There are two points of inflection in the graph of f(x).
Option B is the correct answer.
What is a function?A function has an input and an output.
A function can be one-to-one or onto one.
It simply indicated the relationships between the input and the output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
To find the inflection points of a function, we need to find its second derivative and set it equal to zero.
So,
Let's start by finding the first and second derivatives of f(x).
First, we find the first derivative of f(x).
f'(x) = 15[tex]x^4[/tex] + 8x³ - 260x² - 5x²
Then,
We find the second derivative of f(x):
f''(x) = 60x³ + 24x² - 520x - 10x
Next, we set f''(x) equal to zero and solve for x.
60x³ + 24x² - 520x - 10 = 0
10 (2x² - 13x - 1) = 0
2x² - 13x - 1 = 0
Now,
Using the quadratic formula,
we find the roots of this equation:
x = (13 ± √(13² + 8))/4
x = 13 ± √177) / 4
x = (13 + √177)/4 and x = )13 - √177)/4
x = 2.22 and x = -0.23
Therefore,
There are two points of inflection in the graph of f(x).
Learn more about functions here:
https://brainly.com/question/28533782
#SPJ5
If f(x) = 5x + 6 and g(x) = x + 5, what is (fºg)(31)?
Consider the line y=−4x+2.
Find the equation of the line that is perpendicular to this line and passes through the point , (−3,5).
Find the equation of the line that is parallel to this line and passes through the point , (−3, 5).
equation of perpendicular line:
equation of parallel line:
Answer and step by step esplanation:
The perpendicular line has the slope opposite and inverse, in our case [tex]-4 \rightarrow +\frac14[/tex]
Line passing through the point will have then equation - using the point-slope form [tex]y-y_0=m(x-x_0)[/tex]
[tex]y-5=\frac14 (x-(-5))\\y-5=\frac14(x+5)[/tex]
The parallel line will have the same slope as the given line, in our case -4. Again with the point-slope equation:
[tex]y-5=-4(x-(-5)\\y-5=-4(x+5)[/tex]
Answer:
Perpendicular: y = 1/4x + 5 3/4
Parallel: y = -4x - 7
Step-by-step explanation:
Hello!
A perpendicular line would have a negative reciprocal slope, meaning you flip the sign of the slope, and the numerator and denominator.
Perpendicular LineGiven our equation: y = -4x + 2, we can find the perpendicular slope by finding the negative reciprocal:
-44 -> negative1/4 -> reciprocal (4/1 -> 1/4)So the perpendicular slope is 1/4.
We can now solve for the y-intercept by plugging in the x and y-value of the point into the equation y = 1/4x + b:
y = 1/4x + b; (-3,5)5 = 1/4(-3) + b5 = -3/4 + bb = 5 3/4.The y-intercept is 5 3/4, so the equation of the line would be y = 1/4x + 5 3/4.
_____________________
Parallel LineParallel lines have the same slope. So we can use -4 as our slope, and plug in the points to find the y-intercept.
y = -4x + b; (-3,5)5 = -4(-3) + b5 = 12 + b-7 = bSo the equation of the parallel line would be y = -4x - 7.
Multiply: (x + 3) (x + 7) Simplify and write your answer in Standard Form.
Answer:
[tex](x + 3)(x + 7) \\ (x)(x) + (x)(7) + (3)(x) + (3)(7) \\ = {x}^{2} + 7x + 3x + 21 \\ = {x}^{2} + 10x + 21[/tex]
you have a credit card that has a balance of $3589.90 if you have a good credit rating how much must you pay at the end of the month to get the balance to acceptable debt ratio percentage?
Answer:
$1107.55
Step-by-step explanation:
3,589.90 x .0590/12 = $17.653,589.90 + 17.65 =3,607.553,607.55 - 2,500 = $1,107.55
The quadrilateral shown is a rhombus. What is angle 4?
A; 28
B; 32
C; 58
D; 90
Hi is 19,683 the answer?
Answer:
No
Step-by-step explanation:
the answer is 3.
3×3×3=27.
therefore the cube root of 27 is 3.
PLS HELP 40PTS Select the inequality that models the problem.
