Consider the quadratic function shown in the table below. x y 0 0 1 3 2 12 3 27 Which exponential function grows at a faster rate than the quadratic function for 0< x < 3?
Answers
So values are
(0,0)(1,3)(2,12)(3,27)The rule is
3/1=312/2=627/3=9Explicit formula
x(3x) where x is set of integersEquation here is
y=3x²Answer:
[tex]f(x)=4^x[/tex] grows at a faster rate than the given quadratic function.
Step-by-step explanation:
Given table:
[tex]\large \begin{array}{| c | c |}\cline{1-2} x & y \\\cline{1-2} 0 & 0 \\\cline{1-2} 1 & 3 \\\cline{1-2} 2 & 12 \\\cline{1-2} 3 & 27 \\\cline{1-2}\end{array}[/tex]
First Differences in y-values:
[tex]0 \overset{+3}{\longrightarrow} 3 \overset{+9}{\longrightarrow} 12 \overset{+15}{\longrightarrow} 27[/tex]
Second Differences in y-values:
[tex]3 \overset{+6}{\longrightarrow} 9 \overset{+6}{\longrightarrow} 15[/tex]
As the second differences are the same, the function is quadratic.
The coefficient of [tex]x^2[/tex] is always half of the second difference.
Therefore, the quadratic function is:
[tex]f(x)=3x^2[/tex]
The average rate of change of function f(x) over the interval a ≤ x ≤ b is given by:
[tex]\dfrac{f(b)-f(a)}{b-a}[/tex]
Therefore, the average rate of change for [tex]f(x)=3x^2[/tex] over the interval
0 ≤ x ≤ 3 is:
[tex]\textsf{Average rate of change}=\dfrac{f(3)-f(0)}{3-0}=\dfrac{27-0}{3-0}=9[/tex]
An exponential function that grows at a faster rate than [tex]f(x)=3x^2[/tex] over the interval 0 ≤ x ≤ 3 is [tex]f(x)=4^x[/tex]
[tex]\large \begin{array}{| c | c | c | c | c |}\cline{1-5} x & 0 & 1 & 2 & 3 \\\cline{1-5} f(x)=4^x & 1 & 4 & 16 & 64\\\cline{1-5} \end{array}[/tex]
[tex]\textsf{Average rate of change}=\dfrac{f(3)-f(0)}{3-0}=\dfrac{64-1}{3-0}=21[/tex]
As 21 > 9, [tex]f(x)=4^x[/tex] grows at a faster rate than [tex]f(x)=3x^2[/tex] over the interval 0 ≤ x ≤ 3.
Related Questions
21. The solution(s) is/are b =
Please help me solve this
Answers
Answer:
b = -4, 0
Step-by-step explanation:
Given :
b² + 4b = 0Take b as a common factor.
b(b + 4) = 0Solutions
b = 0b + 4 = 0 ⇒ b = -4b = -4, 0Answer:
b = - 4, b = 0
Step-by-step explanation:
b² + 4b = 0 ← factor out b from each term
b(b + 4) = 0
equate each factor to zero and solve for b
b = 0
b + 4 = 0 ⇒ b = - 4
Last school year, trent kept track of the amount of time he spent on homework each night. this box plot shows the results. time spent on homework (min.) 20 40 60 80 100 120 what percent of the time did trent spend at least 80 minutes on homework?
Answers
The percentage of time spend at least 80 minutes on homework will be 66.66%.
What is the percentage?The Percentage is defined as representing any number with respect to the 100. It is denoted by the sign %.
Given that:-
The time he spent on homework each night. this box plot shows the results.
The time spent on homework (min.) 20 40 60 80 100 120.
The percentage will be calculated as:-
Maximum time spent = 120 minutes
The percentage for 80 minutes of homework will be:-
= 120 / 80
= 0.66=66 = 66.66%
Therefore the percentage of time spend at least 80 minutes on homework will be 66.66%.
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Answer: 25%
Step-by-step explanation:
need help on this geometry problem
Answers
Mona's bank charges a $10 fee per month plus a $0.12 fee per check. The formula below gives f, the total fee in dollars for a month in which Mona writes n checks.
f=10+0.12n
How many checks did Mona write during a month in which her total fee was $12.52?
Answers
Answer: Mona wrote 21 checks during a month where her total fee was $12.52
Step-by-step explanation:
f = 10 + 0.12n
12.52 = 10 + 0.12n
[tex]\frac{2.52}{0.12}[/tex] = [tex]\frac{0.12n}{0.12}[/tex]
n = 21
Mona wrote 21 checks during a month where her total fee was $12.52
Two runners are saving money to attend a marathon. the first runner has $112 in savings, received a $45 gift from a friend, and will save $25 each month. the second runner has $50 in savings and will save $60 each month. which equation can be used to find m, the number of months it will take for both accounts to have the same amount of money? 112 – 25m 45 = 50 – 60m 112 25 45m = 50m 60 112 25 – 45m = –50m 60 112 25m 45 = 50 60m
Answers
The equation that we need to solve is:
$157 + $50*m = $50 + $60*m
And the solution is m = 10.7 months.
