The average rate of change over an interval is the same as the slope between those two values. The formulate for slope is:
[tex]m=\frac{y_{2}-y_{1} }{x_{2}-x_{1}}[/tex]
You are given the x values: x2=3 and x1=-9. Plug in these x values to g(x) find the y values:
g(3)=3^2+5(3)-2=9+15-2=22
g(-9)=(-9)^2+5(-9)-2=81-45-2=34
Now, you can solve for m:
m=(22-34)/(3--9)
m=-12/12
m=1
Hope this helps!!
the average rate of change of the function over the interval -9 ≤ x ≤ 3 is -1
The average rate is the change of expression with respect to time.
Given the expression g(x)=x^2+5x-2 within the interval -9 ≤ x ≤ 3
At the lower interval x = -9
g(-9) = (-9)²+5(-9)-2
g(-9)= 81-45-2
g(-9) = 34
At the upper interval x = 3
g(3) = (3)²+5(3)-2
g(3)= 9+15-2
g(3) = 22
The average change of the function will be expressed as:
[tex]\frac{\triangle y}{\triangle x} =\dfrac{g(b)-g(a)}{b-a}\\ \frac{\triangle y}{\triangle x} =\dfrac{g(3)-g(-9)}{3-(-9)}\\\frac{\triangle y}{\triangle x} =\dfrac{22-34}{12}\\\\\frac{\triangle y}{\triangle x} =\dfrac{-12}{12} \\\frac{\triangle y}{\triangle x} =-1[/tex]
Hence the average rate of change of the function over the interval -9 ≤ x ≤ 3 is -1
Learn more here: https://brainly.com/question/7590674
Jennifer has already driven 160 miles on her trip to her grandparents' house. For every hour she travels, she drives an additional 55 miles. Which equation represents
the relationship between the total miles driven, y, and the number of hours, X.
Y=
Answer:
y=55x+160
Step-by-step explanation:
i might be wrong, but i think it would be y=55x+160
Answer:
y=55x+160
Step-by-step explanation:
she starts at 160 mi which is like your y-intercept so the "b" in y=mx+b. the slope or "m" would be 55 because thats how much she's travelling per 1 x or 1 hour
a. Find (f + g)(x).
b. Find (f + g)(3).
Use the functions f(x)=x+5 g(x)=2x+1
Answer:
Step-by-step explanation:
[tex](f+g)(x) =f(x) + g(x)\\f(x) = x+ 5\\g(x) = 2x + 1\\(f+g)(x) = x+ 5 + 2x + 1\\(f+g)(x) = 3x + 6\\\\(f+g)(3) = 3(3) + 6 = 15[/tex]
There are 8 big fish for every
small fish.
There are 4 big fish for every
small fish.
I need help, confused.
Answer:
x=90
Step-by-step explanation:
it is a square so: 360/4=90
Find the midpoint of the segment with the following endpoints.
(5,5) and (1,1)
Answer:
(3,3)
Step-by-step explanation:
x=(5+1)/2=3
y=(5+1)/2=3
Please please help me i'm begging you!
Answer:
A is 8 ounces/ 12 cupcakes is 12 cupcakes/8 ounces I'm not sure about C and D is 18 cupcakes for 12 ounces of frosting
Step-by-step explanation:
Please answer !!!!!!!!!!!!!!!!!!! Will mark brainliest !!!!!!!!!!!!!!!!!!!!!!!!!
Plzz help!!
Are the two triangles below similar?
(6 points)
1) No, because the corresponding sides are not proportional
2) Yes, because the corresponding sides are proportional
3) No, because there are not two pairs of congruent corresponding angles
4) Yes, because there are two pairs of congruent corresponding angles
Answer:
Step-by-step explanation:
Yes plzz give me brainliest
Betsy participates in a scavenger hunt that requires her to retrieve items from 4 locations. The locations are on a map with the coordinates as given:
Location 1 is at (−4, −1).
Location 2 is at (−4, 4).
Location 3 is at (3, 4).
Location 4 is at (3, −1).
The paths from one location to another are straight lines. One unit on the coordinate grid equals 10 yd. Betsy starts at location 1 and goes to location 2, then location 3, and then location 4, and then returns back to location 1.
What is the total distance Betsy has traveled?
Answer:
240 yd
Step-by-step explanation:
Let A, B, C, and D represent location 1, location 2, location 3, and location 4 respectively.
Consider the figure in the attached file.
We need to find the total distance traveled by Betsy.
The distance covered by Betsy is
length of segment AB length of segment BC length of segment CD length of segment DA.
To find the distance AB, we need to find the distance from A to B on y-axis.