The sum of two consecutive odd integers is at least 76. Find the least possible pair of integers.
n + n + 2 ≥ 76
n + n + 2 > 76
n + n + 1 > 76
n + n + 1 ≥ 76
Answer:
n + n + 2 ≥ 76Explanation:
To find odd numbers, we have to use n + n + 2
For example let the number be 1, the 1 + 2 = 3, 3 + 2 = 5.
Therefore, used: n + n + 2 expression and it should be equals or at least 76. so finally n + n + 2 ≥ 76 applies.
Show all work below to answer the following for a certain city that had a population of 150,000 in the year 2010. In 2020, the population was 185,000.
a. Find the constant rate of continuous growth, k, for this population. (Please round to 5 decimal places)
b. When will the population reach 250,000 people?
The constant rate of continuous growth, k, for this population is equal to 2.11935%. And the population will reach 250,000 people in 24.36 years.
For solving this question, you should apply the Population Growth Equation.
Population Growth EquationThe formula for the Population Growth Equation is:
[tex]P_f=P_o*(1+\frac{R}{100} )^t[/tex]
Pf= future population
Po=initial population
r=growth rate
t= time (years)
STEP 1 - Find the constant rate of continuous growth, k, for this population.
For this exercise, you have:
Pf= future population= 185,000 in 2020.
Po=initial population =150,000 in 2010.
r=growth rate= ?
t= time (years)=2020-2010=10
Then,
[tex]P_f=P_o*(1+\frac{R}{100} )^t\\ \\ 185000=150000\cdot \left(1+\frac{R}{100}\:\right)^{10}\\ \\ \left(1+\frac{R}{100}\right)^{10}=\frac{185000}{150000} \\ \\ \left(1+\frac{R}{100}\right)^{10}=\frac{37}{30}\\ \\ R=100\sqrt[10]{\frac{37}{30}}-100=2.11935\%[/tex]
STEP 2 - Find the t for population 250,000 people.
[tex]P_f=P_o*(1+\frac{R}{100} )^t\\ \\ 250000=150000\cdot \left(1+\frac{2.11935}{100}\:\right)^{10}\\ \\ \left(1+\frac{2.11935}{100}\right)^{10}=\frac{250000}{150000} \\ \\ \left(1+\frac{2.11935}{100}\right)^t=\frac{5}{3}\\ \\ t\ln \left(1+\frac{2.11935}{100}\right)=\ln \left(\frac{5}{3}\right)\\ \\ t=\frac{\ln \left(\frac{5}{3}\right)}{\ln \left(\frac{102.11935}{100}\right)}\\ \\ t=24.36[/tex]
Read more about the population growth equation here:
brainly.com/question/25630111
which fraction is closest to 1 a) 8/7 b) 9/11 b) 6/5 c) 1 whole 2/9
Step-by-step explanation:
a) 8/7
hope it helps u...
Find the solutions to x2 = 24.
O A. x = 6/4
O B. x = 14 16
O C. *= +62
D. X = +2.16
Answer:
b.× = 14 16
Step-by-step explanation:
#stay safe
hope it helps
An architect’s drawing was drawn so the scale of 1/2 inch represented 6 feet. What was the actual height of a wall marked 4 1/2 inches high?
Ratio remains same
Let that be x4 -1/2=9/2[tex]\\ \rm{:}\dashrightarrow 1/2/6=9/2/x[/tex]
[tex]\\ \rm{:}\dashrightarrow x/2=27[/tex]
[tex]\\ \rm{:}\dashrightarrow x=54ft[/tex]
2^3 + 4m divided by 2 when m = 1.5
PLS HELP ME RN!!!
Answer:
14
Step-by-step explanation:
2^3 is 8. 8+4(1.5) is 8+6 is 14.
Answer:
Answer is 7 after simplifying and solving.Step-by-step explanation:
Equation that we have been provided with :
[tex]\boxed{ \tt {\dfrac{2 {}^{3} \: + \: 4m}{2}\: }} \: \red\bigstar[/tex]And the value of m is 1.5. So we would be simply substituting the value of m in the equation given above and divide it by 2 as per the demand of the question.
