The rate of change of the quadratic function over the interval −4≤x≤−2 is 2.
To find the rate of change of the quadratic function [tex]$f(x)=x^2+4 x+5$[/tex] , over the interval −4≤x≤−2, we need to find the average rate of change over that interval.
The average rate of change of a function f(x) over an interval [a,b] is given by:
[tex]Average Rate of Change =\frac{f(b)-f(a)}{b-a}$[/tex]
So, in this case:
a=−4
b=−2
We calculate f(−4) and f(−2):
[tex]$\begin{aligned} & f(-4)=(-4)^2+4(-4)+5=16-16+5=5 \\ & f(-2)=(-2)^2+4(-2)+5=4-8+5=1\end{aligned}$[/tex]
Now we can find the rate of change:
Rate of Change = [tex]$\frac{1-5}{-2-(-4)}=\frac{-4}{-2}=2$[/tex]
The average rate of change of the function f(x)=x² + 4x + 5 over the interval from x = -4 to x = -2 is -2.
The rate of change for the quadratic function f(x)=x² + 4x + 5 over the interval from x = -4 to x = -2 can be calculated using the average rate of change formula. This formula is given by:
Rate of Change = [f(x2) - f(x1)] / (x2 - x1)
Where x1 = -4 and x2 = -2. We first calculate f(-4) and f(-2) by plugging these values into the function:
f(-4) = (-4)² + 4(-4) + 5 = 16 - 16 + 5 = 5
f(-2) = (-2)² + 4(-2) + 5 = 4 - 8 + 5 = 1
Now we use these results in our rate of change formula:
Rate of Change = (1 - 5) / (-2 + 4) = -4 / 2 = -2
The average rate of change of the function f(x) over the interval from x = -4 to x = -2 is -2.
Rearrange the formula v = GM r for r.
The correct formula for [tex]\( r \)[/tex] rearranged from [tex]\( v = \frac{GM}{r} \) is \( r = \frac{GM}{v} \)[/tex].
To rearrange the formula [tex]\( v = \frac{GM}{r} \)[/tex] to solve for [tex]\( r \)[/tex], follow these steps:
1. Start with the given formula:
[tex]\[ v = \frac{GM}{r} \][/tex]
2. Multiply both sides of the equation by [tex]\( r \)[/tex] to get rid of the denominator:
[tex]\[ vr = GM \][/tex]
3. Divide both sides of the equation by [tex]\( v \)[/tex] to isolate [tex]\( r \)[/tex]:
[tex]\[ r = \frac{GM}{v} \][/tex]
This gives us the rearranged formula for [tex]\( r \)[/tex] in terms of [tex]\( G \), \( M \), and \( v \)[/tex]
On Call 3.5 hours: $10 Talk Time 1/2 hours: $1.25 What is the unit rate in dollars per hour for each company?
If 3 (x+1) =7 find the value of 3x
Please HELP FAST
Which system of inequalities is represented by the graph?
A. y ≤ –1/2x
y > –1
B. y ≥ –1/2x
y < –1
C. y < –1/2x
y ≥ –1
D. y > –1/2x
y ≤ –1
the probability that it will rain today is 0.3 what is the probability that it will not rain?
Answer: 0.7
Step-by-step explanation: 1-0.3 = 0.7
6-ounce bag of rice noodles makes 5 servings. at that rate, find how many ounces of noodles are needed for 88 servings, to the nearest ounce
Why did helga the witch sign up for anger management classes
Helga enrolled in anger management classes to control her temper, realizing it affected others and herself negatively, hoping to improve her witchcraft and life.
Helga the witch signed up for anger management classes because her temper was causing issues not just for others, but also for herself. Constantly flying off the handle and hexing everything in sight led to her feeling isolated and out of control. Plus, her cottage was starting to look like a scene from a horror movie, with all the shattered potion bottles and singed curtains. She realized that mastering her emotions would not only make her a better witch but also improve her quality of life. So, begrudgingly, she enrolled in the classes, hoping to learn some magical techniques for keeping her cool.
If (a+b)^2=25, and a^2+b^2=17, then what is a*b equal to? Thanks.
Sales fall from 300 per week to 270 per week what’s the percentage change
If molly walks 4 miles in 70 minutes, then molly will walk how far in 100 minutes if she walks at the same speed the whole time? if necessary, round your answer to the nearest tenth of a mile.
which equation represents a line that passes trough (-9,-3) abd has a slope of -6?
What time is 3 hours and 30 minutes before 5:00 P.M.?
I conceived on september 27 when will the test show the results
Find two numbers whose sum is 49 and whose product is 544
The two numbers are 16 and 33. They satisfy the conditions that their sum is 49 and their product is 544, as verified by setting up and solving a system of equations.
To find two numbers whose sum is 49 and whose product is 544, we can set up a system of equations based on the information given. Let's call the two numbers x and y. So, we have two equations:
x + y = 49xy = 544By solving these equations simultaneously, we can find the values of x and y.
