Quadratic function for the given properties is [tex]y=-4x^{2} +24x-28[/tex].
The roots are [tex]3+\sqrt{2}[/tex] and [tex]3-\sqrt{2}[/tex]; that means the axis of symmetry is x=3; which means the vertex has x coordinate 3. Then the vertex form of the equation is
[tex]y = a(x-3)^{2}+k[/tex]
Then since y is 0 when x is [tex]3+\sqrt{2}[/tex],
[tex]0=a(\sqrt{2} )^{2} +k[/tex]
[tex]0=2a+k[/tex] (1)
And when x = 1, y = -8,
[tex]-8 = a(-2)^{2}+k[/tex]
[tex]-8=4a+k[/tex] (2)
Then from equations (1) and (2)
[tex]-8=2a[/tex]
[tex]a = -4[/tex]
And then from either equation (1) or (2), k = 8.
So the equation is
[tex]y = -4(x-3)^{2}+8[/tex]
[tex]y=-4(x^{2} -6x+9)+8[/tex]
[tex]y=-4x^{2} +24x-28[/tex]
Solving this equation using the quadratic formula verifies that the roots are [tex]3+\sqrt{2}[/tex] and [tex]3-\sqrt{2}[/tex]; evaluating the expression for x=1 verifies that the y value is -8.
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identify the vertex, axis of symmetry, maximum or minimum, and domain and range of each function. f(x)
The vertex is (7, -27)
The line of symmetry is x = 7.
The minimum is y = -27
The domain is the set of all real numbers.
The range is y ≥ -27.
Given,
The quadratic equation is as follows:
f(x) = (x - 7)^2 - 27
The quadratic equation is in vertex form, hence if the vertex is (h, k), the vertex form will be as follows:
f(x) = (x - h)^2 + k
Then the vertex in this instance is (7, -27).
A line of the form x = h is the line of symmetry, and in this instance the line is x = 7.
The minimum of the quadratic equation is y = -27 since the function has a positive leading coefficient, indicating that the vertex is a minimum.
Finally, the domain is the set of all real numbers, much like the domain of any quadratic equation.
The range includes all real numbers that are greater than or equal to -27.
R = y ≥ -27.
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The given question is incomplete. Completed question is given below;
Identify the vertex, the axis of symmetry, the maximum or minimum value, and the domain and range of the function. f(x)=(x-7)^(2)-27
In 2012 a dolphin named M007 was tracked as he swam through the Atlantic waters.
He swam 600 miles in 67 days. For 26.4 miles, M007 was tracked off the eastern
coast of Florida. How long did M007 spend near the coast of Florida? Round your
answer to nearest tenth of a day if necessary.
Answer:
2.9 days
Step-by-step explanation:
Need days / mile
67 days / 600 mi = .1116666 day/mile
.1116666 day/mi * 26.4 mi = 2.948 day ~ 2.9 days
OR
Miles per day
600 mi / 67 day = 8.9552 mi / day
26.4 mi / (8.9552 mi/day) = 2.948 ~ 2.9 day
Aright circular cylinder, its volume is 343 π cm3 .if its height
Equals its base radius length, then its height equals
explain why it is reasonable to use a one-sample t confidence interval to estimate the population mean even though the population distribution is not approximately normal. (select all that apply.)
The general form of a Confidence Interval Estimate for a population mean is
Sample mean ± Critical Value × Standard Error of statistics.
Confidence intervals are one type of statistical interference. They allow us to range values where we can be relatively confident the true value will be. In this case, we are constructing a confidence interval for a population mean. For example: - Suppose that our sample has a mean of X bar = 10 and have constructed the 90% confidence interval.
From the above discussion, we get to know that:
It is reasonable to use a one sample t confidence interval to estimate the population mean since all freshman at a mid western university where surveyed.
It is reasonable to use a one sample t confidence interval to estimate the population mean since the sample size is at least 30.
It is reasonable to use a one sample t confidence interval to estimate the population mean since the sample size is the sample is representative of the population.
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Your uncle Jim lives in England, where the current exchange rate iS 1.64 US dollars for each
British pound. Solve for the amount of your monthly bill,
England.
to the nearest hundredth, if you lived in
Answer:
Since we need your monthly bill we will call it the variable B for now, (Unless you have the bill, if so replace it with the variable)
Multiply 1.64 x B since the exchange rate is different than the US bill,
For example, say your bill is $100 in the U.S.
You do 1.64 x 100 = A monthly bill of $164 if you lived in Britain
Step-by-step explanation:
what is -12+6xz equivalent to
Step-by-step explanation:
-12+6xz is equivalent to 6(-2 + xz) or 6(xz - 2)
A basketball player recorded for 11 consecutive games her points 13 20 15 22 24 21 18 20 25 17 27 how many points would she need to score in her 12th game in order to decrease the interquartile range by 1 point?
She need 6 points to score in her 12th game in order to decrease the interquartile range by 1 point.
What is Interquartile range?
An Interquartile range is one of the measure of variability that measures the spread of middle 50% of the data.
Given that;
A basketball player recorded for 11 consecutive games her points as;
13, 20, 15, 22, 24, 21, 18, 20, 25, 17, 27
Now,
Since, We know that;
The formula for the interquartile range is,
⇒ IQR = Q₃ - Q₁
Where, Q₃ is the third quartile , Q₁ is the first quartile.