So, length of segment AB units
To find the distance BC, we need to find the distance from B to C on x-axis.
So, length of segment BC units
To find the distance CD, we need to find the distance from C to D on y-axis.
So, length of segment CD units
To find the distance DA, we need to find the distance from D to A on x-axis.
So, length of segment DA units
Hence, the total distance covered is units
It is given that 1 unit equals 10 yd, so distance traveled by Besty is yd
Find the surface area of the rectangular prism.
8 yd
4 yd
5 yd
Answer:
A=184
Step-by-step explanation:
don leaves home 2pm. he drives 45 miles from home in the first hour
Answer:
if he leave at 2pm 45 miles in the first hr is the correct answer 3 pm
Step-by-step explanation:
MORE.FREE.POINTSS.
"I'm a cowboyy babyy"
this ones less points, BUT STILL
Answer:
thx may i have brainliest to plz i so close to next rank
Step-by-step explanation:
Answer:
bbbbbbbbbbbbbbbbbb
Step-by-step explanation:
popppppppppppppppppppppppppppppp
2.5 miles into _______inches
3(a+b)=a+2 make a subject of the formula
Answer:
a = 2 - 3b
2
Step-by-step explanation:
3(a + b) = a + 2 expand
3a + 3b = a + 2
3a - a = 2 - 3b
2a = 2 - 3b
a = 2 - 3b
2
SOS MY CLASS JUST STARTED THIS AND I HAVE NO CLUE WHAT TO DO!!!!!!
Answer:
REEEEEEEEEEEE
Step-by-step explanation:
In 1902, the yearly attendance at a major league baseball park was 3.4×10^5 people. One hundred years later, the yearly attendance was 1.7×10^6 people. How many times greater was the attendance in 2002 than in 1902?
Answer:
1,360,000
Step-by-step explanation:
1,700,000-340,000 = 1,360,000 or 1.36×10^5
identify the equation in the point-slope form the line parallel to y=3/4x-4 that passes through (-1,7)
If this function is differentials at x=1/2, what is a+b?
===============================================
Work Shown:
Let
g(x) = ax^3 + 2
h(x) = bx^2 + 1
Plug x = 1/2 into each function
g(x) = ax^3 + 2
g(1/2) = a(1/2)^3 + 2
g(1/2) = (1/8)a + 2
and
h(x) = bx^2 + 1
h(1/2) = b(1/2)^2 + 1
h(1/2) = (1/4)b + 1
In order for f(x) to be differentiable at x = 1/2, the function f(x) must be continuous at x = 1/2. If we had a jump discontinuity here, then there is no way the function is differentiable here.
f(x) is continuous at x = 1/2 when g(1/2) = h(1/2).
This means,
g(1/2) = h(1/2)
(1/8)a + 2 = (1/4)b + 1
8*[(1/8)a + 2] = 8*[(1/4)b + 1]
a+16 = 2b+8
a = 2b+8-16
a = 2b-8
We'll keep this in mind for later.
--------------------------------------------------
Now let's compute the derivatives
g(x) = ax^3 + 2
g ' (x) = 3ax^2
h(x) = bx^2 + 1
h ' (x) = 2bx
Now plug in x = 1/2
g ' (x) = 3ax^2
g ' (1/2) = 3a(1/2)^2
g ' (1/2) = (3/4)a
and
h ' (x) = 2bx
h ' (1/2) = 2b(1/2)
h ' (1/2) = b
Equate the two items. We do so because we want f(x) to be differentiable at x = 1/2, so that means g ' (1/2) = h ' (1/2)
So,
g ' (1/2) = h ' (1/2)
(3/4)a = b
3a = 4b
a = (4b)/3
--------------------------------------------------
Earlier we found a = 2b-8.
Since both a = 2b-8 and a = (4b)/3, this means we can equate the right hand sides to solve for b
2b-8 = (4b)/3
3*(2b-8) = 3*(4b)/3
6b-24 = 4b
6b-4b = 24
2b = 24
b = 24/2
b = 12
Which leads to
a = 4b/3
a = 4*12/3
a = 48/3
a = 16
--------------------------------------------------
The piecewise function
[tex]f(x) = \begin{cases}ax^3+2, \ \ x < \frac{1}{2}\\bx^2+1, \ \ x \ge \frac{1}{2}\end{cases}[/tex]
will update to
[tex]f(x) = \begin{cases}16x^3+2, \ \ x < \frac{1}{2}\\12x^2+1, \ \ x \ge \frac{1}{2}\end{cases}[/tex]
To verify f(x) is differentiable at x = 1/2, you should check to see if both pieces evaluate to the same output when you plug in x = 1/2. In other words, you should check to see if g(1/2) = h(1/2).
