Place the three functions in order from the fastest decreasing average rate of change to the slowest decreasing average rate of change on the interval (0,3)
Answers
Answer:
g(x), f(x) and h(x)
Step-by-step explanation:
Given
Interval: (0,3)
See attachment for functions f(x), g(x) and h(x)
Required
Order from fastest to slowest decreasing average rate of change
The average rate of change is calculated as:
[tex]Rate = \frac{f(b) - f(a)}{b - a}[/tex]
In this case:
[tex](a,b) = (0,3)[/tex]
i.e.
[tex]a = 0\\b=3[/tex]
For f(x)
[tex]f(x) = 16(\frac{1}{2})^x[/tex]
[tex]Rate = \frac{f(b) - f(a)}{b - a}[/tex]
[tex]Rate = \frac{f(3) - f(0)}{3 - 0}[/tex]
[tex]Rate = \frac{f(3) - f(0)}{3}[/tex]
Calculate f(3) and f(0)
[tex]f(x) = 16(\frac{1}{2})^x[/tex]
[tex]f(3) = 16(\frac{1}{2})^3 = 16 * \frac{1}{8} = 2[/tex]
[tex]f(0) = 16(\frac{1}{2})^0 = 16 * 1 = 16[/tex]
So:
[tex]Rate = \frac{f(3) - f(0)}{3}[/tex]
[tex]Rate = \frac{2 - 16}{3}[/tex]
[tex]Rate = -\frac{14}{3}[/tex]
For g(x)
[tex]Rate = \frac{g(b) - g(a)}{b - a}[/tex]
[tex]Rate = \frac{g(3) - g(0)}{3 - 0}[/tex]
[tex]Rate = \frac{g(3) - g(0)}{3}[/tex]
From the table of g(x)
[tex]g(3) = 1[/tex]
[tex]g(1) = 27[/tex]
So:
[tex]Rate = \frac{1 - 27}{3}[/tex]
[tex]Rate = -\frac{26}{3}[/tex]
For h(x)
[tex]Rate = \frac{h(b) - h(a)}{b - a}[/tex]
[tex]Rate = \frac{h(3) - h(0)}{3 - 0}[/tex]
[tex]Rate = \frac{h(3) - h(0)}{3}[/tex]
From the graph of h(x)
[tex]h(3) = -3[/tex]
[tex]h(0) = 4[/tex]
So:
[tex]Rate = \frac{-3 - 4}{3}[/tex]
[tex]Rate = -\frac{7}{3}[/tex]
So, the calculated rates of change are:
[tex]f(x) = -\frac{14}{3}[/tex] [tex]= -4.67[/tex]
[tex]g(x) = -\frac{26}{3}[/tex] [tex]=-8.67[/tex]
[tex]h(x) = -\frac{7}{3}[/tex] [tex]=-2.33[/tex]
By comparison:
From the fastest decreasing to slowest, the order is: g(x), f(x) and h(x)
Answer: IN THIS ORDER!! g(x), f(x), h(x).
Related Questions
Emilio compra 3,6 kg de manzanas a 1,45 euros el kilo ¿Cuánto pagara por las manzanas?
Answers
Answer:
Emilio compra kg De manzanas a euros el kilo cuanto pagara por Las manzanas
Answer:
emilio compra de manzanas a euros el kilo cuanta pagara por las manzanas
Solve for n: 9^(n-1) = (1/3)^(4n-1) Show your work.
Answers
Answer:
n=1/2 after being simplified
Step-by-step explanation:
Use Division Distributive Property:
9^n-1=1/3^4n-1 then convert both sides to the same base
3^2(n-1) = 3^-(4n-1)
cancel the base of 3 on both sides
2(n-1) = -4n+1
then expand 2n-2=-4n+1
add 2 to both sides 2n=4n+1+2
simplify: -4n+1+2 to -4n+3
2n=-4n+3
add 4n to both sides: 2n+4n=3
simplify: 2n+4n to 6n
6n=3
divide both sides by 6
n=3/6
simplify and n=1/2
A crane cable can support a maximum load of 21,000 kg. If a bucket has a mass of 4,000 kg and gravel has a mass of 1,500 kg for every cubic meter, how many cubic meters of gravel (g) can be safely lifted by the crane? Enter any fractions as reduced improper fractions.
