The quadratic function f(x) = x² - 6x + 9 has a minimum at point (3,0).
What is a quadratic function?
A polynomial function with one or more variables, where the largest exponent of the variable is two, is referred to as a quadratic function. It is also known as the polynomial of degree 2 since the greatest degree term in a quadratic function is of second degree.
The given quadratic function is - f(x) = x² - 6x + 9.
Find the differentiation of f(x) -
dy/dx = d/dx (x² - 6x + 9)
d/dx (x²) - d/dx (6x) + d/dx (9)
2x - 6 + 0
2x - 6 = 0
For stationary values, dy/dx = 0
2x - 6 = 0
2x = 6
x = 6/2
x = 3
At x = 3 we get stationary values.
Now, d²y/dx² = 2x - 6
d/dx (2x - 6)
d/dx (2x) - d/dx (6)
2 - 0 = 0
2 = 0
(d²y/dx²) x=3 = 2 (positive)
Therefore, at x = 3 the function is minimum.
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Please Hurry!
A box of apples sells for $17. At this rate, which expression represents the cost, in dollars, of 100 apples?
A) 5/17•20
B) 5/20•17
C) 100/17•20
D) 100/20•17
E) 17•5•20
Answer: D
Step-by-step explanation:
20 apples cost $17
100 apples = 100/20 * 17 = D
Use the Midpoint Rule with the given value of n to approximate the integral. Round the answer to four decimal places.
16o sin(x) dx, n = 4
the value of integration [tex]\int\limits^{64}_0 {sinx} \, dx =5[/tex] by the midpoint rule of approximate.
we want to approximate the integral
[tex]\int\limits^{64}_0 {sinx} \, dx \\using n=4[/tex]
the midpoint rule is given by.
[tex]\int^b_af(x)dx=\triangle x(f(\frac{x_{0} +x_1)}{2})+f(\frac{x_1+x_2}{2} )+....+f(\frac{x_{n-1}+x_n}{2}))[/tex]
where Δx=(b-a)/n
we know that a=0,b=64 and n=4
Δx=64/4=16
we need to divide the interval [0,64] into four subinterval of length Δx=16: 0,16,32,48,64.
now, we just evaluate the function at these endpoints.
[tex]f(\frac{x_1+x_0}{2} ) =f(\frac{0+64}{2} )\\f(8)=sin8=0.9894\\\\f(\frac{x_1+x_2}{2}) =f(\frac{16+32}{2} )\\\\f(24)=sin24=-0.9056\\\\similarly\\\\f(40)=sin(40)=0.7451\\\\f(56)=sin56=-0.5216[/tex]
finally, just sum up above values and multiply by Δx=16.
[tex]\int\limits^{64}_0 {sinx} \, dx=4.9168= 5[/tex]
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A person borrowed $2100 from his home equity line of credit to pay off his car loan. He then borrowed another $1200 to have his kitchen repainted. Represent how much
he owed on his home equity line of credit as a real number.
What is the real number that represents the amount he owed on his home equity line of credit?
The real number that represents the amount he owed on his home equity line of credit would be = $3,300
What is a real number?A real number is defined as the type of number that can be used to represent a one directional measurement which can be rational or irrational.
The first amount of money borrowed by a person from his home equity line of credit = $2100
The second amount of money borrowed by a person from his home equity line of credit = $1200
Therefore, the total amount that was borrowed= 2100+1200 = $3,300.
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Which equation can be used to find the area in square feet of the piece of glass?
Answer:
Area = length x width (in feet)
Step-by-step explanation:
The area of a 2-dimensional shape can be found by multiplying its length by its width. The equation to find the area of a rectangle is:
Area = length x width
So if you know the length and width of a piece of glass in feet, you can use the above equation to find its area in square feet. For example, if the length of the glass is 10 feet and the width is 5 feet, the area would be:
Area = 10 feet x 5 feet = 50 square feet
So the equation to find the area of a piece of glass in square feet is:
Area = length x width (in feet)
It's worth noting that this equation applies to any 2-dimensional shape that has a length and a width, not just a rectangle.
The graph below represents the distance of a dog from a trainer after a command is given.
A graph titled Dog Obedience School. The horizontal axis shows Time (seconds), numbered 1 to 10, and the vertical axis shows Distance (yards) numbered 4 to 40. The line shows an increase, then decrease, then constant distance.