Which equation models the situation?For the first runer we have a initial amount of $112 + $45 = $157 plus $50 per month, so we can write:
f(m) = $157 + $50*m
And the second runner has an initial amount of $50 and saves $60 per month, so we can write the linear equation:
g(x) = $50 + $60*m
They will have the same amount of money when:
f(x) = g(x)
$157 + $50*m = $50 + $60*m
$107 = $10*m
$107/$10 = m = 10.7
So, after 10.7 months, both accounts will have the same money.
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HELP PLS I'LL MARK U BRAINLISTT
Answers
Answer:
KM = 7
LM = 7
KL = 11
Step-by-step explanation:
Isosceles triangles have 2 congruent sides (in this case they are KM and LM
This means 4d-13 = 12-d
We can now solve for d
4d-13 = 12-d | add d to both sides
5d-13 = 12 | add 13 to both sides
5d = 25 | divide both sides by 5
d = 5
Now we can solve for the 3 sides of triangle KLM
KM = 7
LM = 7
KL = 11
That is your answer
- Kan Academy Advance
somebody please help me?
Answers
Answer:
Step-by-step explanation:
Comment
There are 9 marbles all together.
2 are green4 are red3 are blueThe important fact is that he draws 1 marble to begin with and does not replace it. That means that the next marble is out of 8.
Solution
First marble: Blue = 3/9 = 1/3
Second marble: Green 2/8 = 1/4
The probability of that happening is
P(blue,Green) = 1/3 * 1/4 = 1/12
Answer P(blue, green) = 1/12
If n is an integer, what is the possible value of n for which 1,116n is the square of an integer? Explain.
E. 24
F. 28
G. 31
H. 33
Answers
Answer:
G.31
Step-by-step explanation:
when n = 31
1116n = 1116*31 = 34596
34596 is square of 186.
= 186^2
= 34596
and other values (24,28,33) of n does not give square during 1,116n but 31 gives.
Hence, 31 is the possible value of n for which 1,116n is the square of an integer(186).
What is the longest line segment that can be drawn in a right rectangular prism that is 14cm long, 13cm wide, and 11cm tall?
Answers
The longest line segment that can be drawn in a right rectangular prism that is 14cm long, 13cm wide and 11cm tall is 19.1cm.
What is a right rectangular prism?A right rectangular prism is a three dimensional solid shape formed by 6 rectangles.
it is also called the cuboid.
Analysis:
The diagonal of the face of the prism with dimensions 14cm long and 13cm wide is the longest line segment that can be drawn.
Since rectangles have 90° on each vertex, we can use Pythagoras theorem to calculate for the length of the diagonal.
[tex](diagonal)^{2}[/tex] = [tex](length)^{2}[/tex] + [tex](width)^{2}[/tex]
[tex](diagonal)^{2}[/tex] = [tex](14)^{2}[/tex] + [tex](13)^{2}[/tex]
= 196 + 169 = 365
[tex](diagonal)^{2}[/tex] = 365
diagonal = [tex]\sqrt{365}[/tex] = 19.1cm
In conclusion, the length of the longest diameter is 19.1cm
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What is the slope of a line that goes through (2, -2) and (5, 6)
8/3
4/3
3/4
3/8
Answers
Answer:
correct option is A i.e. 8/3
Here is a list of Numbers:
8 7 12 7 11 10 7 12
Find:
a) median
b) range
c) mode
Answers
The median, mode and range of the numbers are 9, 5 and 7 respectively.
How to find median, range and mode?
The median is the middle number when the data is arranged in ascending order.
Therefore,
7, 7, 7, 8, 10, 11, 12, 12
median = 8 + 10 / 2 = 18 / 2 = 9
median = 9
The range is the largest number minus the smallest number.
Therefore,
range = 12 - 7 = 5
range = 5
The mode is the number that appears most. Therefore,
mode = 7
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Mrs. gellar works at a diner. at the end of
her shift, she was putting away pies in the
display case. there were 5 pies, and of 3/8
each pie left. what fraction of the pies did
mrs. gellar put away?
Answers
please hepl will give brainly, 30 points
Answers
Answer:
∠G = 53°
∠H = 90°
∠I = 37°
Step-by-step explanation:
∠H = 90° because it is a right angle and all right angles = 90°
The sum of all angles in a triangle = 180°
∠H + ∠G + ∠I = 180°
90° + (5x - 7)° + (3x + 1)° = 180°
5x - 7 + 3x + 1 = 90° Subtract 90° from both sides
8x - 6 = 90 Adding like terms
8x = 96 Adding 6 to both sides
x = 12 Dividing both sides by 8
Now solve for ∠G and ∠I using 12 as the value for x
∠G = (5x - 7)° ∠I = (3x + 1)°
∠G = 5·12 - 7 ∠I = 3·12 + 1
∠G = 53° ∠I = 37°
find the probability of a freshman being called on in class if there are 12 sophomores, 10 juniors, 14 seniors, and 8 freshmen.