The crane can safely lift up to _____ cubic meters.
Answers
Answer:
k hh kn gigih ih jodoh Iin om i j OB yoh gih bogoh UB
D
100%
+
X
Which is the best estimate for V34 to the nearest whole number?
A. 36
ОО
B. 35
C. 17
O
O
D. 8
E. 6
Answers
Answer:
The answer would be B 35.
Step-by-step explanation:
34 is closest to 35.
BRAINLIST!!!! SHOW YOUR WORK!!!!
In the above figure, m∠P = 130° and m∠Q = (5x)°. If angles P and Q are supplementary angles, what are the value of x and the measure of angle Q?
A.
x = 62, m∠Q = 50°
B.
x = 44, m∠Q = 220°
C.
x = 10, m∠Q = 50°
D.
x = 10, m∠Q = 15°
Answers
Answer:
C x = 10 Q = 50
Step-by-step explanation:
supplemantary means adds to 180 deg.
so 130 + 5x = 180
5x = 50 = ang. Q
x = 50/5 = 10 deg.
30 POINTS ANSWER ASAP
Sal's Sandwich Shop sells wraps and sandwiches as part of its lunch specials. The profit on every sandwich is $2, and the profit on every wrap is $3. Sal made a profit of $1,470 from lunch specials last month. The equation 2x + 3y = 1,470 represents Sal's profits last month, where x is the number of sandwich lunch specials sold and y is the number of wrap lunch specials sold.
Change the equation to slope-intercept form. Identify the slope and y-intercept of the equation. Be sure to show all your work.
Describe how you would graph this line using the slope-intercept method. Be sure to write using complete sentences.
Write the equation in function notation. Explain what the graph of the function represents. Be sure to use complete sentences.
Graph the function. On the graph, make sure to label the intercepts. You may graph your equation by hand on a piece of paper and scan your work or you may use graphing technology.
Suppose Sal's total profit on lunch specials for the next month is $1,593. The profit amounts are the same: $2 for each sandwich and $3 for each wrap. In a paragraph of at least three complete sentences, explain how the graphs of the functions for the two months are similar and how they are different.
Answers
2x + 3y = 1470
3y = -2x + 1470
y = -2/3x + 490 is the equation in slope intercept form.
slope = -2/3
y intercept = 490
allso, can u mark brainlist
PLEASE HELP! I’m almost finished with this assignment if someone could answer these questions correctly I’ll give you Brainliest for saving me haha!
c. When a rational and an irrational number are added, is the sum rational or irrational?
Explain.
Type your response here:
d. When a nonzero rational and an irrational number are multiplied, is the product rational or
irrational? Explain.
Type your response here:
e. Which system of numbers is most similar to the system of polynomials?
Type your response here:
f. For each of the operations—addition, subtraction, multiplication, and division—determine
whether the set of polynomials of order 0 or 1 is closed or not closed. Consider any two
polynomials of degree 0 or 1.
Type your response here:
Answers
C. The sum of any rational number and any irrational number will always be an irrational number.
Explanation: Each time they assume the sum is rational; however, upon rearranging the terms if their equation, they get a contradiction (that an irrational number is equal to a rational number). Since the assumption that the sum of a rational and irrational number is rational leads to a contradiction, the sum must be irrational.
Answer:
D. Any nonzero rational number times an irrational number is irrational.
Explanation: Assume r is nonzero and rational, and x is irrational. If rx = q, and q is rational, then x = q/r, which is rational. This is a contradiction.
Answer:
E. The system of polynomials is almost the same with the system of whole numbers.
Explanation: We count with and use a base 10 (decimal) system. Polynomials such as the function above are a “base x” system.
