What is the vertex of y =- X² 4?
Answers
The vertex of a parabola is the point at which the parabola changes direction, the vertex of y =-x² + 4 is (0, 4).
The equation for a parabola in standard form is y = ax² + bx + c. To find the vertex of y = -x² + 4, we need to use the formula x = -b/2a. In this equation, a is -1, and b is 0, so x = 0. Therefore, the vertex of y = -x² + 4 is (0, 4).
To find the vertex of a parabola, we can use the formula x = -b/2a. In this formula, a is the coefficient of x², and b is the coefficient of x. Therefore, to find the vertex of a parabola, we need to find the coefficients of x² and x and then plug them into the formula. This formula will give us the x-coordinate of the vertex, and we can then use the equation of the parabola to find the y-coordinate of the vertex. In the case of y = -x² + 4, the coefficient of x² is -1 and the coefficient of x is 0. Plugging these values into the formula, we get x = 0. We can then use the equation of the parabola to find the y-coordinate of the vertex, which is 4. Therefore, the vertex of y =-x² + 4 is (0, 4).
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Related Questions
algorithm depth-first search : find the order of visit: 2. algorithm breadth first search : find the order of visit
Answers
The order of visit for DFS and BFS will differ based on the structure of the graph or tree and the starting node. DFS will typically visit nodes in a deeper order, while BFS will visit nodes in a breadth-first order.
Both algorithm depth-first search and algorithm breadth-first search are used to traverse or search a graph or tree data structure. The difference between them lies in their traversal strategy.
Depth-first search (DFS) starts at a root node and explores as far as possible along each branch before backtracking. It follows a content-loaded algorithm, meaning that it prioritizes exploring deeper into the structure before considering other branches. In terms of visit order, DFS starts at the root node, then moves to its first child node, and continues to explore its descendants until it reaches a leaf node. Once it has visited all descendants of the current node, it backtracks to the previous node and repeats the process until it has visited all nodes.
On the other hand, breadth-first search (BFS) starts at the root node and explores all the neighboring nodes at the current depth level before moving on to the next depth level. It follows a breadth-first algorithm, meaning that it prioritizes exploring all nodes at a given depth level before moving on to deeper levels. In terms of visit order, BFS visits all nodes at a given depth level before moving on to the next level.
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terri's computer screen is 4/9 yards wide and 1/3 yard long. What is the area of Terri's computer screen?
Answers
Answer:
Step-by-step explanation:
Length x width
\(\frac{4}{9} *\frac{1}{3} =\frac{4}{27}\)
Answer question with steps get brainliest! Please answer ASAP with steps. Use picture above
Answers
If you refer to the table it gives you the values of what would x be for each; therefore, looking at the table:
f(2)=1
You would plug in the 1 into g(x) so it would be g(1) which is looking at the table:
g(1)=5
Ian’s mom sang him S songs. Then his sister sang him two times as many as his mom had. If Ian listened to nine songs in all, Ian's mom sang _____songs.
Answers
Ian’s mom sang him S songs. Then his sister sang him two times as many as his mom had. If Ian listened to nine songs in all, Ian's mom sanghim twIan’s mom sang him S songs. Then his sister sang him two times as many as his mom had. If Ian listened to nine songs in all, Ian's mom sango times as many as his mom had. If Ian listened to nine songs in all, Ian's mom sang _____songs.
PERSEVERE ABCD is a parallelogram with side lengths as indicated in the given figure. The perimeter of ABCD is 22. Find AB.
Answers
The value of side AB is 6 units for parallelogram ABCD with perimeter is 22 units.
What is an equation?An equation is an expression that shows how two or more numbers and variables are related to each other. Types of equations can either be linear, quadratic or cubic
Parallelogram is a quadrilateral (four angles and sides) in which opposite sides are equal and parallel.