[tex]: \longmapsto \: \sf{\dfrac{2 {}^{3} \: + \: 4 \: (1.5)}{2}\: }[/tex]
[tex]: \longmapsto \: \sf{\dfrac{(2 \times 2 \times 2) \: + \: 4 \: (1.5)}{2}\: }[/tex]
[tex]: \longmapsto \: \sf{\dfrac{(4 \times 2) \: + \: 4 \: (1.5)}{2}\: }[/tex]
[tex]: \longmapsto \: \sf{\dfrac{8 \: + \: 4 \: (1.5)}{2}\: }[/tex]
[tex]: \longmapsto \: \sf{\dfrac{8 \: + \: 4 \: \times (1.5)}{2}\: }[/tex]
[tex]: \longmapsto \: \sf{\dfrac{8 \: + \: 6}{2}\: }[/tex]
[tex] : \longmapsto \: \sf{\dfrac{14}{2}\: }[/tex]
[tex]: \longmapsto \: \cancel{\sf{\dfrac{14}{2}\: }}[/tex]
[tex]: \longmapsto \: \red{\bf{7}}[/tex]
Jack rides in a motorboat against a river current for 36 km. Then he returns to his
starting point by floating down river on a raft. Tommy travels 9 hours less on the
motorboat than on the raft. Find the speed of the river current if the speed of the
motorboat in still water is 15 km/h.
The speed of the river current is 11.5 km/h.
What is speed?
Speed is the ratio of total distance travelled to total time taken. IT is given by:
Speed = distance / time
Let b represent the speed of the current and t represent the time, hence:
(15 + b)= 36/t
t = 36 / (15 + b)
Also:
(15 - b)= 36/(t + 9)
t = [36 - 9(15 - b)]/(15 - b)
Hence:
36 / (15 + b) = [36 - 9(15 - b)]/(15 - b)
b = 11.5 km/h
The speed of the river current is 11.5 km/h.
Find out more on speed at: https://brainly.com/question/4931057
RSM VERIFIED ANSWER
this answer was written by an RSM student, and has been confirmed by the portal
Answer:
3km/hr
not sure how to do it i just copied off my rsm teacher, but its right lol
also would rly appreciate brainliest but i know i didnt have an explaination. I would also really appreciate if other users would thank and rate this answer so people looking at a later date would know its reliable
Nonsense will be reported!!
[tex]\qquad \qquad\huge \underline{\boxed{\sf Answer}}[/tex]
The required additional information required to prove the Triangles congruent are :
[tex]\qquad \sf \dashrightarrow \: 1. \: X V= FD[/tex]
The Triangles will be congruent by HL congruency.
[tex]\qquad \sf \dashrightarrow \: 2. \: MH = MI[/tex]
The Triangles are congruent by LL congruency.
[tex]\qquad \sf \dashrightarrow \: 3. \: \angle EDC = \angle VUC[/tex]
The Triangles are congruent by HA congruency.
[tex]\qquad \sf \dashrightarrow \: 4. \: \angle J = \angle C[/tex]
The Triangles are congruent by LA congruency.
help guys plsss i don't know this one ;( plsss i will wait
Answer:
1/4
Step-by-step explanation:
Answer:
1/4
Step-by-step explanation:
there are 4 cans of soup and 1 of them is tomato
you have a 1 out of 4 chance of picking tomato soup
Convert: 8 quarts = _____ pints
2 pints
4 pints
16 pints
32 pints
Answer:
C. 16 pints
Step-by-step explanation:
1 quart equals to 2 pints
Answer:
answer is 2 pints
Step-by-step explanation:
2 x 4 is 8
help choose if you do i will give branlest to right answer
EGA and AGB aka the fourth option
Step-by-step explanation:
EGA and AGB create a 180 degree angle together
Over 40 hours a person earns $1,000. How much money does she earn per hour?
Question 6 of 10
Find the sum of the complex numbers.
(3 + 5i) + (10 + 7i)
A. 13 + 2i
B. 7 + 2i
c. 7+12i
D. 13 + 12i
The equation computed shows that the sum of the complex number is D. 13 + 12i.