Answer:
F. Addition, subtraction, and multiplication would all be closed because every answer would be a polynomial. Division is not closed because when we divide numbers, sometimes they don’t divide evenly, leaving us with a remainder, which we can write as a fraction.
Explanation: (in answer)
I hope this at least semi helps!
For my Homework tomorrow
Answers
0.8% of 150 is what numbers and how do you write the equation with a variable in it.
Answers
Answer:
1.2
Step-by-step explanation:
1. First, we have to write an equation with a variable! Given 0.8%, we know that it's equal to (0.8/100), and "of" means to multiply. Therefore, the equation will looks like this: [tex]\frac{0.8}{100} * 150 = x[/tex]
2. Now, let's solve for x!
[tex]\frac{0.8}{100} * 150 = (0.008)(150)[/tex] [tex](0.008)(150) = \frac{6}{5}[/tex] [tex]\frac{6}{5} = 1\frac{1}{5}[/tex] [tex]1\frac{1}{5} = 1.2[/tex] [tex]1.2[/tex]Therefore, 0.8% of 150 is 1.2!
Diberi f-'(x) = x # m dan g(x) = 1 + x, cari
(a) f(x) dalam sebutan , 11 - 1
b) nilai h jika ff-'(12 - 2) = 8[(1 – h)?].
Answers
I dont know it sorry. im only a 6th grader :p
Find the measure of the angle plz help
Answers
Answer:
Please give a picture
Step-by-step explanation:
Answer:
what do i measure?????????
Step-by-step explanation:
Weight of Male Dogs (Ib.)
The most appropriate measure of center for this
data is the median
4
5
COMPLETE
5
0
2.
8
00
Which statement about the data is true?
6
N
2
8
7
2
8
O The mean is greater than the median.
O The mean is equal to the median.
The mean is less than the median.
8
1
9
on
5
DONE
8|1 means 81
Answers
Answer:
65
Step-by-step explanation:
45, 50, 52, 58, 62, 68, 72, 78, 81, 95
62 + 68 = 130/2 = 65
The median is 65
The median of the weight of the male dogs is M = 65 lb
What is Median?The median is the value that's exactly in the middle of a data set when it is ordered. It's a measure of central tendency that separates the lowest 50% from the highest 50% of values. The steps for finding the median differ depending on whether you have an odd or an even number of data points
Arrange the data points from smallest to largest.
If the number of data points is odd, the median is the middle data point in the list.
If the number of data points is even, the median is the average of the two middle data points in the list.
Given data ,
Let the weights of the male dogs be represented as set A
where the value of A is
Set A = { 45, 50, 52, 58, 62, 68, 72, 78, 81, 95 }
On simplifying , we get
The number of terms = 10
So , the median M = ( 62 + 68 ) / 2
The median M = 130/2 = 65 lb
where the mean is C = 66.1 lb
Hence , the median is M = 65 lb
To learn more about median click :
https://brainly.com/question/28687994
#SPJ7
This is due in 20 minutes, help, please.
Sergio spent $65 at the gas station. He paid $3 per gallon for gas and $7 on candy and soft drinks. How many gallons of gas did Sergio buy?
Write a algebraic equation for the word problem above.
Question 1 options:
3 + 7 + g = 65
65 + g = 7
7g + 3 = 65
3g + 7 = 65 (What I chose)
Question 2
Write an algebraic equation for the word problem below.
How old am I if 226 reduced by three times my age is 133?
Question 2 options:
3a - 226 = 133
226 - 3a = 133 (My answer)
133 - 3a = 226
3a - 226 = 133
Question 3
rite an algebraic expression for the word problem below.
The sum of three consecutive numbers is 72. What are the three numbers?
Question 3 options:
3n = 72
1 + 2 + 3 = 72
a + b + c = 72
n + (n + 1) + (n + 2) = 72 (My answer)
Question 4
Write an equation for the word problem below.
It costs $5 plus $2 per mile to ride in a taxi. Hannah took a taxi from her house to school this morning. She paid the taxi driver $25 when she got to the school. How many miles is it from Hannah's house to her school?