From the diagram:
AB = DC (opposite sides are equal)
2y + 1 = 4 - 4w
2y + 4w = 3 (1)
AD = BC (opposite sides are equal)
3x - 2 = x - w + 1
2x + w = 3 (2)
The perimeter of ABCD is 22:
2(AB + AD) = Perimeter
2(2y + 1 + 3 - 4w) = 22
2(2y - 4w + 4) = 22
4y - 8w + 8 = 22
4y - 8w = 14 (3)
From the three equations:
w = -0.5, x = 1.75, y = 2.5
AB = 2y + 1 = 2(2.5) + 1 = 6 units
The value of side AB is 6 units
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Which function increases at the fastest rate between x = 0 and x = 8? A 2-column table with 5 rows titled Linear Function with the equation f of x = 2 x + 2. The first column is labeled x with entries 0, 2, 4, 6, 8. The second column is labeled f of x with entries 2, 6, 10, 14, 18. A 2-column table with 5 rows titled Exponential Function with the equation f of x = 2 Superscript x Baseline + 2. The first column is labeled x with entries 0, 2, 4, 6, 8. The second column is labeled f of x with entries 3, 6, 18, 66, 258. A 2-column table with 5 rows titled Quadratic Function with the equation f of x = 2 x squared + 2. The first column is labeled x with entries 0, 2, 4, 6, 8. The second column is labeled f of x with entries 2, 10, 34, 74, 130. A 2-column table with 5 rows titled Linear Function with the equation f of x = 3 x + 2. The first column is labeled x with entries 0, 2, 4, 6, 8. The second column is labeled f of x with entries 2, 8, 14, 20, 26.
Answers
Answer:
The correct option is;
Exponential function 2ˣ + 2
x = 0, 2, 4, 6, 8
f(x) = 3, 6, 18, 66, 258
Step-by-step explanation:
The given functions are;
f(x) = 2x + 2
x = 0, 2, 4, 6, 8
f(x) = 2, 6, 10, 14, 18
f(x) = 2ˣ + 2
x = 0, 2, 4, 6, 8
f(x) = 3, 6, 18, 66, 258
f(x) = 2·x² + 2
x = 0, 2, 4, 6, 8
f(x) = 2, 10, 34, 74, 130
f(x) = 3·x + 2
x = 0, 2, 4, 6, 8
f(x) = 2, 8, 14, 20, 26
By comparison, the function that increases at the fastest rate between x = 0 and x = 8 is Exponential function 2ˣ + 2
Answer: The answer is B on edg
Step-by-step explanation:
The frequency of occurrence of something within a specifically defined area is the.
Answers
Density –The frequency with which something exists with a given unit of area.
Definition of density: A material's density is determined by how closely it is packed. As the mass per unit volume, it has that definition. Symbol for density: D or Formula for Density: Where is the density, m is the object's mass, and V is its volume, the equation is: = m/V.
How much "stuff" is contained in a specific quantity of space is determined by its density. For instance, a block of the harder, lighter element gold (Au) will be denser than a block of the heavier element lead (Pb) (Au). Styrofoam blocks are less dense than bricks. Mass per unit volume serves as its definition.
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is the equation minumum or maximum
Answers
Answer:
Minimum
Step-by-step explanation:
A minimum occurs when the line goes from decreasing to increasing
Answer:
minimum bc it shows the lowest point of the graph
at your local carnival, there is a game where 40 rubber duckies are floating in a kiddie tub, and they each have their bottoms painted one of three colors. 6 are painted pink, 15 are painted blue, and 19 are painted purple. if the player selects a duck with a pink bottom, they receive three pieces of candy. if they select blue, they receive two pieces of candy. and if they select purple, they receive one piece of candy. if the game is played 49 times, what are the minimum and maximum amounts of candy that could be handed out?
Answers
The minimum amount of candy that could be handed out is 19 pieces, and the maximum amount of candy that could be handed out is 104 pieces.
Minimum amount of candy can ve observed by selecting the least amount of candy.
The number of the least amount of candy is purple duckies, which are 19.