How to solve an equation?From the information given, the thing that we have to do is to simply collect the like terms and solve the equation.
Therefore, the sum of (3 + 5i) + (10 + 7i) will be calculated thus:
= (3 + 5i) + (10 + 7i)
= 3 + 10 + 5i + 7i
= 13 + 12i
Learn more about equations on:
https://brainly.com/question/2972832
Q. A room measure 3m 55cm by 2m 25 cm. What is the perimeter of the room?
Ans. Given L=3m,55cm
B=2m,25cm
Perimeter = 2(l+b)
=2 (3m,55cm + 2m, 25cm)
3m 55cm
2m 25cm +
_____________
5m 80cm
______________
2×(5cm,80) 5×2=10 , 80×2=160
So 10m 160cm
but the answer is 11m 60 cm why and how to convert?
Answer:
100cm = 1m
Thus, one more step should be added to your working to arrive at the final answer:
Perimeter
= 10m 160cm
= 11m 60cm
This is because 160cm= 100cm +60cm, which is also equivalent to 1m 60cm.
Alternative working:
Convert all the units to cm first.
[tex]\boxed{1 \: m= 100 \: cm}[/tex]
Length
= 5m 55cm
= 300cm +55cm
= 355cm
Breadth
= 2m 25cm
= 200cm +25cm
= 225cm
Perimeter
= 2(length +breadth)
= 2(355 cm +225 cm)
= 2(580 cm)
= 1160 cm
= 11m 60cm
From the second last step to the last step, you could divide 1160 by 100 to find how many meters are there. You would get a quotient of 11 and a remainder of 60. Since this 60 cannot be changed into meters as a whole number, we can leave it as 11m 60cm. Otherwise, it is also correct to leave it as 1160cm or 11.6m unless otherwise stated.
However, 10m 160cm is not preferred since the conversion of cm to m is done partially, as the 160 cm can still be further simplified.
You purchase a car for $36,000. Five years later, the car is worth $28,500.
a. By how much is the car decreasing in value per year? (3 points)
Hint: Find the slope
Find the equation that would give the worth of the car for any given year. (4 points)
*y = mx +b
Answer:
36,000-28,500
=7,500 decrease per year
Correct answers only please put number with answer ex:(1.A, 2.B, 3.C etc.)
Answer:
See below for answers and explanations
Step-by-step explanation:
Problem 1
Here, [tex]\frac{3}{4}v[/tex] tells us that the vector [tex]v[/tex] is impacted by a scale factor of [tex]\frac{3}{4}[/tex], so we are doing scalar multiplication basically for both components of the vector. This only impacts the magnitude of the vector and not its direction. If we were to assume that [tex]v=\langle4,8\rangle[/tex], then [tex]\frac{3}{4}v=\langle\frac{3}{4}(4),\frac{3}{4}(8)\rangle=\langle3,6\rangle[/tex]. Therefore, this matches vector [tex]u[/tex], so D is the correct answer
Problem 2
Cannot be able to read as the text is too small
Problem 3
Cannot be able to read as the text is too small
Problem 4
[tex]-7u=\langle-7(8),-7(-4)\rangle=\langle-56,28\rangle=-56i+28j[/tex], so A is correct. Remember to use scalar multiplication for each component.
Problem 5
[tex]r-s=\langle5-9,11-(-8)\rangle=\langle-4,19\rangle[/tex], so B is correct. Remember to subtract the horizontal and vertical components seperately.
**Find all x - coordinates on the curve y = 2x ^ 3 - 3x ^ 2 - 12x + 20 where the tangent line is parallel to the x-axis.
Answer:
openup 1 em We want to find the points on the curve y=2x^3-3x^2-12x+20y where the tangent line is parallel to the xx-axis, which means that the slope=0
Below is the graph of a trigonometric function. It has a maximum point at
(1/4pi,-2.2)
and a minimum
point at
(3/4pi,-8.5) what is the amplitude
Step-by-step explanation:
Amplitude is the distance between the center line of the function and the top or bottom of the function.
