The average rate of change of f(x) on the interval [1,1+h] is [1/(h + 6) - 1/6]/h
How to find the average rate of change of f(x) on the interval [1,1+h]?The function is given as
f(x) = 1/(x + 5)
The interval is given as
[1, 1 + h]
Calculate f(1) as follows
So, we have
f(1) = 1/(1 + 5)
f(1) = 1/6
Calculate f(1 + h) as follows
So, we have
f(1 + h) = 1/(1 + h + 5)
f(1 + h) = 1/(h + 6)
The average rate of change of f(x) on the interval [1,1+h] is then calculated as
Rate = [f(1 + h) - f(1)]/[1 + h - 1]
This gives
Rate = [1/(h + 6) - 1/6]/h
Hence, the average rate of change of f(x) on the interval [1,1+h] is [1/(h + 6) - 1/6]/h
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doug entered a canoe race. He rowed 3 1/3 miles in 1/3 hour. What is his average speed in miles per hour?
Answer:
10 MPH
Step-by-step explanation:
Doug entered a canoe race. He rowed 3 1/3 miles in 1/3 hour. What is his average speed in miles per hour?
If Doug rowed 3 1/3 miles in 1/3 hour the equation is:
3 1/3x = 1/3
multiply both sides by 3:
3(3 1/3x) = 3(1/3)
10x = 1 hour
Doug rowed 10 MPH
Answer:
10 mile per hour
Step-by-step explanation:
3 1/3 mile = 3.3333333333333333333333333333333 mile
1/3 hour = 0.3333333333333333333333333333333333 hour
divide 3.33333333333333333333333 by 0.3333333333333333333333333
= 3.333333333333333333333333333333333 * 1/.33333333333333333333
= 3.3333333333333333333333333 * 3
= 9.99999999999999999999999
= 10
the distance between given points. (-4,1) and (0, 4)
Your friend says that the line with the equation 2x + 3y = 7 has a slope of 2. explain to them the error in their thinking.
Answer:
The error of their thinking is that they did not convert the equation to slope intercept form, so they assumed that the 2x was the slope. They got the standard form mixed up with slope intercept.
I hope this helps you!
What kind of transformation converts the graph of f(x)=
–
9(x+6)2–3 into the graph of g(x)=
–
9(x–4)2–3?
The kind of transformation which converts the graph of f(x) into the graph of g(x) is vertical shrink .
What is transformation in graph?
A graph transformation is a procedure that modifies an existing graph or graphed equation to create different version of the following graph.
It is given that the functions are :
f(x) = -9(x+6)2 - 3
g(x) = -9(x-4)2 - 3
We know that if we perform transformation that meant the graph of f(x) is transformed into the graph of g(x).
i.e.,
f(x) = -9(x+6)2 - 3
f(x) = -18(x+6) - 3
f(x) = -18x - 128 - 3
f(x) = -18x - 72 - 56 - 3
f(x) = -9(x-4)2 - 3 - 56
f(x) = g(x) - 56
or g(x) = f(x) + (-56)
So , as we are adding f(x), this suggests that the transformation is one of the vertical shrink type.
Therefore, the kind of transformation which converts the graph of f(x) into the graph of g(x) is vertical shrink .
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Could someone help explain this asap
x-7/8=-3/4
Answer: x=1/8
Step-by-step explanation:
[tex]\displaystyle\\x-\frac{7}{8}=-\frac{3}{4} \\\\ x-\frac{7}{8}+\frac{7}{8}=-\frac{3}{4}+\frac{7}{8}\\\\x=-\frac{3}{4} +\frac{7}{8} \\\\ x=\frac{7}{8}-\frac{3*2}{4*2}\\\\ x=\frac{7}{8} -\frac{6}{8} \\\\x=\frac{7-6}{8} \\\\x=\frac{1}{8}[/tex]
what is the term for tying individual events together to provide meaningful alerts? event correlation
The correct answer is event correlation.
Event correlation is a technique for making sense of a large number of events and pinpointing the few events that are really important in that mass of information. This is accomplished by looking for and analyzing relationships between events.