Answers
Answer:
18%
Step-by-step explanation:
8/44
Answer:
18% or 8/44
Step-by-step explanation:
add 12+10+14+8=44 then do 8/44
6) What will be the new position of the given
point (0, 6) after translation of 6 units down
and 3 units right?
a) (6, 3)
b) (3, 0)
c) (-6, 3)
d) (-3,0)
Please help omg
Answers
Translating 6 units down - 6-6=3
Translating 3 units right - 0+3=3
A rectangular plot measures 140m by 20m find the area in ares
Answers
Answer:
28ares
Step-by-step explanation:
that's the correct way.i hope you will understand it. if there's any question feel free to ask. nice day.
Riya's biking app says that she rides at a speed of 5 miles per hour.
At this speed, how far does Riya ride in 1 hour?
At this speed, how far does Riya ride in 3 hours?
Write an equation for the relationship between Riya's distance biked, d,and time t
Answers
Answer:
Step-by-step explanation:
Formula
d = speed * time
d = s * t
Givens
t = 1 hour
t2 = 3 hours
s = 5 miles / hour
Solution
t = 1 hour
d = s * t
d = 5 mph * 1 hour
d = 5 miles
t = 3 hours
d = s * t
d = 5 miles / hour * 3 hours
d = 15 miles
Answer
d = s * t
d = 5 miles
d = 15 miles
I'm in 7th grade and am doing high school math! Help!
Answers
Answer:
Step-by-step explanation:
(x - 5)(x + 2) = 0
x - 5 = 0
x = 5
x + 2 = 0
x = -2
x = 5, -2
please help me answer this question
Answers
Answer:
The answer is21
can someone help me pls
Answers
Answer:
90
Step-by-step explanation:
Formula : 180 ( n - 2 ) / n n being the amount of sides
180 ( 4 - 2 ) / 4 = 90
What is the equation?
Answers
There is no answer? So how am I supposed to answer it?
Answer:
Yeah How am I supposed to answer it?
Step-by-step explanation:
Multiply.
(−8)⋅(−15)⋅(4)
Enter your answer in the box.
Answers
Answer:
la respuesta es 480
Step-by-step explanation:
(-8)(-15)=8*15=120
120*(4)
480
(-8)*(-15)*(4)=480
Step-by-step explanation:
(-8)*(-15)*(4)=480
You are in charge of purchasing breakfast for an upcoming service activity involving about 50 people.
You have the choice to pick one of the following food items:
donuts ($0.30/each)
muffins ($0.50/each)
bagels ($0.40/each)
You have the choice to pick one of the following drinks:
individual cartons of milk or chocolate milk ($0.50/each)
individual bottles of orange juice or apple juice ($0.75/each)
You must stay within a budget of $100.
Write the following in your notebook.
What food item did you choose? What drink did you choose? Why?
Write an inequality to represent the cost of the items (less than or equal to $100) in standard form. Use x to represent the number of food items and y to represent the number of drinks.
Solve the inequality for y (slope-intercept form). Interpret the slope in context of the drinks and food items that are being purchased.
Graph the inequality and describe your graph and the process you used; for example, is your line dotted, solid, or shaded up or down? What does the shaded region represent?
What are the x and y-intercepts? Explain what these would represent in this situation.
What are the domain and range in this problem? Explain why you would or would not use the minimum and maximum values of the domain and range. How are the domain and range in the context of this problem different from the domain and range of any linear equation? What are the limits?
Answers
The limits of the domain and the range are 0 to 200, respectively; and you would use the minimum and maximum values of the domain and range because the graph of the inequality uses a solid line.
The items chosenThe items selected here could be any of the listed drinks and food items.
To solve this question, we use the following selection:
Muffins ($0.50/each) -- xindividual cartons of milk or chocolate milk ($0.50/each) -- yBudget of $100The inequality of the cost of itemsIn this case, we use the less than or equal to inequality.
So, we have:
0.5x + 0.5y ≤ 100
Solve the inequality for y (slope-intercept form).In (b), we have:
0.5x + 0.5y ≤ 100
Subtract 0.5x from both sides
0.5y ≤ -0.5x + 100
Divide through by 0.5
y ≤ -x + 200
This means that the slope is -1, and it means that for every food item bought, there is a decrement of 1 in the drink.