Number of times the game is played = 49
The minimum amount of candy, can be calculated as:
Minimum candy = 19 \(\times\) 1
Minimum candy = 19 pieces
The maximum amount of candy can be calculated as:
The number of the maximum amount of candy is 6 pink duckies, which are 6.
Number of pieces of candy per pink ducky = 3
Number of candies for remaining selections = 2
Maximum candy = (6\(\times\) 3) + (remaining selections \(\times\) 2 pieces of candy per blue ducky)
The remaining selections can be calculated as:
Remaining selections = 49 (total selections) - 6 (pink duckies) = 43 selections
Maximum candy = (6 \(\times\)3) + (43 \(\times\) 2)
= 18 + 86
= 104 pieces of candy.
So, the minimum amount of candy that could be handed out is 19 pieces, and the maximum amount of candy that could be handed out is 104 pieces.
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he accompanying histogram shows the life expectancies at birth for 190 countries as collected by an international health agency.
a) Which would you expect to be larger: the median or the mean? Explain briefly.
b) Which would you report: the median or the mean? Explain briefly.
Answers
a) The median would be larger than the mean because the life expectancy of some countries may be much lower than the others, thus affecting the mean.
b) The median should be reported as it is a better measure of central tendency, as it is not affected by outliers.
a) The median is expected to be larger than the mean because the life expectancy of some countries may be much lower than the others, thus affecting the mean. The mean is calculated by adding all the values together and dividing by the number of values, and if there are any values that are much lower or higher than the rest, this will affect the mean significantly. The median, however, is the midpoint of the values, so outliers have less of an influence on it.
b) The median should be reported as it is a better measure of central tendency, as it is not affected by outliers. The median is the midpoint of the values, which means that if there are any values that are much lower or higher than the rest, it will not affect the median as much as it does the mean. This makes the median more accurate in representing the life expectancy of countries, as it is not skewed by outliers. Furthermore, the median is generally more reliable when dealing with skewed distributions, which is often the case with life expectancy data.
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there are a cup of milk and a cup of water. take one teaspoon of milk, put into the water cup; mix well. take one teaspoon of the mixture in the water cup and put into the milk cup then mix well. which is higher: the percentage of water in the milk cup or the percentage of milk in the water cup ?
Answers
The percentage of water in the milk cup and the percentage of milk in the water cup are same.
What is milk?
A white liquid meal called milk is generated by mammals' mammary glands. Before they can digest solid food, it is the main source of nutrition for young mammals. Milk immunity is influenced by immune components and immune-modulating elements.
Given:
There are a cup of milk and a cup of water.
Take one teaspoon of milk, put into the water cup; mix well.
Take one teaspoon of the mixture in the water cup and put into the milk cup then mix well.
Suppose the percentage of water cup are 'p' and the percentage of milk cup are 'q'.
When we add one teaspoon of milk and put into water cup then the percentage of water cup are 'p + 1'.
And the percentage of milk cup are 'q - 1'.
Again one teaspoon of mixture in the water cup put into the milk cup.
So, the percentage of milk cup are, q - 1 + 1 = q.
And the percentage of water cup are p + 1 - 1 = p.
The percentage will be same for both milk cup and water cup.
Hence, the percentage of water in the milk cup and the percentage of milk in the water cup are same.
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domnics video game has a perimeter of 18 inches the width is 4 inches what is the height of the video game
Answers
The height of the video game is 4.5
if 5 apples cost 0.60 then how much does 6 apples cost
Answers
Answer:
$0.72 for 6 apples
Step-by-step explanation:
0.60 / 5 = 0.12
0.12 * 6 = 0.72Find the area of the region that lies inside the first curve and outside the second curve.
r= 10cos( θ)
r= 5
An exact answer is necessary.
Answers
The formula becomes ½(10cos(θ)² - 5²)dθ, integrated from θ = π/3 to θ = 5π/3. Simplifying, we have ½(100cos²(θ) - 25)dθ.