Event can be defined as a set of outcomes of an experiment. In other words, an event in probability is the subset of the respective sample space. So, what is sample space? The entire possible set of outcomes of a random experiment is the sample space or the individual space of that experiment
One example of event correlation can occur with intrusion detection. Perhaps there is an employee account that hasn't been accessed for years, and suddenly a large number of login attempts are noticed. That account may start executing suspicious commands.
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I need help with these!
The results of the three cases are listed below:
g ° f (x) = 8 · x + 5 h ° g (- 3 · x) = - 36 · x - 9 f ° g (- 3) = - 14How to evaluate the composition between two functionsIn this problem we find three cases of composition between two functions, each of which has to be evaluated. The definition of the composition between the two functions f and g is presented below:
f ° g (x) = f( g(x) ) (1)
Where x is the input variable of the composite function.
In other words, the input of the function f is the output of the function g.
Now we proceed to find the expressions of the each of the two cases:
Case 1
g ° f (x) = g( f(x) )
g ° f (x) = 4 · (2 · x + 2) - 3
g ° f (x) = 8 · x + 8 - 3
g ° f (x) = 8 · x + 5
Case 2
h ° g (- 3 · x) = h [g (- 3 · x)]
h ° g (- 3 · x) = 3 · [4 · (- 3 · x) - 3]
h ° g (- 3 · x) = 3 · (- 12 · x - 3)
h ° g (- 3 · x) = - 36 · x - 9
Case 3
f ° g (- 3) = f( g(- 3) )
f ° g (- 3) = 3 · [2 · (- 3) + 1] + 1
f ° g (- 3) = 3 · (- 5) + 1
f ° g (- 3) = - 15 + 1
f ° g (- 3) = - 14
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why does the inequality sign have to be flipped when dividing by a negative number?
The inequality sign have to be flipped when dividing by a negative number.
What is inequality?
The relation between two expressions that are not equal, employing a sign such as ≠ ‘not equal to’, > ‘greater than’, or < ‘less than’.
Given:
The given statement is the inequality sign have to be flipped when dividing by a negative number.
According to given question we have
A number that is larger when positive becomes "more negative," and thus smaller when negative, and vice versa.
Dividing by a negative number is the same as dividing by a positive number and then multiplying by −1. Dividing an inequality by a positive number retains the same inequality. But, multiplying by −1 is the same as switching the signs of the numbers on both sides of the inequality, which reverses the inequality:
a<b⟺−a>−b.
Ex:
when dividing both sides by a negative number, we reverse the inequality sign.
Take −3x<9
To solve for x, we divide both sides by −3 and get
x>−3.
Therefore, the inequality sign have to be flipped when dividing by a negative number.
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Which is larger?
3/5 or 4/7
Answer:
3/5 is bigger
Step-by-step explanation:
if the numerator is the same then the one with the smaller denominator is bigger
The midpoint of JK is point L at (–1, 8). One endpoint is J(4, –15). Which equations can be solved to determine the coordinates of the other endpoint, K? Select two options. = –1 = 4 –15 + y1 =16 = y1
The equations which can be solved to determine the coordinates of the other endpoints are; -1 = (4 + x2)/ 2 and 8 = (-15 + y2)/2.
What equations can be solved to determine the other endpoint K of the line JK?It follows from the task content that the equation which can be solved to obtain the coordinates of the other endpoint, K be identified.
Since the coordinates of the midpoint can be determined as follows;
x-coordinate of the midpoint;
x = (x1 + x2)/2; where x1 = 4 and x = -1.
Therefore, -1 = (4 + x2)/2 is the first required equation.
y-coordinate of the midpoint;
y = (y1 + y2)/2; where y1 = -15 and y = 8.
Therefore, 8 = (-15 + y2)/2 is the other required equation.
Ultimately, the required equations are; -1 = (4 + x2)/ 2 and 8 = (-15 + y2)/2.
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1/100,1/4,0.2 least to greatest
1/100 < 0.2 < 1/4 is the correct order of the given numbers arranged from least to greatest.