Question 4 options:
2m + 5 = 25
5m - 2 = 25
25 + 2m = 5
5m + 2m = 25 (My answer)
Question 5 (Unsure if I'm correct)
rder the steps for writing an algebraic equation from real life word problems.
Question 5 options:
2
Identify all the important information
3
Define the variable
4
Write an equation using the important information and the variable
1
Read through the entire problem
Answers
Answer:
1) You were right
2) Also correct
3) Again, correct
4) Wrong, the correct answer is 2m + 5 = 25
5) Correct
Step-by-step explanation:
1) Sergio spent a total of 65 dollars at the gas station. He spent 3 dollars per gallon and 7 on snacks.The equation will be:
3g + 7 = 65
2) 226 reduced by ( - ) 3 times your age ( 3a ) is ( = ) 133?
226 - 3a = 133
3) The sum of three consecutive numbers is 72.
n + ( n + 1 ) + ( n + 2 ) = 73
4) It cost 5 plus 2 per mile.The total spent was 25
2m + 5 = 25
5)
1. Read the entire problem.
2. Identify all the important info.
3. Define the variable
4. Write an equation using the important information and the variable
Seven people went to the movies. The
number of adults was one more than the
Children. Write a system of equations that
represents the number of adults and child-
ren. Solve the system algebraically.
Answers
Answer:
3 kids, 4 Adults
Step-by-step explanation:
x = kids
y = adults
Total = 7
x + y = 7
y = x + 1
do a bit of solvin, too much to type lol
2x = 6
x = 3
And since X = 3 and Y = X + 1
Y = 3 + 1 = 4
Given the following sets.
A = (0, 1, 2, 3}
B =[a, b, c, d)
C = (0, a, 2, b}
Find A n C.
O [0, 2}
O [a, b, c, d)
O [0, 1, 2, 3)
O empty set
O (0, a, 2, b)
Answers
find AnC
given,
A=(0,1,2,3)
C=(0,a,2,b)
now,
AnC=(0,1,2,3)n(0,a,2,b)
AnC=(0,2)ans.
Please I need help I am so lost
Answers
Answer:
[tex] \sqrt{ \frac{25}{64} } \\ \\ \frac{ \sqrt{25} }{ \sqrt{64} } \\ \\ 25 \: equal \: to \: 5 {}^{2} \\ and \: 64 \: equl \: to \: 8 {}^{2} \\ \frac{ \sqrt{5 {}^{2} } }{ \sqrt{8 {}^{2} } } \\ = \frac{5}{8} [/tex]
so its + or - 5/8
Have a great day
Can I get help on 1,2 and 5?
Answers
Answer:
Question 1: [tex]x=4[/tex]
Question 2: [tex]x= \pm7[/tex]
Question 5: The dimensions of one face of the container are 6 by 6 inches.
Step-by-step explanation:
Hi there!
Question 1
[tex]x^3=64[/tex]
Rewrite 64 as a power of 3:
[tex]x^3=4^3[/tex]
(We could find that 4³ = 64 through trial and error)
This above equation makes it true that x=4. If aⁿ = bⁿ, then a=b:
[tex]x=4[/tex]
Question 2
[tex]x^2=49[/tex]
Rewrite 49 as a power of 2:
[tex]x^2=7^2[/tex]
Again, we could have found this through trial and error, or by looking at our multiplication tables.
[tex]x=7[/tex]
However, remember that positive and negative numbers will all square to be a positive number. So, therefore, x can be -7 OR 7 (since both, when squared, equal 49):
[tex]x= \pm7[/tex]
Question 5
Let x be equal to the length of one edge of the cube.
Volume of a cube formula: [tex]V=x^3[/tex]
Plug in the given information, when V is the volume:
[tex]216=x^3[/tex]
Rewrite 216 as a power of 3:
[tex]6^3=x^3[/tex]
^ We could have found this through trial and error.