The easiest way to solve this might be to express y in terms of x from the first equation: y = 49 - x. Then, substitute this into the second equation:
x(49 - x) = 544
This simplifies to a quadratic equation:
x^2 - 49x + 544 = 0
Factoring this quadratic equation, we get:
(x - 16)(x - 33) = 0
Which gives us two possible values for x:
x = 16x = 33Plugging these back into the equation for y, we get:
y = 49 - 16 = 33y = 49 - 33 = 16So the two numbers are 16 and 33.
A rancher needs to enclose two adjacent rectangular corrals, one for cattle and one for sheep. if the river forms one side of the corrals and 180 yd of fencing is available, find the largest total area that can be enclosed.
What is the perimeter of the rectangle shown on the coordinate plane, to the nearest tenth of a unit?
15.3 units
20.4 units
30.6 units
52.0 units
If 5kg more than 3 times mac’s mass is decreased by twice his mass the result is 60 kg. What is mac’s mass?
Mac's mass can be found by setting up the equation 3m + 5kg - 2m = 60kg, simplifying to m + 5kg = 60kg, and solving for m to get m = 55kg. Therefore, Mac's mass is 55kg.
The equation, according to the problem statement, is: 3m + 5kg - 2m = 60kg. This simplifies to m + 5kg = 60kg, from which we can subtract 5kg from both sides resulting in m = 55kg. So, Mac's mass is 55kg.
Steps to solve the problem:
Let m represent Mac's mass.
Write the equation according to the problem statement: 3m + 5kg - 2m = 60kg.
Simplify the equation: m + 5kg = 60kg.
Subtract 5kg from both sides: m = 55kg.
Conclude that Mac's mass is 55kg.
A line contains the points (34, 12)(34, 12) and (32, 48)(32, 48) .
What is the slope of the line in simplified form?
a rectangle is three centimeters.longer than it is wide. if its length were to be decreased by two centimeters, its area would decrease by thirty square centimeters.
A) what are the dimensions?
B) what is it’s area?
Show your work using an equation
How to determine the probability of an event with a small chance repeating?
1.) How could you describe the pair of lines y = 2x – 5 and 4x – 2y = 9: parallel, perpendicular, or neither?
2.) Explain why you chose parallel, perpendicular, or neither in #1.
What is the value of the function at x=−3?
y = 4
y = 3
y = 0
y=−3
Answer:
y=4
Step-by-step explanation:
A polynomial function P(x) has a degree n. If n is even is the number of turning points of the graph of p(x) even or odd? What can you say about the number of turning points if n is odd?
The number of turning points if n is odd if A polynomial function P(x) has a degree n, is even.
What is polynomial?A polynomial is a mathematical expression that solely uses the operations of addition, subtraction, multiplication, and positive-integer powers of variables. It is made up of indeterminate (also known as variables) and coefficients.
Given:
A polynomial function P(x) has a degree n,
A turning point is when the derivative's sign changes. A relative maximum or relative minimum might mark a turning point (also known as local minimum and maximum). A turning point is a stationary point if the function is differentiable, however not all stationary points are turning points.
For example, if the degree is 2 then the number of turning points will be 1
The general formula is, the number of turning points = n - 1
Thus, for odd n, the turning point will be even.
To know more about polynomials:
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"in how many ways can 6 people be lined up to get on a bus?"
Which of the following is the contrapositive of the conditional below?
If 3 + 4 = 6, then 2 · 5 = 10.
A. If 2 · 5 = 10, then 3 + 4 = 6.
B. If 3 + 4 ≠ 6, then 2 · 5 ≠ 10.
C. If 2 · 5 ≠ 10, then 3 + 4 ≠ 6.
D. If 3 + 4 ≠ 6, then 2 · 5 = 10.
Answer: If 2 · 5 ≠ 10, then 3 + 4 ≠ 6.
Step-by-step explanation:
Because a contrapositive is the contradiction the hypothesis and conclusion of something given and interchanging them. For example: "if not-B then not-A " is the contrapositive of "if A then B "
Answer:
If 2 · 5 ≠ 10, then 3 + 4 ≠ 6.
Step-by-step explanation: Hope This Helps You!!! :)))
Need help on an Algebra 2 question??!
Select the correct inequality for the graph below:
A. y > −2x + 2
B. y ≥ −2x + 2
C. y < −2x + 2
D. y ≤ −2x + 2
What is the first step in solving an equation by completing the square?
Evaluate the expression below when x = 5.
3x(2x - 7)
A.) 0
B.) 24
C.) 45
D.) 143
Identify the Asymptotes for the graphs below help pls!
Janine has two important tests to study for. If she plans to divide her study time equally between both tests, how long should she spend studying for each test if she wants to study for at most 90 minutes?