Given that, 1/100, 1/4 and 0.2 and we have to arrange them from least to greatest. So, basically we have to arrange them in ascending order.
1/100 can be written in decimal form as 0.01
1/4 can be written in the decimal form as 0.25
and 0.2 is already in the decimal form.
Now, we have 0.01, 0.25 and 0.2 and we have to arrange them from least to greatest.
Out of 0.01, 0.25 and 0.2, 0.01 is the smallest and 0.25 is the greatest.
0.01 < 0.2 < 0.25
This is the arrangement of the given number in decimal form.
1/100 < 0.2 < 1/4
This is the correct order of 1/100, 1/4 and 0.2 arranged in ascending order.
Therefore, 1/100 < 0.2 < 1/4 is the required answer.
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shane is standing at the base of a truck-mounted stairway to board an aircraft. the stairway begins at the ground. the length of the stairway is 18 feet, and the elevation of the top of the stairway from the ground is 13 feet. what is the approximate angle made by the stairway with the ground? a. 46.24° b. 54.16° c. 43.76° d. 35.84°
The approximate angle will be made by the stairway with the ground is 46.24°.
As we are been given that, the length of the stairway from the ground is 18 feet, under the right angle triangle, that will be the length of the hypotenuse. Next, since the elevation of the top of the stairway from, the ground is 13 feet, which is considered to be the length of the perpendicular of the assumed right angled triangle.
Now, we are asked to find the angle x,
Since, we know that
sin θ = perpendicular/ hypotenuse
So, substituting the required values the desired angle we get is :
sin θ = 13/18
sin θ = 0.7222
θ = sin ⁻¹ (0.7222)
= 46.2364
x = 46.24
the angle θ or x is 46. 24°.
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'
at 111111:55\text{ p.m.}55 p.m.55, start text, space, p, point, m, point, end text, thomas ties a weight to the minute hand of a clock. the clockwise torque applied by the weight (i.e. the force it applies on the clock's hand to move clockwise) varies in a periodic way that can be modeled by a trigonometric function. the torque peaks 151515 minutes after each whole hour, when the minute hand is pointing directly to the right, at 3\text{ nm}3 nm3, start text, space, n, m, end text (newton metre, the si unit for torque). the minimum torque of -3\text{ nm}−3 nmminus, 3, start text, space, n, m, end text occurs 151515 minutes before each whole hour, when the minute hand is pointing directly to the left. find the formula of the trigonometric function that models the torque \tauτtau applied by the weight ttt minutes after thomas attached the weight. define the function using radians.
The trigonometric function's formula, which simulates the torque (tau) that the weight applied t minutes after Thomas attached it is
[tex]3 Sin (\frac{2\frac{22}{7} }{60} (t-51))[/tex]
The angular speed of the minutes hand is
[tex]w = \frac{2 (\frac{22}{7}) }{60}[/tex] rad/min
Following the application of weight, the torque as a function of time t is,
[tex]t= t_{0} sin (w (t-5) min)\\ = (3 Nm) sin ((\frac{2 (\frac{22}{7} }{60} ) rad/min (t-5) min)[/tex]
[tex]= (3 Nm) sin ( \frac{2 (\frac{22}{7} }{60} (t-5) rad ) \\= 3 sin (\frac{2 \frac{22}{7} }{60} (t-5)[/tex]
What is torque ?Torque, which is also known as the moment of a force, is the propensity of a force to rotate the body to which it is applied. Force (F) x Distance (r) = Torque is how torque is calculated. The distance (r) between the pivot point and the force's action point. A vector quantity is a torque. As a vector quantity, torque always has a direction that is perpendicular to the plane that contains the vectors of force and displacement.
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if a number is divisible by two co-prime numbers then it is also divisibe by their product true or false
Answer:
Hello,
Answer TRUE.