The amplitude is half the distance between the max and the min, so
Amplitude = 1/2(max - min)
Amplitude = 1/2(-2.2 -(-8.5))
So amplitude = 1/2(6.3)
= 3.15
It takes 56 pounds of seed to completely plant an 8-acre field. How many acres can be planted per pound of seed?
Answer:
About 0.14 acres
Step-by-step explanation:
56 lb = 8 acres
1 lb = x
We can cross multiply:
(8 acres)(1 lb) = (56 lb)(x)
Solving for x:
x = 8 ÷ 56 ≈ 0.14 acres
Write a completely simplified rational expression that represents the exchange rate Salma will receive in dollars per euro. Explain how you came up with your expression.
The exchange rate that She will receive is an algebraic expression
The exchange rate that Salma will receive in dollars per euro is [tex]\frac{12x - 9}{4x -6}[/tex]
How to determine the exchange rateThe amount of dollars with Salma is given as:
[tex]Dollar = \frac{12x^2 + 15x - 18}{2x^2 + 14x + 20}[/tex]
The amount of Euro she can buy is:
[tex]Euro = \frac{2x^2 -x-3}{x^2 + 6x +5}[/tex]
Let the exchange rate be r.
So, we have:
[tex]Dollar * \frac 1r = Euro[/tex]
The equation becomes
[tex]\frac{12x^2 + 15x - 18}{2x^2 + 14x + 20}* \frac 1r = \frac{2x^2 -x-3}{x^2 + 6x +5}[/tex]
Factorize the expressions
[tex]\frac{3(x + 2)(4x - 3)}{2(x + 5)(x +2)}* \frac 1r = \frac{(x +1)(2x -3)}{(x + 5)*x + 1)}[/tex]
Cancel out the common factors
[tex]\frac{3(4x - 3)}{2}* \frac 1r = \frac{(2x -3)}{1}[/tex]
Make r the subject
[tex]\frac 1r = \frac{2(2x -3)}{3(4x - 3)}[/tex]
Expand
[tex]\frac 1r = \frac{4x -6}{12x - 9}[/tex]
Make r the subject
[tex]r = \frac{12x - 9}{4x -6}[/tex]
Hence, the exchange rate is [tex]\frac{12x - 9}{4x -6}[/tex]
Read more about algebraic expressions at:
https://brainly.com/question/4344214
how many solutions does "-4x" + 10 y = 6 2x - 5y = 8
Answer:
Infinitely many
Step-by-step explanation:
There are many solutions because 0=0.
Consider the line y=5x-4
What is the slope of a line perpendicular to this line?
What is the slope of a line parallel to this line?
Answer:
slope of perpendicular line= -⅕
slope of parallel line= 5
Step-by-step explanation:
y= 5x -4
The equation is in the slope-intercept form, thus the slope is the coefficient of x.
Slope of given equation= 5
The product of the slopes of perpendicular lines is -1.
Let the slope of the perpendicular line be m.
m(5)= -1
[tex]m = - \frac{1}{5} [/tex]
Thus, the slope of the perpendicular line is -⅕.
Parallel lines have the same gradient.
Slope of parallel line= 5
What is slope-intercept form?
y= mx +c, where m is the slope and c is the y-interceptIn this form, the coefficient of y is 1, while all the other terms and constant is on the right hand side of the equationBRAINLIEST?
Graph the line whose y-intercept is 9 and whose x-intercept is -2.
Answer:
y = 4.5x + 9, graphing done below.
Solving steps:
( -2 , 0 ), ( 0, 9)
slope:
[tex]\sf \frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]\sf \frac{9-0}{0+2}[/tex]
[tex]\sf 4.5[/tex]
equation:
y - 9 = 4.5 ( x - 0 )
y = 4.5x + 9
note: point -2 on x axis and 9 on y axis, and keep the ruler on those two points and draw a straight linear line, ta-daa you are done.
Variables y and x have a proportional relationship, where y = 18 when x = 2.
What is the value of x when y = 36?
Enter your answer in the box.
x=
Answer:
x = 4
Step-by-step explanation:
If y = 36, that means the original y = 18 was multiplied by 2. So, we have to multiply x = 2 by 2 as well.
2 * 2 = 4, so x = 4