Which statement could describe the dog’s movement at 5 seconds once the command was given?
The dog stopped to lie down and obey the trainer’s command.
The dog was running towards the trainer.
The dog was running away from the trainer.
The dog was stopped but began running towards the trainer.
The correct statement regarding the dog’s movement at 5 seconds once the command was given is given as follows:
The dog was running towards the trainer.
How to obtain the correct statement regarding the graph?The input and output variables for the function graphed are given as follows:
Input: time.Output: distance.At a time of 5 seconds, the distance between the dog and the trainer is decreasing, meaning that the dog was moving towards the trainer, and thus the second option is the correct option.
Missing InformationThe graph is given by the image presented at the end of the answer.
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Answer:
The dog was running towards the trainer.
What is 26,430,000 in expanded form
Answer: 20,000,000 + 6,000,000 + 400,000 + 30,000
Step-by-step explanation:
The baker made a batch of chocolate chip, oatmeal raisin, and sugar cookies. If P(chocolate chip) = 0.25, interpret the likelihood of randomly selecting a chocolate chip cookie from the batch.
A. Equally likely and unlikely
B. Likely
C. Unlikely
D. This value is not possible to represent probability of a chance event.
The baker made a batch of chocolate chips, oatmeal raisin, and sugar cookies. If P(chocolate chip) = 0.25, the likelihood of randomly selecting a chocolate chip is B. Likely.
What is probability?Generally, Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, with 0 indicating that an event is impossible and 1 indicating that an event is certain.
A probability of 0.5, for example, would indicate that an event has a 50% chance of occurring. Probability can be used to make predictions and inform decision-making in a wide range of fields, including statistics, finance, and engineering.
A probability of 0.25 represents a 25% chance of a randomly selected cookie from the batch being a chocolate chip cookie, which is considered "likely" to occur.
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Distributive property c3/c when c=3
Answer: The answer is 9
Step-by-step explanation: 3^3/3=9
(07.01 mc) select the general solution to x squared dy over dx equals 3 plus 2y period one half ln absolute value of quantity 3 plus 2y close absolute value equals ln absolute value of x squared close absolute value plus c one half ln absolute value of quantity 3 plus 2y close absolute value equals negative 1 over x plus c
The general solution to x squared dy over dx equals 3 plus 2y is given by 1/2 ln|3 + 2y| = -1/x + c, where c is an arbitrary constant.
To calculate this, we begin by taking the derivative of both sides of the equation with respect to x. We then rearrange the equation to yield 2y + x^2 dy/dx = 3. We divide both sides by x^2 so that dy/dx is isolated on one side of the equation, yielding dy/dx = (3 - 2y) / x^2. We can then integrate both sides of the equation, with respect to x, to yield 1/2 ln|3 + 2y| = -1/x + c, where c is an arbitrary constant. This equation is the general solution to x squared dy over dx equals 3 plus 2y.
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1) Differentiate following equations with respect to x.
a) x² + xy + y² = 0
b) 1/x + 1/y =e^y
The differential equations are dy/dx = -x/y and dy/dx = e^y * (-1/x² + 1/y²).
What is the differential equation?
A solution of a differential equation is an expression for the dependent variable in terms of the independent one(s) which satisfies the relation. The general solution includes all possible solutions and typically includes arbitrary constants (in the case of an ODE) or arbitrary functions (in the case of a PDE.)
a) To differentiate x² + xy + y² = 0 with respect to x, we can use the power rule and the chain rule.
The power rule states that the derivative of x^n is nx^(n-1)
The chain rule states that if y = f(u) and x = g(u) then dy/dx = dy/du * du/dx
x² + xy + y² = 0
dx/dx (x² + xy + y²) = dx/dx (0)
2x + y = 0
dy/dx = -x/y
b) To differentiate 1/x + 1/y = e^y with respect to x, we can use the chain rule and the reciprocal rule.
The chain rule states that if y = f(u) and x = g(u) then dy/dx = dy/du * du/dx
The reciprocal rule states that the derivative of 1/x is -1/x²
1/x + 1/y = e^y
dy/dx = dy/dx (e^y)
dx/dx (1/x + 1/y) = dx/dx (e^y)
-1/x² - 1/y² = e^y
dy/dx = e^y * (-1/x² + 1/y²)
Hence, the differential equations are dy/dx = -x/y and dy/dx = e^y * (-1/x² + 1/y²).