Step-by-step explanation:
a | n is read, a divide n.
if a | n => n=a*q
if b | n => b | a*q , since gcd(a,b)=1, b | q ==> b=q*k
n=a*q=a*b*k=(a*b)*k so a*b | n
please answer and thanks
Answer:
c=(d-4a)/3
Step-by-step explanation:
d=4a+3c, solve for c
d-4a=4a-4a+3c ==> isolate the 3c by subtracting 4a from both sides
d-4a=3c
(d-4a)/3=3c/3 ==> isolate c by dividing 3 on both sides of the equation
c=(d-4a)/3
PLEASE HELP ILL GIVE BRAINLEST
A. divide 2x by 2
B. add 5 to both sides of the equation
C. divide both sides of the equation by 26
D. subtract 5 from the left side of the equation
Find the distance between each pair of points. Round to one decimal place. A(-4, 6) and B(3, -7), and E(-6, -5) and F(2, 0).
AB=(
EF=
To one decimal place, round. points A(-4, 6), B(3, -7), E(-6, -5) and F (2, 0).
The distance between AB is [tex]\sqrt{185}[/tex]=13.601 and EF is [tex]\sqrt{89}[/tex]=9.433.
Given that,
To one decimal place, round.
A(-4, 6), B(3, -7), E(-6, -5) and F (2, 0).
We have to find the distance between two points that are AB and EF.
1. The distance between 2 points A and B.
A(-4, 6) and B(3, -7).
Distance formula is [tex]\sqrt{(x_{2} -x_{1} )^{2} +(y_{2} -y_{1} )^{2} }[/tex]
Here, x₁=-1,x₂=3 and y₁=6,y₂=-7
After substituting we get,
[tex]\sqrt{{(3 -(-1)} )^{2} +(-7 -6 )^{2} }\\[/tex]
[tex]\sqrt{{(3 +1} )^{2} +(-7 -6 )^{2} }\\[/tex]
[tex]\sqrt{{(4} )^{2} +(-13 )^{2} }\\[/tex]
[tex]\sqrt{16 +163}\\[/tex]
[tex]\sqrt{185}[/tex]
13.601
Therefore, the distance between AB is [tex]\sqrt{185}[/tex]=13.601.
2.The distance between 2 points E and F.
E(-6, -5) and F (2, 0).
Distance formula is [tex]\sqrt{(x_{2} -x_{1} )^{2} +(y_{2} -y_{1} )^{2} }[/tex]
Here, x₁=-6,x₂=2 and y₁=-5,y₂=0
After substituting we get,
[tex]\sqrt{{(2 -(-6)} )^{2} +(0 -(-5) )^{2} }\\[/tex]
[tex]\sqrt{{(2 +6} )^{2} +(0 +5 )^{2} }\\[/tex]
[tex]\sqrt{{(8} )^{2} +(5 )^{2} }\\[/tex]
[tex]\sqrt{64 +25}\\[/tex]
[tex]\sqrt{89}[/tex]
9.433
Therefore, the distance between EF is [tex]\sqrt{89}[/tex]=9.433.
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if the federal debt is $24 trillion, and if this debt were divided equally among 300 million people, then how much would each person owe? describe how to estimate mentally the answer to the federal debt problem, and explain briefly why your strategy makes sense.
Using the concept of division we can find the amount of money each person owes.
Why should we use Division?Division is one of the fundamental operations used in mathematics which involves breaking a bigger value into smaller groups with the same number of components.
The federal debt =$24 trillion=$24000000
(one trillion=1000000 million)
The value in trillion is converted to million by multiplying by 1000000.
The number of people the amount to be equally distributed= 300 million
Amount of money equally distributed among each person
=[tex]\frac{Total debt amount}{number of people}[/tex]
=[tex]\frac{24000000}{300}[/tex]
=80000
The amount each person owes is $80000
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Draw an area model that demonstrates that the quotient of 2080 and 40 is 52 explain how the model relates to the calculation
We can see in the picture an area model that demonstrates that the quotient of 2080 and 40 is 52.
Given that,
52 is the quotient of 2080 and 40.
