The average rate of change of function f(x)= [tex]\frac{1}{x+5}[/tex] on the interval [1,1+h] is [tex]-\frac{1}{36+6h}[/tex]
Given,
The function = [tex]\frac{1}{x+5}[/tex]
We know the average rate of change of the function is [tex]\frac{f(b)-f(a)}{b-a}[/tex]
Where a and b are the intervals
a= 1
b=1+h
f(a) =f(1)= [tex]\frac{1}{1+5}[/tex]
=[tex]\frac{1}{6}[/tex]
f(b)= f(1+h)
=[tex]\frac{1}{1+h+5}[/tex]
=[tex]\frac{1}{6+h}[/tex]
f(b)-f(a)= [tex]\frac{1}{6+h}-\frac{1}{6}[/tex]
[tex]=\frac{6-(6+h)}{6(6+h)} \\=\frac{6-6-h}{36+6h}\\ =-\frac{h}{36+6h}[/tex]
Then,
[tex]\frac{f(b)-f(a)}{b-a} =\frac{-\frac{h}{36+6h} }{1+h-1}[/tex]
[tex]=\frac{-\frac{h}{36+6h} }{h} \\=-\frac{1}{36+6h}[/tex]
Hence, the average rate of change of function f(x)= [tex]\frac{1}{x+5}[/tex] on the interval [1,1+h] is [tex]-\frac{1}{36+6h}[/tex]
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A carpenter has a wooden dowel that is 72 cm long. She wants to cut it into two pieces so that one piece is 7 times as long as the other. What is the length of the longer piece?
Answer: 39.5 cm long
Step-by-step explanation: The equation can also be written s 72=2x+7, (x= length of short piece) (x+7+length of long piece.):
72=2x+7
72-7=2x
65=2x
x=32.5
Then to find out the long piece:
x+7
32.5+7=39.5
What must be added to 3x + y to get 2x + 3y?
Answer:
-x+2yStep-by-step explanation:
What must be added to 3x + y to get 2x + 3y?
3x + y + z = 2x + 3y
3x + z = 2x + 3y - y
3x + z = 2x + 2y
z = 2x-3x+2y
z = -x+2y
-------------------
check
3x + y + (-x) +2y =
2x + 3y
the answer is good
I meed you to explain this
Answer:
Bread
Step-by-step explanation:
What is the solution set of the quadratic inequality 6x² + 1 ≤0?
O {X[XER}
O
{X1 X=-1}
Answer:
The empty set
Step-by-step explanation:
The square of a real number is non-negative, and thus the left hand side is always positive.
( x - 10) (4x - 10) find the measure of each angle
Answer:
Step-by-step explanation:
disribute it
What is the equation of the line that passes through the point (-1, 5) and is parallel to the line y = -3x + 5?
y=-x3+143
y=3x+8
y=-3x+2
y=x3+163
Step-by-step explanation:
Lines which are parallel have equal gradients.The gradient of the given straight line is -3 meaning that the gradient of the new equation will be -3now we have y=-3x +c following the general equation of a straightline.Substituting the given point we have [tex]5 = -3( - 1) + c \\ c = 5 - 3 \\ c = 2 \\ the \: new \: equation \: will \: then \: be \: y = - 3x + 2[/tex]Answer:
I have completed it also
Step-by-step explanation:
what the person ontop of me said it correct
What is the sum of [4 -6 8] and [10 2 0]
Answer:
[14 -4 8]
Step-by-step explanation:
[4+10 -6+2 8+0]
[14 -4 8]
1. Kia said she could put
together 14 out of 25 gift bags
for a contest. She has already
made 5 gift bags. What
percent of the 25 gift bags
does Kia still have to make?
The percentage of bags that Kia still has to make for the contest is 36 %.
We are given that:
Kia has to make 14 bags out of 25 bags.
Now, she has already made 5 gift bags.
The number of bags she still has to make = 14 - 5 = 9
Now ,we need to find the percentage of 9 from the total of 25 so to get the percentage of bags that Kia still has to make.
So, we get that:
Percentage = 9 / 25 × 100 %
Percentage = 9 × 4 %
Percentage = 36 %
Therefore, we get that, the percentage of bags that Kia still has to make for the contest is 36 %.
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an object moves along a parabolic path defined by the equation in such a way that the y-value is decreasing at a constant rate of 2 units per second. at what rate is the x-coordinate changing when x
So the change of rate of x is -1/3 .
The Derivative of a function of a real variable measures the sensitivity to change of the function value with respect to a change in its argument. Derivatives are a fundamental tool of calculus.
Given that object is decreasing at constant rate of 2 units per second so we have [tex]y = 2x^2 + 1[/tex]
[tex]\frac{dy}{dt} = 4x \frac{dx}{dt}[/tex]
given dy/dt = -2
when x = 3/2
-2 = 4(3/2) dx/dt
-2 = 6 dx/dt
dx/dt = -2/6
= -1/3
Hence the change of rate of x is -1/3 .
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question the benefit of using inferential statistics is that it allows a researcher to describe the data describe the data find the measures of central tendency find the measures of central tendency find the spread of the data find the spread of the data make generalizations about a population make generalizations about a population visualize the raw data
A researcher can make generalizations about a population by utilizing inferential statistics, which is a benefit.
What kind of statistics are inferential, for instance?Two purposes dominate the use of inferential statistics: estimating population numbers (for example, the mean SAT score of all 11th graders in the US). testing hypotheses to make population-level judgments (for example, the relationship between SAT scores and family income).
Inferential statistics that are helpful in the design of experimental and quasi-experimental studies or in the assessment of program outcomes.
When comparing the average performance of two groups on a single measure to check if there is a difference, one of the simplest inferential tests may be performed. You might be interested in learning whether math test results between eighth-grade boys and girls differ or if a program group differs from a control group in terms of the outcome measure.
The t-test for differences between groups should always be taken into consideration when comparing the average performance of two groups.
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in simple linear regression the estimated slope from the regression of y on x is the same as the estimated slope in the regression of x on y.
In the given statement is:
In simple linear regression the estimated slope from the regression of y on x is the same as the estimated slope in the regression of x on y.
If Y depends on X then the regression line is Y on X.
Y is dependent variable and X is independent variable. If X depends on Y, then regression line is X on Y and X is dependent variable and Y is independent variable. The regression equation Y on X is Y = a + bx, is used to estimate value of Y when X is known.
What is Simple linear regression?
Simple linear regression is a regression model that estimates the relationship between one independent variable and one dependent variable using a straight line. Both variables should be quantitative.
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Help please quite immediate am pro
i need help with this question please
Answer:
5x-30
Step-by-step explanation:
x+15+4x-45
5x+14-45
5x-30
A flower bed is in the shape of a triangle with one side twice the length of the shortest side, and the third side is 28 feet more
than the length of the shortest side. Find the dimensions if the perimeter is 144 feet.
According to the solving the dimensions of the triangles are as follow:
a . 29
b. 58
c. 57
What is meant by dimensions?A mathematical space's dimension is defined informally as the smallest number of coordinates required to specify any point within it. Thus, a line has a dimension of one since only one coordinate is required to identify a point on it - for example, the point at 5 on a number line.
How many dimensions are contained within a triangle?2-D shapes really had no thickness and they can only be measured on two sides. Two-dimensional objects include the square, circle, rectangle, and triangle.
According to the given data:x=length of the shortest side
2x=length of another side
x+28=length of the third side
144=x+2x+x+28
144=4x+28
144-28=4x
116=4x
x=116/4
x=29 feet (one side)
Putting the value of x to find second side
2x=58 feet (second side)
x+28= 57 feet (third side)
the perimeter of the triangle = sum of all the sides
= 29+58+57
=144
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2-78.
Decide if each pair of triangles below is similar. If the triangles are similar,
justify your conclusion by stating the similarity condition you used. Also,
describe a possible sequence of transformations that would carry one onto
the other. If the triangles are not similar, explain how you know they are
not similar.
The pair of triangles is similar with the ASA similarity condition
How to decide if each pair of triangles is similar?The figure that completes the question is added as an attachment
From the figure, we have the following properties:
Two angles are congruent; This is indicated by the marks on one angle, and the corresponding right angleAlso, the hypotenuse of both triangles are similarThis means that the pair of triangles is similar with the ASA similarity condition.
Since the triangles share the same point
So, the transformation to carry the triangles onto one another is dilation
Hence, the pair of triangles is similar with the ASA similarity condition
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Someone help with this, need it for hw,thanks!
Answer: B
Step-by-step explanation: you see how its by the 2 that means that its going to be where the 3 is
Helppp!!!! Quick as anyone can!!! will give brainliest!!!!!
Answer: A is the same and equivalent
B is different not equivalent
C is the same and equivalent
Step-by-step explanation:
I'm on Edmund
a subset $b$ of the set of integers from 1 to 100, inclusive, has the property that no two elements of $b$ sum to 125. what is the maximum possible number of elements in $b$? (a) 50 (b) 51 (c) 62 (d) 65 (e) 68
We get the number of elements in the set B will be 62.
The universal set is A consists of the primary one hundred positive integers.
Set B is a subset of A.
One possibility is that B consists of the primary 62 positive integers.
Then only, the greatest quantity that may be shaped through the sum of any factors of set B is 123.
The number of elements in set B is equal to 62.
We also can selectively interchange one or more elements of B and and add them in complement of B
In most of these instances the number of elements in set B might be 62.
Therefore, we get the number of elements in the set B will be 62.
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What is the area of a rectangle with a length of 9 feet and a width of 7 grade
Answer:
63
Step-by-step explanation:
area=length×width so 9×7=63
Trey bakes 70 cupcakes for the school Bake Sale. Worried they might run out, he bakes some extra and now has 112 cupcakes.
What is the Percent Change in the number of cupcakes?
The Percent Change in the number of cupcakes is 60%
How to determine the Percent Change in the number of cupcakes?The given parameters are:
Initial number of cupcakes = 70
Final number of cupcakes = 112
The Percent Change in the number of cupcakes:
Percent = (Final number of cupcakes - Initial number of cupcakes)/Initial number of cupcakes * 100%
This gives
Percent = (112 - 70)/70 * 100%
Evaluate the quotient
So, we have
Percent = 0.6 * 100%
Evaluate the product
So, we have
Percent = 60%
Hence, the Percent Change in the number of cupcakes is 60%
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you work as an assistant coach on the university swim team and earn $13 per hour. one day, you decide to skip the hour-long practice and go to the county fair instead, which has an admission fee of $10
23$ is the total cost .
What is cost and example?
The definition of cost is to be valued at something or to lose. A loaf of bread costing $3 is an example of a cost. Giving up your freedom in order to grant freedom to another person is an illustration of cost.Fixed and variable costs are the two main categories of expenses incurred by enterprises. Variable costs change with output, whereas fixed costs do not. Overhead costs are another name for fixed expenses. They must be paid whether a company produces 100 or 1,000 widgets.the total cost = 13$ + 10$= 23$ because he losses a hour in work .
13$ and additionally spending 10$ in carnival .
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Is the given point interior,exterior, or on the circle (x+2^)2+(y-3^)2=81? Q(3,0)
A
line passes through the point (-4, 3) and has a slope of 4
Write an equation in slope-intercept form for this line.
Step-by-step explanation:
the slope-intercept form :
y = ax + b
"a" being the slope, "b" being the y-intercept (the y value when x = 0).
but we have the slope and a point.
so, we can start with the point-slope form and then transform it :
y - y1 = a(x - x1)
"a" is again the slope, (x1, y1) is the given point.
so, we have
y - 3 = 4(x - -4) = 4(x + 4) = 4x + 16
y = 4x + 19
and that's it.
17 cm/min=________m/h
Answer: .17 m/h
Step-by-step explanation: One centimeter is .01 meters/one hundredth of a meter, so you just need to move the decimal two digits to the right to convert.
Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used. Find the average rate of change of each function over the interval [0, 3]. Match each representation with its respective average rate of change.
The identify each representation's associated average rate of change. The average rate of change for the functions r, q, p is 5, 5, 7/3 over the range [0.3].
Given that,
We have to find over the range [0, 3], calculate each function's average rate of change. The identify each representation's associated average rate of change.
The equation for f(x) average's rate of change across [a,b] is
m=[tex]\frac{f(b)-f(a)}{b-a}[/tex]
The function provided is
r(x)=x²+2x-5
r(0)=(0)²+2(0)-5=-5
r(3)=(3)²+2(3)-5=9+6-5=15-5=10
Now,
m₁=[tex]\frac{r(3)-r(0)}{3-0}[/tex]
m₁=[tex]\frac{10+5}{3}[/tex]
m₁=15/3
m₁=5
It is clear from the graph that q(0)=2 and q(1)=3.
Now,
m₂=[tex]\frac{q(1)-q(0)}{1-0}[/tex]
m₂=[tex]\frac{3+2}{1}[/tex]
m₂=5/1
m₂=5
It is evident from the above table that s(0)=-2 and s(3)=5.
Now,
m₃=[tex]\frac{s(3)-s(0)}{3-0}[/tex]
m₃=[tex]\frac{5+2}{3}[/tex]
m₃=7/3
Therefore, The average rate of change for the functions r, q, p is 5, 5, 7/3.
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100⁰ - 2x 2x + 20° 5x -40°
solve for x
This could be wrong, but I think your answer is [tex]x=-2x^3+\frac{900^{\circ \:}x-360^{\circ \:}}{9}[/tex]
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Hope this helps!
Have a great day and God bless! :)
The graph of y=f(x) is shown below. Find all values of xx where f(x)=3
twice the sum of 9 and y is less than or equal to 5y
Answer:
y [tex]\leq[/tex] -6.5
Step-by-step explanation:
2(9+y) [tex]\leq[/tex] 5
(distribute)
18 + 2y [tex]\leq[/tex] 5
(isolate variable)
2y [tex]\leq[/tex] 5 - 18
(simplify)
2y [tex]\leq[/tex] -13
(isolate variable)
y [tex]\leq[/tex] -6.5
a. How much do 4 dozen buttons cost?
It costs 6$ for 48 buttons
b. How many dozens of buttons can the organizers buy for $27?
the cost of 4 dozens of buttons will be $ 6 and the organizers can buy 216 buttons for $ 27.
We are given that:
Cost of 48 buttons = $ 6
48 buttons = $ 6
Divide both sides by 48:
1 button = $ 6 / 48 = $ 1 / 8
Now, the cost of 4 dozen buttons will be:
4 dozen buttons = 12 × 4 = 48
So, the cost will be 4 6 only.
For $ 27, the organizers can buy:
Number of buttons = 27 ÷ 1 / 8
Number of buttons = 27 × 8
Number of buttons = 216 buttons.
Therefore, the cost of 4 dozens of buttons will be $ 6 and the organizers can buy 216 buttons for $ 27.
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Pleaseee help me I need this done rn.
Area of a right triangle ABC is 120 sq feet. If AABC goes through a dilation transformation with a scale
factor of 1.5, then what will be the area of the transformed triangle (in sq feet)?
Answer:
270
Step-by-step explanation:
The area is the same as the original area multiplied by the square of the scale factor.