The area of the region that lies inside the first curve (r = 10cos(θ)) and outside the second curve (r = 5) can be found by evaluating the definite integral of ½(r₁² - r₂²)dθ, where r₁ represents the outer curve and r₂ represents the inner curve.
To find the limits of integration, we need to determine the values of θ where the two curves intersect. Setting r₁ equal to r₂, we have 10cos(θ) = 5. Solving this equation, we find cos(θ) = ½, which corresponds to θ = π/3 and θ = 5π/3.
Now we can calculate the area using the definite integral. The formula becomes ½(10cos(θ)² - 5²)dθ, integrated from θ = π/3 to θ = 5π/3. Simplifying, we have ½(100cos²(θ) - 25)dθ.
Integrating this expression will give us the exact area of the region. Evaluating the integral over the given limits will provide the desired result.
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A student has $810.00 in her account and withdraws
of it.
How much money, in dollars, remains in the account?
Answers
Money, in dollars, that remains in the account is $(810 - x) using subtraction.
What is subtraction?The operation of subtraction is used to calculate the difference between two numbers. If you have an object group and remove a couple of them, the object group gets smaller.
In mathematics, there are various symbols. One of the crucial arithmetic symbols we employ while subtracting is the subtraction symbol(-).
For instance, your friends consumed 7 of the 9 cupcakes you purchased for your birthday party. You are now down to two cupcakes.
The money the student has in the account = $810
Let the money withdraw is x.
The remaining amount left is given by the expression
$(810 - x).
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Solve for x 5z-8=-28
Answers
U said solve for x do u mean z?
z=-4
Answer: z = -4
Step-by-step explanation:
Simplifying
5z + -8 = -28
Reorder the terms:
-8 + 5z = -28
Solving
-8 + 5z = -28
Solving for variable 'z'.
Move all terms containing z to the left, all other terms to the right.
Add '8' to each side of the equation.
-8 + 8 + 5z = -28 + 8
Combine like terms: -8 + 8 = 0
0 + 5z = -28 + 8
5z = -28 + 8
Combine like terms: -28 + 8 = -20
5z = -20
Divide each side by '5'.
z = -4
Simplifying
z = -4 Hope this helps !
Julia has walked 5000 steps each day for one week. Her weekly steps target is to walk 50 000 steps.
What percent of her weekly steps target did she achieve?
help... :( I suck at math
Answers
Goal = 50,000
5000/50,000 x 100 = 10% -> Final Answer.
Answer:
70%
Step-by-step explanation:
Let's start by finding how many steps she walked in one week...
5000 steps per day*7 days=35000 steps
Now we find what percent of 50000 steps 35000 is...
35000=n%*50000
35000=n/100*50000
35000=500n
Divide both sides by 500
n=70
70%
A store sells 6 bananas for $4. Determine how much it would cost to buy 15 bananas
Answers
Answer:
$10
Step-by-step explanation:
Since 6 cost four dollars 3 would cost 2 dollars multiply 3 to get 15 bananas and 2 to get $10
Answer:
$10
Step-by-step explanation:
Make proportion:
?= cost of bananas
6 - 4
15 - ?
?= 15×4÷6=10
Round each decimal to the nearest tenth
4. 13.392
5. 27.149
6.8.84858
Help!!
Answers
Answer:
13.4
27.1
8.8
Step-by-step explanation:
hope that helps
Solve for y math problem
Answers
Answer:
The answer is 4/5
Step-by-step explanation:
-1/2 y ≤ -2/5
1/2y ≤ 2/5
y ≤ 2 × 2/5
y ≤ 4/5
Thus, The value of y is 4/5
-TheUnknownScientist 72
a car travel 20kph faster than a truck. the car cover 350 km in two hours less than the time it takes the truck to travel the same distance. what is the speed of the car? how about the truck?
Answers
A car travel 20kph faster than a truck. the car cover 350 km in two hours less than the time. The speed of the car is 50 km/h. The speed of truck is 70 km/h.