The graph of the inequalitySee attachment for the graph of the inequality
The features of the graph include
Straight and solid lineIt is shaded downThe shaded region represents the acceptable solutionsWhat are the x and y-intercepts?From the attached graph, we have:
x-intercept = 200y-intercept = 200This means that you can buy 200 food items, when you buy no drinks or buy 200 drinks when you buy no food item
What are the domain and range in this problem?These are the acceptable x and y values of the graph.
From the attached graph, we have:
Domain: 0 ≤ x ≤ 200Range: 0 ≤ y ≤ 200The domain and range are different from the domain and range of any linear equation because the domain and the range of a linear equation is the set of all real numbers, while this domain and range are limited to 0 to 200
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Mr. Edwards surveyed a total of 80 students in his first three classes in order to determine the numbers of students that have pets. Out of the 30 students in his 1st period class, 12 have no pets. Eighteen of the 27 students in his 2nd period class do have pets. Fourteen of the students in his 3rd period class do have pets. Construct a two-way table summarizing the data. Write the answers as whole numbers.
Answers
Answer:
the numbers of students that have pets 44
Step-by-step explanation:
help please!! ⬇️⬇️
find the volume
Answers
What is the equation of a line that has an x-intercept of 5 and a slope of 4?
Answers
Answer:
y=4x-20
Explanation:
Since we already have a slope, all we need to do is just find the y-intercept. To do this we can make an XY t-chart.
Using the chart we can see that for every x that decreases, a y decreases 4 times. So if we subtract 5 from x, we will multiply 5 times y. Note that this graph is increasing so the y-intercept is negative. -5 · 4 = -20
X | Y
6 | 4
5 | 0
0 | -20
Hope this Helps!
Monica walks 2 miles each day Monday through Friday. She walks 3 miles on Saturday. She does not walk on Sunday. Monica calculates that she will have walked 127 miles after 29 weeks.
What is an estimate for the number of miles that Monica will have walked after 29 weeks? Is her original calculation reasonable?
A: 137; her original calculation is reasonable
B: 145; her original calculation is not reasonable
C: 310; her original calculation is reasonable
D: 390; her original calculation is not reasonable
Answers
Answer:
390, since the answer I got was 377, and we are estimating so that’s the best estimate.
WILL GIVE 100 POINTS TO WHO ANSWERS THESE!!! Questions in Pictures.
Polynomials and Factoring
Answers
Assuming that you want the product of the two factors given in each problem:
⇒ we solve this problem by timing each unit of a factor to every unit
of the other factor
⇒then add each one of them who shares a common like-term
⇒to get the answer
Let's solve:
Question 9:[tex](4m+n)(m-2n)=4m*m+(-2n)*4m+n*m+n(-2n)\\=4m^2-7nm-2n^2[/tex]
Question 12[tex](2a-4b)(7a-2b)=2a*7a+(-2b)(2a)+(-4b)7a+(-4b)(-2b)\\=14a^2-4ab-28ab+8b^2\\=14a^2-32ab+8b^2[/tex]
Question 15[tex](4m+1)^2=(4m+1)(4m+1)=4m*4m+4m*1+1*4m+1\\=16m^2+4m+4m+1\\=16m^2+8m+1[/tex]
Question 18[tex](2w+1)(2w-1)=2w*2w+2w(-1)+1*(2w)+1(-1)\\=4w^2-1[/tex]
Question 21:[tex](m+3)(m^2+4m+7)\\=m*m^2+m*4m+m*7+3m^2+3*4m+3*7\\=m^3+4m^2+7m+3m^2+12m+21\\=m^3+7m^2+19m+21[/tex]
Question 24:[tex](3x+2)(5x^2-12x-2)\\=3x*5x^2+3x(-12x)+3x(-2)+2(5x^2)+2(-12x)+2(-2)\\=15x^3-36x^2-6x+10x^2-24x-4\\=15x^3-26x^2-30x-4[/tex]
Hope that helps!
Samuel bought an 8-ounce bag of lettuce and a 1-pound bag of carrots. what is the total weight of the lettuce and carrots in ounces?
Answers
Answer:
the answer is 10z
Step-by-step explanation:
7+1=8
8+2=10
10z
Select the correct answer from each drop-down menu.
Three students used factoring to solve a quadratic equation.
x²+17x+72=12.
Jordan's Solution x² + 17x + 72 = 12, (x + 8)(x + 9)= 12, x+8=12 & x+9=12
Keith's Solution x² + 17x + 72 =12, x² + 17x +60 =0, (x +5)(x +12) =0 x + 5 = 0 & x + 12 =0.
Randall's Solution x² +17x +72 = 12,x2 +17x = -60,x(x +17) = -60, -60 & x +17 = -60.
he equation was solved correctly by ____. The solutions of the equation are____.
Answers
Answer:
Keith's Solution-5-12Step-by-step explanation:
x + 5 =0 & x + 12 =0
:- x = -5 & -12