Given:
Consider the given function is:
[tex]f(x)=x^2-8x+13[/tex]
To find:
The average rate of change of the function over the interval [tex]-1\leq x\leq 6[/tex].
Solution:
The average rate of change of the function f(x) over the interval [a,b] is:
[tex]m=\dfrac{f(x_2)-f(x_1)}{x_2-x_1}[/tex]
We have,
[tex]f(x)=x^2-8x+13[/tex]
At [tex]x=-1[/tex],
[tex]f(-1)=(-1)^2-8(-1)+13[/tex]
[tex]f(-1)=1+8+13[/tex]
[tex]f(-1)=22[/tex]
At [tex]x=6[/tex],
[tex]f(6)=(6)^2-8(6)+13[/tex]
[tex]f(6)=36-48+13[/tex]
[tex]f(6)=1[/tex]
Now, the average rate of change of the function f(x) over the interval [tex]-1\leq x\leq 6[/tex] is:
[tex]m=\dfrac{f(6)-f(-1)}{6-(-1)}[/tex]
[tex]m=\dfrac{1-22}{7}[/tex]
[tex]m=\dfrac{-21}{7}[/tex]
[tex]m=-3[/tex]
Therefore, the average rate of change of the function f(x) over the interval [tex]-1\leq x\leq 6[/tex] is -3.
Gilbert purchased a car for 34000. The car depreciates at a rate of 14% per year. The exponential function that represents this situation is y = 34000(0.86)^x.
What is the change factor for this function?
Answer:
.86
Step-by-step explanation:
Exponential function formula
[tex]y = a ( 1 + or - r ) ^t[/tex]
where a = initial value
r = rate of change
and t = number of years
given the equation y = 34000(0.86)^x.
r = .86
Hence the change factor is .86
x = 4 and y = 3.
3x 2 + 5y
A. 27
B. 31
C. 63
D. 159
Answer:
39
Step-by-step explanation:
I did the math
please help convert the improper fractions to mixed numbers
Answer:
1. 1 1/4
2. 2 1/2
3. 2 2/5
4. 1 1/5
5. 4 1/3
2/3 - 3/2y + 1/3y + 4 = 0
Answer:
y = 4
Step-by-step explanation:
(2/3 + 4) + (-3/2y + 1/3y) = 0
(-3/2y + 1/3y) = -4 2/3
-9/6y + 2/6y = -14/3
-7/6y = -14/3
cross-multiply:
-21y = -84
y = 4
Answer:
y = 4
Step-by-step explanation:
Please use parentheses for clarity, remembering what big differences they make in expression values.
I will assume that your "2/3 - 3/2y + 1/3y + 4 = 0" actually means
2/3 - (3/2)y + (1/3)y + 4 = 0
The LCD here is 6, which is the product of the denominators 2 and 3.
Then your "2/3 - 3/2y + 1/3y + 4 = 0" becomes:
4 - 9y + 2y + 24 = 0, which simplifies to:
28 - 7y = 0. Solving this, we get y = 4
There are approximately 3,000 bass in a lake. The population grows at a
rate of 2% per year. What is the average rate of change of the population
of bass from Year 1 to Year 4? Round your answers to the nearest tenth.
62.4 bass per year from year 5 to year 8, the average rate of change from the population was about 67.6 best per year the change of rate increase was about
P - 24 = 13 step explanation
Answer:
p = 37
Step-by-step explanation:
The most important step in beginning algebra is to get all the letters on one side and and all the numbers on the other. In This case it is only all the numbers that need to be transferred.
p - 24 + 24 = 13 + 24
p = 37
Please help fast how to find missing numbers
Answer:
Step-by-step explanation:
In the equation y = -x + 7 what is the value of m
the area is __ square units
Answer:
26 square units
Step-by-step explanation:
hope this helped!
resuelve la inecuación
(3x<15)
Answer:
x<5
Step-by-step explanation:
(3x<15)
Divide both sides by 3. Since 3 is positive, the inequality direction remains the same.
x<15/3
Divide 15 by 3 to get 5.
x<5
This is my third time asking for helpppppppppp
Answer:
The new shape will be like the one that i have drawn for you , i think .