Define speed.You can determine an object's speed if you know how far it moves in a given amount of time. For instance, an automobile is moving at a pace of 70 miles per hour if it covers 70 miles in an hour (miles per hour).
Given,
A car travel 20kph faster than a truck. the car cover 350 km in two hours less than the time.
Let s represent the truck's speed and (s+20) represent the car's speed.
to determine each vehicle's time
Time = Speed / Distance
truck time = 350/s
Time in an automobile is 350/(s+20)
Truck time - car time = 2 hours
So,
(350/s) - [350/(s+20)] = 2
LCM is s(s+20)
[350(s+20) - 350s]/s(s+20) = 2
Cross multiplying,
350(s+20) - 350s = 2s(s+20)
Simplifying the equation,
350s + 7000 - 350s = 2s² + 40s
Now, we have quadratic equation to simplify,
2s² + 40s - 7000 = 0
Dividing the equation by 2
s² + 20s - 3500 = 0
Factorizing,
s= 50
s= -70 (impossible because of the sign)
Hence the truck's speed is s = 50 km/h.
The speed of the car is s + 20 = 70 km/h.
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Please help me Pleaseeeeeeeeee (you also need to find x)
Answers
Answer:
m<CAB = 54°
m<ABC = 21°
m<ACB = 105°
m<DCB = 75°
Step-by-step explanation:
Part 1: Solve for x
The sum of the 3 interior angles of a triangle always equals 180°.
** Take note
Lets call m<CAB, angle A.
Lets call m<ABC, angle B.
Lets call m<ACB, angle C.
Lets call m<DCB, angle D.
So A + B + C = 180
Therefore we have
\((13x-11)+(4x+1)+C=180\)
We have 1 more angle.
They gave us an exterior angle to help us find angle C.
A straight line is 180°.
They gave us one of 2 angles.
So
\(180-(18x-15)=C\)
We can substitute \(180-(18x-15)\) for \(C\) in our first equation.
All together we have.
\((13x-11)+(4x+1)+(180-(18x-15))=180\)\(13x-11+4x+1+180-(18x-15)=180\)
Now lets simplify and solve for \(x\).
Simplify each term.
Apply the distributive property.
\(13x-11+4x+1+180-(18x)--15=180\)
\(13x-11+4x+1+180-18x+15=180\)
Simplify by adding like terms.
Add \(13x\) and \(4x\).
\(17x-11+1+180-18x+15=180\)
Subtract \(18x\) from \(17x\).
\(-x-11+1+180+15=180\)
Simplify by adding numbers.
Add \(-11\) and \(1\).
\(-x-10+180+15=180\)
Add \(-10\) and \(180\).
\(-x+170+15=180\)
Add \(170\) and \(15\).
\(-x+185=180\)
Move all terms not containing \(x\) to the right side of the equation.
Subtract \(185\) from both sides of the equation.
\(-x=180-185\)
Subtract \(185\) from \(180\)
\(-x=5\)
Divide each term by − 1 and simplify.
\(\frac{-x}{-1} =\frac{-5}{-1}\)
\(x=5\)
Part 2: Find the numerical value of each angle
We can now substitute 5 for x into the equations from the picture.
\((13*5-11)+(4*5+1)+C=180\)
Angle A is \(13x-11\)
So A equals 54°
Angle B is \(4x+1\)
So B equals 21°
Remember \(A + B + C = 180\). We can solve for \(C\) and we get.
\(C=180-A-B\)
\(C=180-54-21\)
So C equals 105°
Remember a straight line is 180°.
We have 2 angles on the straight line. C and D
Therefore, \(C+D=180\)
\(D=180-C\)
\(D=180-105\)
So D equals 75°
We can check. It gave us \(D=18x-15\)
\(D=18*5-15\)
\(D=90-15\)
\(D=75\)
What is the forecast for May using a five-month moving average?(Round answer to the nearest whole number.) Nov. 39 Dec. 27 Jan. 40 Feb. 42 Mar. 41 April 47
A. 43 B. 47 C. 52 D. 38 E. 39
Answers
The forecast for May using a five-month moving average is 39 (Option E).