[tex]x=6[/tex]
Therefore, the dimensions of one face of the container are 6 by 6 inches.
I hope this helps!
Heather cut 2 feet of tape. How much is this in inches?
Use the table below. Include the correct unit in your answer.
Unit Symbol Fact
Length inch in
foot ft
1ft = 12in
yard yd
1yd = 3ft
Answers
Answer: 24 inches.
Step-by-step explanation: since theres 12 inches in a foot, and 2 feet altogether, you would multiply 12x2.
Multiply the binomials: (x+6)•(x-8)
Answers
Answer:
[tex]\sf x^2-2x-48[/tex]
Step-by-step explanation:
[tex]\begin{aligned} &\sf (x+6)(x-8) \\=&\sf x^2-8x+6x-48 \\=&\boxed{\sf x^2-2x-48} \end{aligned}[/tex]
Determine the place value of the digit 3 in the whole number. 30,500,421
Answers
Answer:
30,000,000 or Thirty million -------> Ten millions place
Step-by-step explanation:
Hope this helps!
[DUE TOMORROW] Answer using steps: A truck sprang a leak in its radiator, which held 480 ounces of fluid when it started to leak. Assuming the truck continues at 35 mph and it’s radiator leaks 4 ounces of fluid per minute, how many miles will the truck travel before the radiator is empty
Answers
Answer
It will make it 70 miles because it leaks 4 ounces every minute so divide 480 by 4 and get 120 with would be for how many minutes you would be able to drive with the leak. So convert minutes to hours and you get 2 hours and every hour you go 35 miles so multiply 35 by 2 and you get 70.
52 divided by 91, find the quotient then write the remainder as a decimal.
Answers
Answer:
The answer to 52 divided by 91 calculated using Long Division is:
0
52 Remainder
Step-by-step explanation:
please help i need this done soon!!
Answers
Answer:
f(2) = -2
Step-by-step explanation:
plug in 2 to wherever x is in this statement:
f(2) = -2(2^2) - 2(2) + 10
f(2) = -2(4) - 4 + 10
f(2) = -8 - 4 + 10
f(2) = -2
-2(4) -2(2) +10
-8 -4 +10
=-2
100 Points and I WILL mark brainliest for first correct answer.
Someone do this again bc I'm confused!
Use the mapping (x+3, y-5), for the transformation of triangle ABC with vertices A (-2, -4), B (0, 0), and C (1, -3), find the coordinates of the new triangle A’B’C’. You must show all your work.
Answers
Answer:
A(1,-9), B(3,-5),C(4,-8)
Step-by-step explanation:
what is the square root of 50?
Answers
Answer:
7.07
Step-by-step explanation:
Step-by-step explanation:
7.07
or
7.07106781187
enjoy thanks brainliest??
and yes enjo :)
thank you!! Please show your work!
Answers
Answer:
C: 1 1/5 miles per hour
Step-by-step explanation:
if you travel 3/5 miles in 1/2 of an hour then you multiply 1/2 and 3/5 by 2 to get how much you traveled in an hour which you get 1 1/5
A family room has a circular rug with a diameter of 4 meters. What is the rug's circumference? Use 3.14 for . meters
Answers
The diameter is the same as 2r.
So to find the circumference of the rug, we use Pi * 4.
If Pi = 3.14, then the circumference of the rug will be 12.56m.
what is the value of c such that the line y=2x+3 is tangent to the parabola y=cx^2
Answers
The value of [tex]c[/tex] such that the line [tex]y = 2\cdot x + 3[/tex] is tangent to the parabola [tex]y = c\cdot x^{2}[/tex] is [tex]-\frac{1}{3}[/tex].