Step-by-step explanation:
add two ( to base* from both sides of it * )
delete one ( from hights )
Hope it was useful ;)
Before a renovation, a movie theater had 145 seats. After the renovation, the theater has 178 seats. What is the approximate percentage increase of the number of seats in the theater? If necessary, round to the nearest tenth of a percent.
Answer:
Use https://www.bartleby.com/ it has helped me out a lot . Its actual tutors/teachers who answer your questions in about 30 minutes !!!!!!!!
Step-by-step explanation:
6.
A. [tex]-\frac{1}{5}[/tex]
B. [tex]\frac{x1}{5}[/tex]
C. –5
D. 5
Answer:
[tex]\frac{1}{5}[/tex]
Step-by-step explanation:[tex]d=-1\frac{1}{5}-(-2) =-1\frac{1}{5}+2=\frac{1}{5}[/tex]
1. The reciprocal parent function is translated 2 units left and 9 units down.
Write an equation to represent the new function.
Answer:
y= -2x-9
Step-by-step explanation:
x would move left or right, and up and down is y
left or down are negative and up or right are positive
how to solve 9x-5-(-6x)
Answer: 3x-5
Step-by-step explanation:
9x-5(-6x)
9x-5-6x
3x-5
Answer:
15x - 5
Step-by-step explanation:
We have the equation 9x - 5 - (-6x) and are asked to solve it.
We cannot combine 9x and 5 because they have a variable difference, with 9 having x as its variable and 5 having no variable. What we can do is distribute the minus sign to the right of 5 to (-6x), lets do as said :
9x - 5 - (-6x)
Two negatives make a positive, therefore :
9x - 5 + 6x
Since 9x and 6x have the same variable ending, we can combine them, do as followed :
9x - 5 + 6x
9x + 6x
15x - 5
Chloe has enough sand to fill a sandbox with an extra area of 36 square units she wants the outer edge of the sandbox to use as little as Material possible
Answer:
[tex]Length = Width = 6\ units[/tex]
Step-by-step explanation:
Given
[tex]Area=36[/tex]
Required
The least possible material
Sandboxes usually, are rectangles or squares.
Using the above assumption, the area is calculated as:
[tex]Area= Length * Width[/tex]
[tex]Area= L* W[/tex]
[tex]L * W = 36[/tex]
Make L the subject
[tex]L = \frac{36}{W}[/tex]
The material of the outer edge is calculated by the perimeter.
[tex]Perimeter = 2 * (L +W)[/tex]
[tex]P = 2 * (L + W)[/tex]
Substitute [tex]L = \frac{36}{W}[/tex]
[tex]P = 2 * (\frac{36}{W} + W)[/tex]
Open bracket
[tex]P = \frac{72}{W} + 2W[/tex]
[tex]P = 72W^{-1} +2W[/tex]
To get the minimum material needed, we differentiate P
[tex]P' = -72W^{-2} + 2[/tex]
Set: [tex]P' = 0[/tex]
[tex]-72W^{-2} + 2 = 0[/tex]
Collect like terms
[tex]72W^{-2} = 2[/tex]
Divide both sides by 72
[tex]W^{-2} = \frac{2}{72}[/tex]
[tex]W^{-2} = \frac{1}{36}[/tex]
Rewrite as:
[tex]\frac{1}{W^2} = \frac{1}{36}[/tex]
Take positive square roots of both sides
[tex]\frac{1}{W} = \frac{1}{6}[/tex]
Cross multiply
[tex]W = 6[/tex]
Recall that: [tex]L = \frac{36}{W}[/tex]
So, we have:
[tex]L =\frac{36}{6}[/tex]
[tex]L = 6[/tex]
Hence, the dimension with the littlest material as possible is:
[tex]Length = Width = 6\ units[/tex]
A shirt originally cost $41.10, but it is on sale for $36.99. What is the percentage decrease of the price of the shirt? If necessary, round to the nearest percent. A. 10% B. 90% C. 11% D. 8%
Answer:
10%
Step-by-step explanation:
The first step is to calculate the decrease
Original price= $41.10
New price= $36.99
= 41.10-36.99
= 4.11
4.11/41.10 × 100
= 0.1×100
= 10%
Hence the percentage decrease is 10%
Stella wants to buy a $177,000 house, and she is comparing a 7/1 ARM with an interest
rate of 8 75%, amortized over 30 years, with a 7/23 balloon mortgage that has an
interest rate of 8.25%
24. What would Stella's monthly payment be for the 7/1 ARM?
Answer: Are there any answer choices? If there are I could probably help you, thanks <3
Step-by-step explanation:
help me pls T^T this is due today
Which of these n values are solutions to the following equation?