Also, you should check to see if g ' (1/2) = h ' (1/2) so that f(x) is fully differentiable here. I'll let you do the check portions.
--------------------------------------------------
After getting our a and b values, we can finally say that
a+b = 16+12 = 28
36x-2 + 34x+2 = 180 solve
Answer:
First, collect the like terms
36x+34x=180+2-2
Solve,
74x=180
x=180/74
2.43243243243
When you round it, it will be approximately,
x≅2.43
Step-by-step explanation:
I hope it helped please give me brainliest
Answer:
[tex]x = \frac{18}{7} [/tex]
Which of these is equivalent to 8: 5
3:4
3:7
4:2
4:3
Pls help
Answer:
I'm not 100% if its right but I think its 4:2.
Step-by-step explanation:
Answer:
the closest one i think is 4:3(dont get mad at me if its wrong)
Step-by-step explanation:
For football tryouts at a local school, 16 coaches and 44 players split into groups. Each group will have the same numbers of coaches and players. How many players will be in each group?
Answer:
11 players
Step-by-step explanation:
In a football tryouts at a local school there are 16 coaches and 44 players
Therefore spilliting then into group with similar numbers can be illustrated as follows
= 16/4
= 4 coaches each
= 44/4
= 11 players each
Hence sharing them into groups will result in 4 coaches and 11 players for each group
There are three fourth grades classrooms (A, B, and C) at the local elementary school. Room A contains 12 children, Room B contains 18, and Room C contains 24 children. All the fourth graders get together to play a game in the middle of the day. The teachers want the children to be on teams with their own classmates but all the teams also need to be of equal size. Can you find the largest size of the teams so that each team contains only children from the same classroom?
Answer:
The largest size of the teams would be 6 if you wanted all teams to be the same size and consist of only members from their own room.
Step-by-step explanation:
In order to solve this, you need to find the greatest common factor. The highest number that can go into 12, 18, and 24 evenly would be 6.
Answer:
2 teams of 6 for class A, 3 teams of 6 for class B. and 4 teams of 6 for class C
Step-by-step explanation:
We are given the total amount of students in each class. 12,18,24. In order to separate these we have to find the common denominator among all the classes total numbers. 6 is a common denominator between them all as we can break it down to the number thats most common. Take the total number of students in each class and divide it by six. That is the total number of groups to be equal among them all.
What is the mean of the following numbers? 24, 53, 63, 27, 87, 40
Answer:
49
Step-by-step explanation:
Add up all the numbers and divide by how many numbers there are.
Answer:
49
Step-by-step explanation:
the sum of all the numbers is 294
294÷6=49
PLS HELP!!
Find the value of x. Show any calculations used to find your answer.
========================================
Work Shown:
(small vertical)/(large vertical) = (small horizontal)/(large horizontal)
8/x = 16/40
8*40 = x*16 .... cross multiply
320 = 16x
16x = 320
x = 320/16 .... divide both sides by 16
x = 20
Note: there are other proportions you could set up such as 8/16 = x/40. The key here is that whatever equation you set up, it must cross multiply to 16x = 320 so that you get the same solution.
solve the equation
-4(x - 26) = -200
Answer:
x=76
Step-by-step explanation:
-4(x - 26) = -200
x-26=50
x=50+26
x=76
I hope this helped you! If it did, please consider rating, pressing thanks, and giving my answer 'Brainliest.' Have a great day! :)
Step-by-step explanation:
-4x+104=-200
-4x=-200-104
-4x=-304
x=-304÷(-4)
×=76
classify each number as an integer or a not integer
Answer:
can't really do that.
Step-by-step explanation:
whats the numbers lol
Answer:
0, -5, 3 = Integers 8.1, 1/2, =2.5 = Not an Integer
Step-by-step explanation:
Edge 2021
science pls answer I give brainliest
Answer:
I would say B
Step-by-step explanation:
Some inland areas can be warm but cold where-as some places near the coast stay warm most of the time
Find the slope I’m sorry I need help with this one I’m finding the answer but don’t understand it sorry
what is the locus of the tip of a minute hand of a watch
Answer:
The locus of the moving end of the minute hand of the clock will be a circle where radius will be the length of the minute hand
Hello help with question please :)
Answer:
A
Step-by-step explanation:
slope is (y2-y1)/(x2-x1)
anyhow that comes out to -3/2
the only place that actually applies is in A
Answer:
A
Step-by-step explanation:
6=-3/2×-2+3
6=3+3
6=6
-3=-3/2×4 + 3
-3=-6+3
-3=-3