Moving average is used for smoothing out time series data to find any trends or cycles within the data. A five-month moving average is the average of the past five months. To calculate the moving average, add up the sales for the previous five months and divide it by five.
According to the question, the sales for the previous five months are: Nov. 39 Dec. 27 Jan. 40 Feb. 42 Mar. 41 April 47
We have to add the sales of these five months, which gives:
27 + 40 + 42 + 41 + 47 = 197
To find the moving average for May, we divide this sum by 5:
197 / 5 = 39.4
Since we have to round the answer to the nearest whole number, we round 39.4 to 39, which is option E.
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I need help to solve this please!!
Answers
Answer:
Adult is 10$ and Child is 7$.
Unfortunately for the family, they do not have enough to go to the theater. They do not have that extra dollar.
Hope this helps!
Step-by-step explanation:
2x + 4y = 48
5x + 2y = 64
2x + 4y = 48
10x + 4y = 128
( 10x - 2x ) + ( 4y - 4y ) = ( 128 - 48 )
8x = 80
x = 10
2 ( 10 ) + 4y = 48
20 + 4y = 48
4y = 48 - 20
4y = 28
y = 7
What is the vertex of f(x)=x^2−12x+25 ?
Answers
Answer:
vertex is (6, -11)
Step-by-step explanation:
Given equation
f(x) = x² - 12x + 25
is that of an upward-facing parabola(since the coefficient of x² is positive).
The vertex will be at a minimum and its x-coordinate can be found by finding the first derivative of f(x), setting it equal to zero and solving for x
f'(x) = d/dx(x² - 12x + 25)
= 2x - 12
f'(x) = 0 ==> 2x - 12 = 0
2x = 12
x = 6
Substitute x = 6 in f(x) to get
f(6) = 6² - 12(6) + 25
= 36 - 72 + 25
= -11
So the vertex is at (6, -11)
Find the length of the diagonal of an 8cmx 6cmx 10cm rectangular prism. Round to the nearest tenth. (HELP PLEASE!!)
Answers
Answer:
14.1 cm
Step-by-step explanation:
first find the base diagonal :
base di = Square root (8^2 + 6^2) = 10cm
so,
diagonal = Square root (10^2 + 10^2) = 14.1 cm (ANS)
Using Ohm’s law, work out the following basic formula’s. V = 2
Amps × 6 Ohms I = 12V ÷ 6R R = 12V ÷ 4I
Answers
The answers to the given formulas are as follows:
1. V = 2 Amps × 6 Ohms
2. I = 12V ÷ 6R
3. R = 12V ÷ 4I
1. Using Ohm's law, the formula V = I × R calculates the voltage (V) when the current (I) and resistance (R) are known. In this case, the given formula V = 2 Amps × 6 Ohms simplifies to V = 12 Volts.
2. The formula I = V ÷ R determines the current (I) when the voltage (V) and resistance (R) are known. In the provided formula I = 12V ÷ 6R, we can rewrite it as I = (12 Volts) ÷ (6 Ohms), resulting in I = 2 Amps.
3. Lastly, the formula R = V ÷ I calculates the resistance (R) when the voltage (V) and current (I) are known. The given formula R = 12V ÷ 4I can be expressed as R = (12 Volts) ÷ (4 Amps), leading to R = 3 Ohms.
By applying Ohm's law, these formulas allow for the calculation of voltage, current, or resistance in a circuit when the other two values are given.
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write an equation for a hyperbola with center at (1, 4), vertex at (3,4) and focus at (7,4)
Answers
With the given information, the equation of the hyperbola can be expressed as: \(\frac{(x-1)^2}{4 } - \frac{(y-4)^2}{32} = 1\)
Understanding Equation of HyperbolaThe general equation of a hyperbola with center (h, k), vertex (a, k), and focus (c, k) on the x-axis can be written as:
\(\frac{(x-h)^2}{a^{2} } - \frac{(y-k)^2}{b^{2} } = 1\)
From the question,
center is (1, 4),
vertex is (3, 4), and
focus is (7, 4).