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pls help me
Josh is the owner of CranBog, a Cranberry Bog in Massachusetts. Cranberry production at CranBod can be represented by the inequality y ≤ 150x - 3100
under normal climate conditions, where y
is the annual production of cranberries at CranBog, in thousands of pounds, and x
is the number of acres of land that produce cranberries.
The TRUE statements about the inequality y ≤ 150x - 3100 are:
A) For a solution to be viable, both x and y must be integers.E) The ordered pair (40, 2900) is a solution to the inequality and means that with 40 acres of land, CranBog can produce 2,900 (in thousands of) pounds of cranberries.What is inequality?Inequality is a mathematical statement showing that two or more mathematical expressions are unequal or not equivalent.
Inequalities are represented by the following types and inequality symbols:
Less than (<)Greater than (>)Not equal to (≠)Less than or equal to (≤)Greater than or equal to (≥).Check:
Ordered pairs (40, 2900)
y ≤ 150x - 3100
y ≤ 150(40) - 3100
y ≤ 6,000 - 3100
y ≤ 2900
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Nancy and Martin are making kites. The kites are similar figures. The side lengths of Nancy's kite are 16 inches, 16 inches, 24 inches, and 24 inches. The side lengths of Martin's kite are (5x + 5) inches, (5x + 5) inches, 10x inches, and 10x inches. Assume that 10x > 5x + 5. Find the perimeter of Martin's kite.
Answer: 100 inches
Step-by-step explanation:
Corresponding sides of similar figures have proportional side lengths, so:
[tex]\frac{10x}{24}=\frac{5x+5}{16} \\\\\frac{2x}{24}=\frac{x+1}{16}\\\\\frac{x}{12}=\frac{x+1}{16}\\\\16x=12x+12\\\\4x=12\\\\x=3\\\\[/tex]
So, the perimeter is [tex]5x+5+5x+5+10x+10x=100[/tex].
Could you help me find the inverse of the function F(n)=n+1
Answer: [tex]F^{-1} (n)=n-1[/tex]
Step-by-step explanation:
[tex]F(n)=n+1[/tex]
[tex]F(n)-1=n[/tex] Subtract 1 from both sides
Done!
We can rewrite as: [tex]F^{-1} (n)=n-1[/tex]
Why is f not a function from R to R if
a) f (x) = 1/x?
The domain of the function is not the set of all real numbers, that is why it is not from R to R
Why is f not a function from R to R?Here we want to see why the function f is not a function from R to R, where R is the set of the real numbers.
The function here is:
f(x) = 1/x
Notice that x is on the denominator, so we can't evaluate that function on x = 0.
So there is a real number that we can't use on that function, then the domain is not R, is R minus the element {0}
That is why f(x) is not a function from R to R, because the domain is not the set of the real numbers.
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find each measure m < 5
The measure of all the angles are estimated.
∠1 = 104 ; ∠4 = 45 ; ∠3 = 65 ; ∠2 = 79.Explain the term linear pair?When two lines cross at one point, a linear pair with angles is created. If the angles follow the intersection of both the two lines in a straight line, they are classified as linear. A linear pair's total angles are indeed equal to 180°.For the stated question:
For ∠1
∠1 = 68 + 36 (sum of opposite interior angle equals exterior angle).
∠1 = 104
For ∠4.
∠4 = 180 - 70 - 65 (linear pair)
∠4 = 45
For ∠3.
∠3 = 65 (vertically opposite angle)
For ∠2.
∠2 = 180 - 65 - 36 (sum of angles of triangle are 180)
∠2 = 79
Thus, the measure of all the angles are estimated.
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my grade depends on this, help!!
Answer:
x ≥ - 3-----------------------
We observe on the graph:
The relation is not a function because it fails the vertical line test. You can see the graph intersects with the y-axis twice.The domain is restricted at x = -3 and unrestricted on the positive side.The domain is:
x ≥ - 3toss a coin three times, and let x be the number of heads. find the probability mass function of x.
The probability mass function of x is P(0)= 1/8, P(1)= 3/8, P(2)= 3/8, P(3)= 1/8.
Here number of trials = 3
In tossing a coin for once, the outcomes of the trial are either head or tail.