If [tex]y = 2\cdot x + 3[/tex] is a line tangent to the parabola [tex]y = c\cdot x^{2}[/tex], then we must observe the following condition, that is, the slope of the line is equal to the first derivative of the parabola:
[tex]2\cdot c \cdot x = 2[/tex] (1)
Then, we have the following system of equations:
[tex]y = 2\cdot x + 3[/tex] (1)
[tex]y = c\cdot x^{2}[/tex] (2)
[tex]c\cdot x = 1[/tex] (3)
Whose solution is shown below:
By (3):
[tex]c =\frac{1}{x}[/tex]
(3) in (2):
[tex]y = x[/tex] (4)
(4) in (1):
[tex]y = -3[/tex]
[tex]x = -3[/tex]
[tex]c = -\frac{1}{3}[/tex]
The value of [tex]c[/tex] such that the line [tex]y = 2\cdot x + 3[/tex] is tangent to the parabola [tex]y = c\cdot x^{2}[/tex] is [tex]-\frac{1}{3}[/tex].
We kindly invite to check this question on tangent lines: https://brainly.com/question/13424370
Translate the sentence into an equation.
Two more than the quotient of a number and 4 equals 8.
use the variable c for the unknown number.
Answers
Step-by-step explanation:
2 + c/4 = 8
2 more than the quotient of equals 8
a number and 4
please help me
please I will make you brainliest
Answers
[tex]\\ \sf\longmapsto a+\dfrac{1}{a}=\sqrt{3}[/tex]
[tex]\\ \sf\longmapsto \left(a+\dfrac{1}{a}\right)^3=\sqrt{3}^3[/tex]
[tex]\\ \sf\longmapsto a^3+\dfrac{1}{a^3}+\dfrac{3a^2}{a}+\dfrac{3a}{a^2}=3\sqrt{3}[/tex]
[tex]\\ \sf\longmapsto a^3+\dfrac{1}{a^3}+3a+\dfrac{3}{a}=3\sqrt{3}[/tex]
[tex]\\ \sf\longmapsto a^3+\dfrac{1}{a^3}=3\sqrt{3}-3a-\dfrac{3}{a}[/tex]
[tex]\\ \sf\longmapsto a^3+\dfrac{1}{a^3}=3\left(\sqrt{3}-a-\dfrac{1}{a}\right)[/tex]
[tex]\\ \sf\longmapsto a^3+\dfrac{1}{a^3}=3(0)[/tex]
[tex]\\ \sf\longmapsto a^3+\dfrac{1}{a^3}=0[/tex]
ProvedAnswer:
Tn=a+(n−1)d, where a= First term, d= Difference between terms ... (2)
Equating (1) and (2)
6n+5=a+(n−1)d
6n+5=a+nd−d ..... (3)
Equating n terms:6n=nd
d=6 ...... (4)
Substituting (4) in (3)
6n+5=a+6n−6
5=a−6
a=11 ..... (5)
Now
Sn=2n(2a+(n−1)d)
Sn=2n(a+Tn) ....... (6)
Substituting (1) and (5) in (6)
Sn=2n(11+6n+5)
Sn=2n(16+6n)
Sn=n(8+3n)
Tn=a+(n−1)d, where a= First term, d= Difference between terms ... (2)
Equating (1) and (2)
6n+5=a+(n−1)d
6n+5=a+nd−d ..... (3)
Equating n terms:6n=nd
d=6 ...... (4)
Substituting (4) in (3)
6n+5=a+6n−6
5=a−6
a=11 ..... (5)
Now
Sn=2n(2a+(n−1)d)
Sn=2n(a+Tn) ....... (6)
Substituting (1) and (5) in (6)
Sn=2n(11+6n+5)
Sn=2n(16+6n)
Sn=n(8+3n)
Tn=a+(n−1)d, where a= First term, d= Difference between terms ... (2)
Equating (1) and (2)
6n+5=a+(n−1)d
6n+5=a+nd−d ..... (3)
Equating n terms:6n=nd
d=6 ...... (4)
Substituting (4) in (3)
6n+5=a+6n−6
5=a−6
a=11 ..... (5)
Now
Sn=2n(2a+(n−1)d)
Sn=2n(a+Tn) ....... (6)
Substituting (1) and (5) in (6)
Sn=2n(11+6n+5)
Sn=2n(16+6n)
Sn=n(8+3n)