(concave up)
At x = 1, (right side of 0),
(concave down)
Then by the definition, we can conclude that x = 0 is a point of inflection.
Therefore, a point of inflection exists where f''(x) = DNE.
Learn more about point of inflection here -
brainly.com/question/5928704
#SPJ10
The sense of "rate<span>" being used is "a quantity, amount, or degree of something measured per unit of something else". This is what is asked in this problem. TO calculate, we divide the number of steps to the time it takes.
Steps/min = 775/12 1/2 = 62 steps per minute
Hope this answers the question. Have a nice day.</span>
So, you put the values on the other sides of the vertical angles, so you get a set of interior angles (can't remeber word at the moment)
Make the angles equal to 180.
So equation looks like 3x+11+5x+9=180.
Now combine like terms, get 8x+20=180.
Subtract 20 from both sides and get 8x=160.
Divde both sides by 8 and get your answer of x= 20
Hope this helps
Answer:
The solutions of the system of equations are (-1,8) and (5,2)
Step-by-step explanation:
-------> equation A (equation of a line)
----> equation B (vertical parabola open upward)
Solve the system of equations by graphing
Remember that the solution is the intersection points both graphs
using a graphing tool
The intersection points are (-1,8) and (5,2)
see the attached figure
therefore
The solutions of the system of equations are (-1,8) and (5,2)