The trials are independent.
probability of getting head(success)=p=1/2
probability of getting tail(failure)=1-p=1-(1/2)=1/2
Number of success=X
Since there are two mutually exclusive outcomes of independent trials, the probability mass function of Binomial = (nx)px(1−p)n−x(nx)px(1 − p)n−x {in this case n=3}
The probability distribution of X is -
= X=0, P(X=0)=1/8
= X=1, P(X=1)=3/8
= X=2, P(X=2)=3/8
= X=3, P(X=3)=1/8
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k2 is 11,194.21 feet higher than mt. kenya. enter and solve an equation to find the elevation of mt. kenya. use x to represent the elevation of mt. kenya.
The elevation of mountain mt.kenya is, x = 17,057.1 feet by substitution method from the elevation of mountain K2 given.
Given that,
K2 is 11,194.21 feet higher than mt.Kenya, write and solve an equation to find the elevation of mt.Kenya.
x = mt. Kenya ( since given that x represents the elevation of mt.kenya)
Let us consider/assume ,
y = K2 (say)
Therefore, the relation between x and y:
x = y - 11,194.21 ( or )
y = x + 11,194.21
( since given that K2 is 11,194.21 more than mt.Kenya )
The elevation of K2 Mountain = 28251.31 feet
= y
substitute the value of y in x = y - 11,194.21
x = 28251.31 - 11,194.21
∴ x = 17,057.1 feet.
Therefore the elevation of mt.kenya found to be, x = 17,057.1 feet by substitution method.
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The complete question is :
K2(Which is 28251.31) is 11,194.21 feet higher than Mt.Kenya Write and solve an equation to find the elevation of Mt.Kenya. use x to represent the elevation of mt. kenya.
describe your sketch. the solid has no negative x-values. the solid has both positive and negative y-values. the solid has no negative z-values. the solid has a straight side and a curved side in the x y-plane. the solid has ---select--- in the x z-plane. the solid has ---select--- in the y z-plane.
The solid has a straight side in the x y-plane and a curved side in the x y-plane. In the x z-plane, the solid has a curved side, and in the y z-plane, the solid has a straight side.
The solid has no negative x-values, meaning all x-values are positive. It has both positive and negative y-values, indicating that it is symmetrical around the x-axis. The solid has no negative z-values, meaning all z-values are positive. In the x y-plane, the solid has a straight side and a curved side. In the x z-plane, the solid has a curved side and in the y z-plane, the solid has a straight side.
The solid has a straight side in the x y-plane and a curved side in the x y-plane. In the x z-plane, the solid has a curved side, and in the y z-plane, the solid has a straight side.
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URGENT PLEASE HELP!!!!!!
Answer:
یه گل یک گل بام میی مه فیلم بام حس بام حس فمس یکم باشگاه هی یک گل یه حس سیم هی فکریه خشک پیل هر یک حس صب زی صب هم گچ نی بلن هر بر قل هم بی دو حس قیین
Step-by-step explanation:
سبک حس بام نی شیک حس
یا کمی سیم حس او
نی یک حس بکشم یک حس بام نی که خیلی تنیام که اما الا دیه انجام نمییم ای موضوع که دعوا خیلی تخفیف خیلی خوعه ای موضوع که اما الا دیمش خوش
۳ خشک هی یک هی بام نی با که اما ۷غ هه بام نی بلن کف بام نی بکر
به نمییم هی بام میی لاک حس بام
بلن هی یک
حالم ای زبونه فراموش که
فخ بیم فک
15. For the graph below, which of the following is a possible function for g?
The graph demonstrates that the function g's line goes through the locations (0,2) and (2,8). The slope of the line is 3, implying that its equation is g(x) = 3x + 2.
What is a slope?The steepness or inclination of a line, route, or surface is measured by slope. It is the vertical distance divided by the horizontal distance between two locations on a line, route, or surface.
According to the graph, the function g is a line with a slope of 3 and a y-intercept of 2. This suggests that the line's equation is g(x) = 3x + 2. According to this equation, increasing the y-coordinate by one increases the x-coordinate by three. The line connects the points (0, 2) and (2, 8), which means that when x = 0, y = 2 and when x = 2, y = 8. This may be demonstrated by plugging the x-values into the equation, which will produce the matching y-values.