The expression can be represented by
2080/40=52
We divide 2080 as 1200+800+80
(1200+800+80)/40=1200/40+800/40+80/40
(1200+800+80)/40=30+20+2
(1200+800+80)/40=52
An area model is a rectangular diagram or model used in mathematics for problems involving multiplication and division, where the length and breadth of the rectangle are determined by the factors, quotient, and divisor. Using number bonds, we may divide the rectangle's enormous area into a number of smaller boxes to simplify the calculation. The product or quotient is then obtained by adding to obtain the area of the entire.
We can see in the picture an area model that demonstrates that the quotient of 2080 and 40 is 52.
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lindsay bedford works at the baseball cap shop. she is paid $6.50 per hour plus $0.45 for each cap she embroiders. how many caps must she embroider to earn at least $85 in an 8-hour day?
15 caps are needed so that she can earn $85 in an [tex]8[/tex]hour day.
How is the direct equation calculated?The direct variation equation has the form y = kx, where k is the constant proportionality. It is a linear equation with two variables. In a coordinate plane, the direct variation graph is a straight line. A constant is the ratio of two quantities that vary directly. Relationship between two variables that can be described mathematically by an equation where one variable equals a constant multiplied by the other.
For each hour she is compensated $6.50 with $0.45.
For an 8 hour day =6.50 *8 + 0.45x
Let x be the caps and earning is $85
6.50*8+0.45*x=85
=> 52+0.45x=85
=> 0.45x=33
=> x=15 (approx.)
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10. ratios that express the same relationship between two quantities
Answer:
In fact, they're called equivalent ratios, which are ratios that express the same relationship between two numbers. The ratios 60/1 and 120/2 are equivalent because the relationship between the two parts of the ratios didn't change. According to the ratio 60/1, you travel 60 miles for every hour you drive.14 Oct 2021
7 gallons = how many pints
Answer:
56 pints hope this helps Brainliest please
Step-by-step explanation:
Answer:
7 gallons = 56 liquid pints!
Explanation= 1 gallon = 8 pints
write an equation to answer the question below.
Lela purchased 3 mechanical pencils and a notebook that cost $5. Her purchase totaled $11. How much was each pencil? Use p to represent the cost of each pencil.
The cost of each pencil is $2
What are algebraic expressions?Algebraic expressions are expressions comprised of variables, terms, factors, coefficients, and constants.
They are also made up of arithmetic operations such as addition, subtraction, multiplication division, etc
From the information given, we have that 'p' represents the cost of each pencil
The equation is represented as;
3p + $5 = $11
collect like terms
3p = $11 - $5
subtract like terms
3p = $6
Make 'p' the subject of formula
p = $6/3
p = $2
Thus, the cost of each pencil is $2
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Suppose xy > 0. Describe the points whose coordinates are solutions to the inequality.
The solutions fo the inequality are all the points (x, y) that meet these 3 conditions.
x ≠ 0y ≠ 0Sign(x) =sign(y)Which points are solutions of the inequality?
We want to find points of the form (x, y) that are solutions of the inequality:
x*y > 0
Clearly x and y must be different than zero.
So, for example if x = -1, y can be any negative number, for example y= -3
x*y > 0
(-1)*(-3) > 0
3 > 0
This is true.
Now if x = 1, y must be positive. LEt's take y = 103, then:
x*y > 0
1*103 > 0
103 > 0
Then we have 3 conditions:
x ≠ 0y ≠ 0Sign(x) =sign(y)The solutions fo the inequality are all the points (x, y) that meet these 3 conditions.
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A bathtub has 8 gallons of water in it. it is draining at a constant rate of 6 gallons every 5 minutes. write an equation that for the amount of water in the tub. when will it be empty?
If a bathtub has 8 gallons of water in it and it is draining at a constant rate of 6 gallons every 5 minutes. then the equation for the amount of water in the tub is f(x) =8-1.2x and it will take 6.67 minutes to drain the bathtub
Given,
The total quantity of water in the tub = 8 gallons
The quantity of water draining for every 5 minutes = 6 gallons
The quantity of water draining for every 1 minutes = [tex]\frac{6}{5} =1.2[/tex] gallons
Consider the number of minutes as x
Then the equation for the amount of water in the tub
f(x)= 8 - 1.2x
The number off minutes take to empty the tub = Total quantity of water / Quantity of water draining per minute
=[tex]\frac{8}{1.2}=6.67[/tex] minutes
Hence, if a bathtub has 8 gallons of water in it and it is draining at a constant rate of 6 gallons every 5 minutes. then the equation for the amount of water in the tub is f(x) =8-1.2x and it will take 6.67 minutes to drain the bathtub.