n2 = 2.25
Choose all answers that apply:
А)
n = 1.1
В)
n = -1.1
C)
n = 1.4
D)
n = -1.4
E)
None of the above
Answer:
None of the above
Step-by-step explanation:
Square root of 2.25 is 1.5, not 1.4
Answer:
none of the above
Step-by-step explanation:
did it on khan
Leo is constructing a tangent line from point Q to circle P. What is his next step?
Mark the point of intersection S of the segment created from the arcs and circle R, and construct line RS.
Mark the point of intersection S of circles R and P, and construct line QS.
Construct arcs from point Q that are greater than half the length of segment PQ.
Construct a circle from point P that has a radius of P and the intersection of circles P and R.
Answer:
hello your question has a missing diagram attached below is the missing diagram
answer :
Mark the point of intersection S of circles R and P, and construct line QS ( option 2 )
Step-by-step explanation:
when constructing a tangent line from one point ( lets say Q as seen in the question ) to a circle P. The next step should be to mark a point of intersection between the given circles and then construct a line through it
Answer:
Mark the point of intersection S of circles R and P, and construct line QS.
Step-by-step explanation:
This is correct because after you create circle R that intersects circle p, you're supposed to mark the intersection points. If your in FLVS, it would be in lesson 7.04. I also got this right on my test. Good luck!
Which equation represents a function?
Answer:
C represents a function
In the diagram, x is a negative number. and it is closer to zero than y.y is a positive number. which expression must be negative
Answer:
you already click the answer
Step-by-step explanation:
Choose the calculation that shows “add 26 to m”. A)
Answer: easy it’s..........
Step-by-step explanation: 26+M
Use the distributive property with factoring to find the equivalent expression. 24n + 32w = (3n + w)
Answer:
Step-by-step explanation:
24n + 32w = (3n + w)
We're asked to use distributive property, this means that we have to find a way that the given expression on the left hand side is equal to the given incomplete exresssion on the right hand side. In so doing, we're fulfilling the distributive property tag.
Given 3n, 3 factorises 24 into 8, and at the same time, factorises 32 into 4. Thus, we can then conclude that
24n + 32w = 8(3n + 4w)
PLEASE PLEASE PLEASEEE HELP I DONT UNDERSTAND
Answer:
29.5 times pi or 3.14
Step-by-step explanation:
this is for math n i dont get it, help pls :,)
Answer:
Ella ran 7.5 meters in 5 seconds
Step-by-step explanation:
d=1.5t
d=1.5(5)
d=7.5
Sophie runs 4 1/2 miles on Saturday. Aubrey jogs 2/3 of that distance. So what is the distance Aubrey jogs in miles?
Answer:
3
Step-by-step explanation:
PLEASE HELP! WILL MARK BRAINLIEST !!
3. Which figure below is a graph of r(x) = 2 + x+1/x+3 ? Explain and show how you know.
Answer:
I believe the answer is B
Step-by-step explanation:
The graph with Vertical Asymptotes: x=-3 and Horizontal Asymptotes: y=3 is given below.
The given function is [tex]r(x)=2+\frac{x+1}{x+3}[/tex].
What is the graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points. A graph consists of some points and lines between them. The length of the lines and position of the points do not matter.
The graph for the given function is
Find the asymptotes.
Vertical Asymptotes: x=-3
Horizontal Asymptotes: y=3
No Oblique Asymptotes
The graph with Vertical Asymptotes: x=-3 and Horizontal Asymptotes: y=3 is given below.
To learn more about the graph visit:
brainly.com/question/14375099.
#SPJ2
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Answer: 4 black marbles, 3 blue, 2 green, and one red.
Step-by-step explanation: