Use the four-step process to find the slope of the tangent line to the graph of the given function at any point. f(x) = -x^2 + 3x Step 1: f(x + h) = ___
Step 2: f(x + h)-f(x) = ___ Step 3: f(x+h)-f(x)/h = ___
Step 4: f'(x) = lim f(x+h)-f(x)/h h→0
Answers
Answer: (1) - 2x + 3
Four-step process to find the slope of the tangent line to the graph of the given function at any point The process to find the slope of the tangent line to the graph of the given function at any point includes four steps. These four steps are mentioned below:Step 1:
f(x + h) = - (x + h)^2 + 3(x + h)
Step 2: f(x + h) - f(x) = - (x + h)^2 + 3(x + h) - [- x^2 + 3x]
Step 3: f(x + h) - f(x) / h
= [- (x + h)^2 + 3(x + h) - (- x^2 + 3x)] / h
Step 4: f'(x) = lim h → 0 [ - (x + h)^2 + 3(x + h) - (- x^2 + 3x)] / h
Putting the given value in the first step, we get:
f(x + h) = - (x + h)^2 + 3(x + h)
= - x^2 - 2xh - h^2 + 3x + 3h
Putting the values in the second step, we get:
f(x + h) - f(x) = - x^2 - 2xh - h^2 + 3x + 3h - [- x^2 + 3x]
= - 2xh - h^2 + 3h
Now, we will substitute the values in step 3 to get the answer.
f(x + h) - f(x) / h = [- 2xh - h^2 + 3h] / h
= - 2x - h + 3
Now, we will put the value in step 4 to get the answer.
f'(x) = lim h → 0 [ - 2x - h + 3]
= - 2x + 3
Thus, the slope of the tangent line to the graph of the given function is - 2x + 3.
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Related Questions
Use the original price and the markup to find the retail price.
Original price: $70; Markup: 20%
The retail price is
Answers
Answer:
$84
Step-by-step explanation:
\(70(1.20)=84\)
Order each set of cards from least to greatest. a. .,⎯⎯⎯⎯√,0.25 , comma , square root of 1 ninth end root , comma , 6 twenty fifths b. ⎯⎯⎯⎯⎯⎯⎯√,.,⎯⎯√square root of 121 over 25 end root , comma , 2.25 , comma square root of 5
Answers
Given:
a. \(\sqrt{0.25},\sqrt{\dfrac{1}{9}},\dfrac{6}{25}\)
b. \(\sqrt{\dfrac{121}{25}},2.25,\sqrt{5}\)
To find:
The correct order for each set of cards from least to greatest.
Solution:
a. \(\sqrt{0.25},\sqrt{\dfrac{1}{9}},\dfrac{6}{25}\)
Convert all numbers in decimal form.
\(\sqrt{0.25}=0.5\)
\(\sqrt{\dfrac{1}{9}}=\dfrac{1}{3}=0.333...\)
\(\dfrac{6}{25}=0.24\)
It is clear that,
\(0.24<0.33...<0.5\)
\(\dfrac{6}{25}<\sqrt{\dfrac{1}{9}}<\sqrt{0.25}\)
Therefore, the required order is \(\dfrac{6}{25},\sqrt{\dfrac{1}{9}},\sqrt{0.25}\).
b. \(\sqrt{\dfrac{121}{25}},2.25,\sqrt{5}\)
Convert all numbers in decimal form.
\(\sqrt{\dfrac{121}{25}}=\dfrac{11}{5}=2.2\)
\(2.25\) already in decimal form.
\(\sqrt{5}\approx 2.236\)
It is clear that,
\(2.2<2.236<2.25\)
\(\sqrt{\dfrac{121}{25}}<\sqrt{5}<2.25\)
Therefore, the required order is \(\sqrt{\dfrac{121}{25}},\sqrt{5},2.25\).
A hockey stick is regularly $54.99, but is on sale for 20% off. What is the price of the hockey stick, including 13% tax?
Answers
Answer:
$49.71
Step-by-step explanation:
Take $54.99 - 20% to get $43.99 add 13% and get $49.71
MULTIPLE CHOICE Which ordered pair is a solution of the linear system
x + y = -2 and7x
4y = 8?
A (-2, 0)
B (0, -2)
C (2, 0)
D (0,2)
Answers
Answer:
A. (-2, 0)
I hope this helps you.
D) 4. Mrs. Smith wants to purchase table pads for her circular
dining room table. If the table has a diameter of 3 feet and
the pads cost 50 cents per square foot, approximately how
much will the table pads cost? Use 3.14 fora.
C
Answers
Answer: 3.53
Step-by-step explanation:
The cost for the table pads that Mrs. Smith will have to pay for her circular dining room table is $3.5325 approx
What is the area of a circle?If the considered circle has got is radius of 'r' units. Then, its area is calculated as:
\(A = \pi r^2 \: \rm unit^2\)
where \(\pi = 3.14159...\)
For this case, we are provided that:
Diameter of the circular dining table of Mrs. Smith = 3 feet
Thus, as radius is half of diameter, thus, radius of table = 3/2 = 1.5 feet
We find the area of the table since the area of the table pad that will be used for table will be equal to the area of the table because it will be applied all over the table.
The area of the table pad = area of the table = \(\pi (1.5)^2 \approx 3.14 \times (1.5)^2 = 7.065 \: \rm ft^2\)
For each sq. foot, Mrs. Smith had to pay 50 cents = 0.5 dollars
Thus, for 7.065 sq. feet, the cost would be:
\(0.5 \times 7.065 = 3.5325\) (in dollars)
Thus, the cost for the table pads that Mrs. Smith will have to pay for her circular dining room table is $3.5325 approx
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A certain triangle has side lengths of 125 feet, 142 feet, and 250 feet. Which of the corresponding side lengths below represent a triangle similar to this one?
25 feet, 42 feet, 175 feet
175 feet, 202 feet, 425.5 feet
275 feet, 312.4 feet, 962.5 feet
100 feet, 113.6 feet, 200 feet
pls answer asap
Answers
Answer: 100ft 113.6ft 200ft
Step-by-step explanation:
These new lengths are all ⅘of the original length
I need help fast please
Answers
Answer:
point H is in quadrant II
Can someone help me?
Answers
Answer:
c aStep-by-step explanation:
The converse of if P then Q simply swaps the clauses: if Q then P. No negation is involved. The biconditional joins them with "if and only if".
All of the answer choices that include not can be rejected.
what are the x and y intercepts of this problem y=-3/8x-9
Answers
Answer:
y=-3/8.0-9 y=1/3 y intercept and for the x intercept is zero
Step-by-step explanation:
Choose all that give the correct expression for the quantity described. The difference of nine times a number x and the quotient of that number and 5. 9x − x 5 Eight more than the quotient of twelve and a number n. n 12 + 8 The product of a number and the quantity 'six minus the number' plus the quotient of eight and the number. x(6 − x) + 8 x Sum of three consecutive even integers. 2x + (2x + 2) + (2x + 4)
Answers
Step-by-step explanation:
We are to get the expression for the following statements;
1) The difference of nine times a number x and the quotient of that number and 5.
The product of nine and a number x is expressed as;
\(=9 \times x\\= 9x\)
The quotient of that number and 5.
\(= \frac{x}{5}\)
The difference between both expression;
\(9x - \frac{x}{5}\)
Hence, the difference of nine times a number x and the quotient of that number and 5 is expressed as \(9x - \frac{x}{5}\)
2) Eight more than the quotient of twelve and a number n
Quotient of twelve and a number n is expressed as:
\(\frac{n}{12}\)
Eight more than the resulting function is;
\(\frac{n}{12}+8\)
Hence eight more than the quotient of twelve and a number n is expressed as \(\frac{n}{12}+8\)
3) The product of a number and the quantity 'six minus the number' plus the quotient of eight and the number.
Let the number be x:
six minus the number is expressed as;
\(6-x\)
product of a number x and the quantity 'six minus the number is;
\(x(6-x)\)
quotient of eight and the number is;
\(\frac{8}{x}\)
Taking the resulting sum of the last two expression
\(x(6-x) + 8x\)
Hence the product of a number and the quantity 'six minus the number' plus the quotient of eight and the number is expressed as;
\(x(6-x) + 8x\)
4) Sum of three consecutive even integers. 2x + (2x + 2) + (2x + 4).
Let the first even number be 2x
The consecutive even numbers are gotten by adding 2 to the preceding number. The two consecutive even integers are 2x+2 and 2x+2+2
the sum of three consecutive even integers is expressed as;
\(= 2x +(2x+2)+(2x+2+2)\\= 2x+(2x+2)+(2x+4)\)
Answer: 1st , 2nd, and 3rd!
Step-by-step explanation:
A construction company is preparing 10 acres of land for a
new housing community. The land contains large rocks that
need to be removed. A machine removes 15 rocks from 360
square feet of land.
1 acre = 43,560 square feet
About how many rocks will need to be removed from the 10
acres of land?
Answers
Answer:
A
Step-by-step explanation:
43560/360 = 121
131x15 = 1815 rocks per acre
1815 x 10 acres = 18150 rocks
Find the slope of the line.
Type your answer as a fraction.
Answers
What is the probability that this spinner will stop on orange when it is spun? write the probability as a fraction in simplest form.
Answers
May someone do this for me I don’t under the top part only but you can do the bottom if you feel like it the first gets branlist
Answers
A container ship left port last week carrying some goods weighing a total of 115,280 tons.
Today, it stopped in another port to unload. As a result, the weight of the goods on the ship
decreased by 30%. What is the weight of the goods on the ship now?
Answers
Answer:
80696,tons
Step-by-step explanation:
let's assume 115280 tons is 100%
100% ‐ 30% = 70%
100% —> 115280tons
70% —> 115280tons ÷ 100 × 70
= 80695.999999997
= 80696 (round to nearest whole number)
Explain the 2 different answers you can get when solving an equation and the variable is eliminated.
Answers
When you're solving an equation, there are three possibilities. Two of which are chosen if your statement is true or not.
If you're able to get x alone, there is one solution. However, If all of the variables are eliminated and you're left with a false statement, that will be no solution. Example: 1=5? False.
If all of the variables are eliminated and you're left with a true statement, that solution is all real numbers. Example: 5=5? True.
Find the area. Leave answer in terms of pi.A) 91 kmC) 647 kmB) 167 kmD) 257 km
Answers
The figure we have is a circle and we need to find its area.
To find the area of any circle we use the following formula:
\(A=\pi r^2\)Where A is the area, and r is the radius of the circle.
Step 1. Identify the radius of the circle.
The radius is a line that goes from the center of the circle to a point in the circumference. In this case, the radius is shown in red in the following diagram:
Thus:
\(r=5kn\)Step 2. Once we know the radius, we can substitute its value into the area formula:
\(A=\pi r^2\)substituting r=5km:
\(A=\pi(5km)^2\)And we solve the operations since 5^2 is equal to 25:
\(A=25\pi km^2\)The indications are to leave the answer in terms of pi, which means that we don't substitute the value of pi in the answer, thus, that is the final answer.
Answer:
\(D)\text{ }25\pi km^2\)
This question has two parts. First, answer Part A. Then, answer Part B. Part A Fill in the blank question. PARKS Rachelle wants to determine the best state park for hiking and fishing. She has developed a metric based on the information she has gathered and the best catch from her previous fishing trips to the parks. Part A Use the metric to calculate a score for each park. Round to the nearest tenth. Park Score = 100[0.2(online rating5)+0.4(miles of trails25)+0.4(fish weight10)] State Park Online Star Rating Hiking Trails (mi) Best Fish (lb) Park Score Gooseberry Falls 4.8 20 9.8 Lake Maria 4.3 14 8.2 Maplewood 4.9 25 7.3 Camden 4.3 15.8 10.1 Part B Part B How might someone who enjoys hiking much more than fishing change this metric? 100 words remaining Tools are not currently accessible
Answers
Answer:
Step-by-step explanation:
If f(x) is given as an equation and g(x) is given as a table, how i can tell they are inverses
Answers
Answer: f(x) and g(x) both represent y of the equations
Step-by-step explanation: f(x) and g(x) both represent the y of the equation for example f(x)=mx+b or g(x)+mx+b both would be to find y of that specific equation and that would also make them inverses because you could use the table to label the inverses on a graph.
Please look at the screenshot below and answer.
Answers
Answer:
-6 4/9, -6.1, 630%, 6.3(repeating 3)
Step-by-step explanation:
Change each number into a decimal.
6.3(repeating 3) = 6.33333...
-6 4/9 = -6.4444...
630% = 6.3
-6.1 = -6.1
From least to greatest:
-6.4444..., -6.1, 6.3, 6.333...
Convert back to original numbers:
-6 4/9, -6.1, 630%, 6.3(repeating 3)
Answer:
D
Step-by-step explanation:
In order to make this easier, let's convert each number into the same format. In this case, decimal form.
\(-6\frac{4}{9}\) = -6.444444...-6.1 remains as is.630% = 6.3 6.3 repeating = 6.333333...(Anything over 9 will result in a repeating number. In order to convert from percentage to decimal, divide by 100.)
The question asks for this to be ordered least to greatest. Start with the negatives.
-6.444... is the smallest.
Then, -6.1.
Then, 6.3.
And finally, 6.3333... is the largest.
Thus, the answer is D.
Using substitution, which value of x makes this equation true?
3+x = 10
A. 13
B. 7
C. -7
D. -13
Answers
Answer:
The answer is B. 7
Step-by-step explanation:
3 + x = 10
3 + 7 = 10
x=7.
Step by step:
x+3=10.
x=7.
(I subtracted 3 on both sides)
Hope this helped!! :)
The equation for the graph shown below in factored form?
Answers
Answer:
The graph is not visible
Step-by-step explanation:
Do something about it
28. Given M₁ = 35, M₂ = 45, and SM1-M2= 6.00, what is the value of t? -2.92 -1.67 O-3.81 2.75
Answers
The t-distribution value is -1.67 for the given mean samples of 35 and 45. Thus, option B is correct.
M₁ = 35
M₂ = 45
SM1-M2 = 6.00
The t-value or t-distribution formula is calculated from the sample mean which consists of real numbers. To calculate the t-value, the formula we need to use here is:
t = (M₁ - M₂) / SM1-M2
Substituting the given values into the formula:
t = (35 - 45) / 6.00
t = -10 / 6.00
t = -1.67
Therefore, we can conclude that the value of t is -1.67 for the samples given.
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The t-distribution value is -1.67 for the given mean samples of 35 and 45. Thus, option B is correct.
Given, M₁ = 35
M₂ = 45
SM1-M2 = 6.00
The t-value or t-distribution formula is calculated from the sample mean which consists of real numbers.
To calculate the t-value,
the formula we need to use here is:
t = (M₁ - M₂) / SM1-M2
Substituting the given values into the formula:
t = (35 - 45) / 6.00
t = -10 / 6.00
t = -1.67
Therefore, we can conclude that the value of t is -1.67 for the samples given.
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A train travels at a speed of 58.6 km/h. Express this speed in
a. m/s
b. cm/min
Answers
Answer:
16.27778 m/s
97666.6667 cm/min
Step-by-step explanation:
a. To convert km/hr into m/sec, multiply the number by 5 and then divide it by 18.
m/s = (58.6 * 5) /18 = 16.27778 m/s
b. 1 Kilometer/Hour = 1666.66666666667 Centimeter/Minute
so 58.6 * 1666.666 =97666.6667 cm/min
Find the equation of the line parallel to y = -3x + 4 with a y-intercept of -10
Answers
when a line is parallel to another line that means the slip of the lines are going to be the same and since the y-intercept of the other line was given to you, you would just put them together in one equation.
Answer:
y=-3x-10
Step-by-step explanation:
Hi there!
We need to find the equation of the line parallel to y=-3x+4 that has the y intercept of -10 (the point (0, -10))
Parallel lines have the same slope
The slope of y=-3x+4 is -3 (it is in the placement of where m (slope) is in y=mx+b)
So the slope of the new line parallel to y=-3x+4 is also -3
Here is the equation of that line so far:
y=-3x+b
b is a placeholder for the y intercept
However, we are given the y intercept as -10, so substitute -10 as b into the equation
y=-3x-10
There's the equation of the line parallel to y=-3x+4 with a y intercept of -10
Hope this helps!
Find the slope of the line that passes through the given points.
(7,3) and (13,8)
Answers
Answer:
\(\frac{5}{6}\)
Step-by-step explanation:
To find the slope, use the equation to find slope. The picture below shows what it looks like.
Using the equation, substitute the values in the x and y values.
\(\frac{8-3}{13-7}\)Then solve
\(\frac{5}{6}\)
What is one way to simplify variables with many, many levels (or decimal places) when creating a frequency distribution?A. Ignore outliers B. Organize data into class intervals C. Graph each level of the variable individually D. Compute a mean, median, and mode
Answers
One way to simplify variables with many levels (or decimal places) when creating a frequency distribution is to organize the data into class intervals (option B).
By grouping the data into intervals, the frequency distribution becomes more manageable and easier to interpret. This process involves dividing the range of values into distinct intervals or categories and then counting the number of observations falling within each interval. Class intervals provide a summary of the data by grouping similar values together, reducing the complexity of individual levels or decimal places.
This simplification technique is particularly useful when dealing with large datasets or continuous variables that have numerous levels or decimal values, allowing for a clearer representation and analysis of the data.
Option B holds true.
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Factoring Explanations Classwork
Directions:
For the following problems, you need to explain what method of factoring you will use and explain all the steps in English words. Do your best to format the math answers. *Some are much easier than others!*
Below are two examples:
Example #1: Factor 18x^2-200y^2 completely.
Answer: For this problem, we will use the difference of squares method.
First, we will factor out the greatest common factor which is 2.
2(9x^2-100y^2 )
Second, we must determine what a and b is.
a=√(〖9x〗^2 )=3x
b=√(〖100y〗^2 )=10y
Third, we put our answer in the form (a+b)(a-b), making sure to include the GCF 2.
Answer: 2(3x+10y)(3x-10y)
Example #2: Factor 2x^2-7x-15 completely.
Answer: For this problem, we will use the X method.
There is no GCF, so we will draw an x and put a*c on top (-30) and b on bottom (-7)
-10 and 3 multiply to get -30 and add to get -7.
Second, we split up the equation to now be this:
2x^2-10x+3x-15
Third, we group it together and factor out the GCF from each group.
(2x^2-10x)+(3x-15)
2x(x-5)+3(x-5)
Fourth and Last, we re-group it together to get our final answer.
Answer: (2x+3)(x-5)
Explain the method used and explain fully how to factor a^2-25
Explain the method used and explain fully how to factor 100-9x^2
Explain the method used and explain fully how to factor 12w^2-300
Explain the method used and explain fully how to factor q^3+125
Explain the method used and explain fully how to factor 27g^3-8f^3
Explain the method used and explain fully how to factor 4xy-14x+16y-56
Explain the method used and explain fully how to factor x^2+13x-30
Explain the method used and explain fully how to factor 9x^2+36
Explain the method used and explain fully how to factor 4x^2+15x+14
Explain the method used and explain fully how to factor 3x^2+15x+18
Answers
Answer: Set your trinomial equal to 160(360), then solve for "x". I think from your instructions that this is what it is asking you to do. But, there is a simpler way.
Step-by-step explanation:
We discussed two algorithms for computing the transitive closure of a given relation. Use the pseudocode given below to complete the questions. 1. In lecture, I mentioned that Warshall's algorithm is more efficient, when compared to Algorithm 0.1, at computing the transitive closure. Verify this claim by doing the following. (a) (15 points) Write python scripts that will perform both algorithms. (b) (10 points) Once your scripts are working correctly, run a sequence of tests using random zero-one matrices with n=10,20,30,…,100 where you record completion time and take a 10 run average for each. Plot your results on an appropriate graph. (c) (5 points) What conclusions can you claim based on your results from part (b)? 2. (20 points) Both algorithms given above can be adapted to find the reflexive closure of the transitive closure for a given relation. Adapt your scripts from 1.(a) so that you have the option to find either the transitive closure, or the reflexive transitive closure, for a given relation. Test your scripts, for each of the four cases, on a random 20×20 zero-one matrix and return the matrices resulting from these tests.
Answers
The results obtained from part (b) can be used to make the following conclusions: Warshall's Algorithm takes less time than Algorithm 0.1 for all values of n between 10 and 100.
The pseudocode for both Algorithm 0.1 and War shall's Algorithm is as follows: Algorithm 0.1:Warshall's Algorithm:
Here is the sequence of steps to calculate and record completion time as well as the 10-run average: Define the range of values n from 10 to 100, and then for each value of n, randomly generate a zero-one matrix M of size nxn (this is an adjacency matrix for a directed graph)
Run Algorithm 0.1 on M and record the time it takes to complete. Repeat this process for ten random matrices of size nxn, then calculate the average of the completion times of the ten runs. Run War shall's Algorithm on M and record the time it takes to complete. Repeat this process for ten random matrices of size nxn, then calculate the average of the completion times of the ten runs. Repeat this for all values of n from 10 to 100. Plot the results on an appropriate graph.
Warshall's Algorithm is more efficient than Algorithm 0.1 in computing the transitive closure of a given relation.
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Tara did a science experiment. The beginning temperature of her saltwater solution was
–
2°C. By the end of the experiment, the solution's temperature was 24°C.
What was the change in the temperature of the solution?
Answers
Step-by-step explanation:
I 2-24 I = 22 degrees Celsius
(absolute value because the change in temperature cannot be negative in this case)
Answer:its -7
Step-by-step explanation:
i got it wrong and said it was -7