The distance between the center and vertex is the value of 'a', which is 3 - 1 = 2.
The distance between the center and focus is the value of 'c', which is 7 - 1 = 6.
The value of 'b' can be found using the relationship
c² = a² + b².
Substituting the known values:
6² = 2² + b²
36 = 4 + b²
b² = 32
Plugging these values into the equation, we have:
\(\frac{(x-1)^2}{2^{2} } - \frac{(y-4)^2}{\sqrt{32} ^{2} } = 1\)
Simplifying further:
\(\frac{(x-1)^2}{4 } - \frac{(y-4)^2}{32} = 1\)
This is the equation of the hyperbola with the given center, vertex, and focus.
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find f'(x) when f(x) = (x^2) - 2x. find the equation of the tangent line and the normal line at x=4
Answers
The derivate of a function f(x) is determinated as:
\(f^{\prime}(x)=\lim _{h\to0}\frac{f(x+h)-f(x)}{h}\)For the function
\(f(x)=x^2-2x\)First we have to determine de f ( x + h ) as follow:
\(f(x+h)=(x+h)^2-2(x+h)\)\(f(x+h)=x^2+2xh+h^2-2x-h^{}\)Then we calculate and simplify the coeficient in the first formula
\(\frac{f(x+h)-f(x)}{h}\)\(\frac{(x^2+2xh+h^2-2x-h^{})-(x^2-2x)}{h}\)\(\frac{x^2+2xh+h^2-2x-h^{}-x^2+2x}{h}=\frac{h^2+2xh-h}{h}\)\(\frac{h^2+2xh-h}{h}\text{ = }\frac{h(h+2x-1)}{h}=h+2x-1\)So the derivate is:\(f^{\prime}(x)=\lim _{h\to0}\frac{f(x+h)-f(x)}{h}=\lim _{h\to0}h+2x-1\)\(f^{\prime}(x)=0+2x-1\)\(f^{\prime}(x)=2x-1\)------------------------------------------------------------------------------------The equation of the tangent:
First you need to know that the derivate of a function is equal to the slope (m) of the tangent of this function
And the equation to thist tangent in a specific point will be find using the next formula:
\(y-f(x_0)=m(x-x_0)_{}\)We have to calculate the slope in the point x =4 using the derivate:
\(m=2x-1\)\(m=2(4)-1=7\)In the point x=4
Calculate the value of f(x0) substituting in the function the given point x:
\(f(4)=4^2-2(4)\text{ = }8\)Knowing that we put the value of m and f(x0) in the equation of the tangent:
\(y-8=7(x-4)_{}\)\(y-8=7x-28\)\(y=7x-28+8\)So the equation of the tangent in x= 4 is:\(y=7x-20\)---------------------------------------------------------------------------
The normal line
The slope of the normal line is the opposite of the slope of theu tangent in an espesific point:
\(m_n=-\frac{1}{m_t}\)So in this situation is:
\(m_n=-\frac{1}{7}\)The equation of the normal line is given by the next formula:
\(y-f(x_0)=m_n(x-x_0)_{}\)Replacing the data we obtain:
\(y-8=-\frac{1}{7}(x-4)_{}\)\(y-8=-\frac{1}{7}x+\frac{4}{7}\)So the equation of the normal line is:\(y=-\frac{1}{7}x+\frac{60}{7}\)solve for m please will give brainlest
Answers
Answer:
55 degrees
Step-by-step explanation:
sum of all angles of a triangle equal 180
to find x we add them all and set them equal to 180
(57+x)+(72+x)+55=180
129+2x+55=180
184+2x=180
-184. -184
2x= -4
/2. /2
x=-2
now to find angle A
57+(-2)
55
hopes this helps