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Lesson 1.10: Daniel works at least 30 hours a week. He works as a math tutor
and as a teacher. The number of hours Daniel works as a tutor (y) is at most
twice the number he works as a teacher (x).
• Write the set of inequalities that represents the constraints of the situation
and state a point (x, y) that is the feasible region.
The set of inequalities that represents the constraints of the situation is y ≤ 2x, x + y ≥ 30 and a point (x, y) that is the feasible region is (10, 20)
How to write the set of inequalities that represents the constraints of the situation and state a point (x, y) that is the feasible region.The given parameters are:
Number of hours = at least 30 hours a week
This means that
x + y ≥ 30
Also, we have:
The number of hours Daniel works as a tutor (y) is at most twice the number he works as a teacher (x).
This means that
y ≤ 2x
Substitute y ≤ 2x in x + y ≥ 30
x + 2x ≥ 30
This gives
3x ≥ 30
Divide
x ≥ 10
Substitute x ≥ 10 in y ≤ 2x
y ≤ 2 x 10
Evaluate
y ≤ 20
Hence, the set of inequalities that represents the constraints of the situation is y ≤ 2x, x + y ≥ 30 and a point (x, y) that is the feasible region is (10, 20)
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a magician designed an unfair coin so that the probability of getting a head on a flip is $60\%$. if he flips the coin three times, what is the probability that he flips more heads than tails? express your answer as a common fraction.
Probability of getting a head is 60%
More heads than tails means these possibilities are
2 Heads - 1 Tail
3 Heads - 0 Tails
Probability of 2 Heads and 1 Tail = C (3,2) (.60) ^2 (.40)
=3 * (.36) (.40)
=3 * .144
=3 (144/1000)
=3 (18/125)
=54/125
Probability of 3 Heads = (.60) ^3
= .6 (.36)
= .216 = 216 / 1000
= 27 / 125
Hence, total probability = 54 / 125 + 27 / 125
= 81 / 125
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Square root of 81/9 - 7 Times Square root of 4
Answer: -125
Step-by-step explanation:
√81/9 = 9/3 =3
√4 = 2∧7 = 128
3-128 = -125
Can someone please help mee (20 points + brainliest!!!)
Answer:
A) x = 225 - 7.5p
B) x = 180 millions of gallons
Step-by-step explanation:
A) Make "x" the subject:
[tex]\sf \rightarrow 0.4x + 3p = 90[/tex]
[tex]\sf \rightarrow 0.4x = 90-3p[/tex]
[tex]\sf \rightarrow x = \dfrac{90-3p}{ 0.4}[/tex]
[tex]\sf \rightarrow x = 225-7.5p[/tex]
B) Demand when the price per gallon is $6:
substitute p = 6
[tex]\sf \rightarrow x = 225-7.5(6)[/tex]
[tex]\sf \rightarrow x = 225-45[/tex]
[tex]\sf \rightarrow x =180[/tex]
a car valued at $28,000 depreciates at a rate of 20% per year. what will the car be worth after 6 years?
The value of the car after 6 years will be $7340 .
The Depreciation can be calculated using the formula
A = P( 1 - r/100)ⁿ
where , A = amount , P = principal , r = rate of deprecation , n = time period
In the question ,
it is given that
the value of the car (P) = $28000
rate of deprecation (r) = 20% per year
time period (t) = 6 years
Substituting the values in the Depreciation formula we get ,
Amount = 28000*( 1 - 20/100 )⁶
= 28000*(80/100)⁶
= 28000*(0.80)⁶
= 28000*0.26214
= 7339.92
≅ 7340
Therefore , the value of the car after 6 years will be $7340 .
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