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What inverse operation is used to solve the equation?
x + 2 = 5
Responses
A multiply by 2 on both sidesmultiply by 2 on both sides
B divide by 2 on both sidesdivide by 2 on both sides
C add 2 to both sidesadd 2 to both sides
D subtract 2 from both sides
Answer:
D subtract 2 from both sides
Step-by-step explanation:
x + 2 - 2 = 5- 2
==> x = 3
The solution of the equation is x = 3.
What is an equation?Two algebraic expressions having same value and symbol '=' in between are called as an equation.
Given:
An equation,
x + 2 = 5.
To solve the equation:
Subtract 2 from both sides,
x +2 -2 = 5 -2
x = 3
Therefore, the solution is x = 3.
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Dr. Chandler wants to print copies of
his thesis in hardcover book format. He
could use Washington Printing, paying a
setup fee of $41 and $6 for every book
printed. Or, he could go through Fairfax
University, paying an up-front fee of
$32 and $9 per book. For how many
books will the costs be the same? How
much is that?
Answer:
For 3 books, costs are the same
$59
Step-by-step explanation:
x = number of books
$41 + ($6/book)(x) = $32 + ($9/book)(x)
41 - 32 = 9x - 6x
9 = 3x
x = 9/3 = 3
41 + 6(3) = 32 + 9(3) = $59
. The following list of monthly expenses for a first-year student at a post-secondary
institution are presented. The student has a monthly income of $1,450. Is the student
following the recommended rule of allocating 50% of monthly income to needs, 30% to
wants and 20% to savings or debt?
Income: $1,450
Based on the information provided, it can be concluded the student is not following the rule of allocating 50% to needs, 30% to wants, and 20% to savings.
What percentage is the student allocating for each category?Needs: 300 +10 + 50 +150 + 100 + 100= $710
Now, let's calculate the percentage this represents:
710 x 100 / 1450 = 48%
Wants: 9.99 + 9.95 +9.99 + 19.99 + 25 + 500 + 65= $639.92
Now, let's calculate the percentage this represents:
639 x 100/ 1450 = 44%
Savings: 48 + 44 = 92 which means he can save 8%
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what is the slope through the line of (9, 10) and (7, 2)
Answer:4
Step-by-step explanation:
I have a candy mix composed of Jolly Ranches, Starburst, and Twizzlers in a ratio of
7:5:3. I have 35 Jolly Ranchers. How many Starburst and Twizzlers do I have?
Answer:
25 Starburst
15 Twizzlers
========================================================
Explanation:
The ratio of Jolly Ranchers to Starburst to Twizzlers is 7:5:3
It means that you could have 7 Jolly Ranchers, 5 Starburst, and 3 Twizzlers.
In reality you actually have 35 Jolly Ranchers. So we'll multiply that "7" by 5. Do the same thing to all parts of the ratio to keep things balanced.
7*5 = 355*5 = 253*5 = 15The ratio 7:5:3 scales up to its equivalent form 35:25:15
35 Jolly Ranchers25 Starburst15 TwizzlersGiven f(x) = 3x^3+kx-13, and x-1 is a factor of f(x), then what is the value of k?
Answer: k=10
Step-by-step explanation:
Which is the common difference for this arithmetic series? 8, 30, 52, 74, 96, 118 a. d = 8 b. d = 22 c. d = 32 d. d = 38
Answer:
d = 22
Step-by-step explanation:
you add 22 to a number in the sequence to get the next number
8 + 22 = 30
30 + 22 = 52 and so on...
please help solve it
Note that if the family is to spend less than $60 dollars without further expenses, then they will have to spend nothing more than 6 hours. The inequality expression is given as: 36+4h < 60
What is the justification for the above result?First, the inequality expression is given as:
36+4h < 60
Where h is the number of hours they could spend.
We arrive at the above because we were given the following:
Cost of Movie = $36
Cost of parking Per Hour= $4
The maximum amount to be spent = $60
Thus, to find the number of hours the can spend without overshooting $60, we must find h. To do this, we must make h the subject of the formula by first removing 36 from both sides:
36+4h-36 < 60-36
4h < 24
h < 24/4
h < 6
What the above result show is that the number of hours that must be spent must be less than 6.
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5 divided by 4/5???????????????????????????????????????????????????????
Answer:
6.94??????‽??????????????
Step-by-step explanation:
5÷4/5?????????
5×5?????????‽?/4
2.777777778/4
=69.4????????????????????