Here, We arrange the points in the increasing order as;
⇒ 13, 15, 17, 18, 20, 20, 21, 22, 24, 25, 27
The first quartile is calculated as;
Q₁ = (n + 1) / 4 th term
Where, n is number of terms.
Q₁ = (11 + 1) / 4
Q₁ = 3rd term
Q₁ = 17
The third quartile Q₃ is calculated as;
Q₃ = 3(n + 1) / 4
Q₃ = 3 x 3
Q₃ = 9th term
Q₃ = 24
Thus, The interquartile range is,
⇒ IQR = Q₃ - Q₁
⇒ IQR = 24 - 17
⇒ IQR = 7
So, The desired interquartile range is,
⇒ IQR = 7 - 1
⇒ IQR = 6
Therefore, She need 6 points to score in her 12th game in order to decrease the interquartile range by 1 point.
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a path diagram allows you to determine the effect of one variable upon another both directly and indirectly through an intervening variable. true false
The given statement "a path diagram allows you to determine the effect of one variable upon another both directly and indirectly through an intervening variable. " is true.
Given that,
To justify the given statement whether it is true or not.
proportionality is defined as between two or more sets of values, and how these values are related to each other in the sense are they directly proportional or inversely proportional to each other.
Here,
According to the question,
Let the two interdependent numbers be x and y,
y ∝ x
y = kx
Or
x = y/k
Thus, a path diagram allows you to determine the effect of one variable upon another both directly and indirectly through an intervening variable.
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y = 6x - 11 Solve for corrdinate
The equation of line possible solution sets of the equation are all the points that lie on the graph of this function.
What is the general equation of a Straight line?The general equation of a straight line is -
[y] = [m]x + [c]
where -
[m] → is slope of line which tells the unit rate of change of [y] with respect to [x].
[c] → is the y - intercept i.e. the point where the graph cuts the [y] axis.
The equation of a straight line can be also written as -
Ax + By + C = 0
By = - Ax - C
y = (- A/B)x - (C/A)
Given is the line y = 6x - 11
Plot the graph on the equation. The coordinates on the line plotted represents all the coordinates that are the solution for the equation -
y = 6x - 11
Therefore, the equation of line possible solution sets of the equation are all the points that lie on the graph of this function.
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What does a 1 2BH equal?.
"1/2BH" represents the formula for finding out the area of the triangle.
What is the area of the triangle?
In a two-dimensional plane, the area of a triangle is the region enclosed by it. As we all know, a triangle is a closed shape with three sides and three vertices. Thus, the area of a triangle is the total space occupied by the triangle's three sides. The general formula for calculating a triangle's area is half the product of its base and height.
The given formula is 1/2BH
so this is the formula for finding out the area of the triangle where 'B' is the base of the triangle and H is the height of the triangle.
Hence, "1/2BH" represents the formula for finding out the area of the triangle.
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Find the length of the side x.
Give your answer rounded to 1 DP.
14.2cm
9.7cm
3.6cm
The diagram is not drawn accurately.
The value of x using the Pythagoras Theorem is 6.08 cm.
What is Pythagoras' Theorem?
The relationship between the three sides of a right-angled triangle is explained by the Pythagoras theorem, commonly known as the Pythagorean theorem. The Pythagoras theorem states that the square of a triangle's hypotenuse is equal to the sum of its other two sides' squares. The relationship between the three sides of a right-angled triangle is explained by the Pythagoras theorem, commonly known as the Pythagorean theorem. The Pythagoras theorem states that the square of a triangle's hypotenuse is equal to the sum of its other two sides' squares.
According to the Pythagoras theorem, the square of the hypotenuse of a triangle, which has a straight angle of 90 degrees, equals the sum of the squares of the other two sides. Look at the triangle ABC,is present. The base in this equation is AB, the height is AC, and the hypotenuse is BC.
In the given figure, we have:
A right angles triangle.
So, the Hypotenuse meaure is 14.2 cm;
The measure of the base side is 3.6 + 9.7 cm = 13.3 cm;
So, we can find the perpendicular side length using the Pythagorean Theorem
So, using the Pythagoras theorem,
[tex]c^{2} = x^{2} + y^{2}[/tex]
[tex](14.2)^{2} = (13.3)^{2} + x^{2}[/tex]
201.64 = 176.89 + [tex]x^{2}[/tex]
24.75 = [tex]x^{2}[/tex]
So, x = 4.97
So, The perpendicular side is 4.97 cm;
Now using the Pythagoras theorem again in the smaller triangle, we get:
[tex](3.6)^{2} + (4.9)^{2} = x^{2}[/tex]
12.96 + 24.01 = [tex]x^{2}[/tex]
36.97 = [tex]x^{2}[/tex]
So, The value of x is 6.08 cm;
Hence,
The value of x is 6.08 cm;.
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Which expression illustrates the identity property?
Equation shows identity property of multiplication is (a + bi) × 1 = (a + bi)
What is Identity property of multiplication?
The identity property of multiplication says that the product of 1 and any number is that number.
We know, Identity property of multiplication states that
"the product of 1 and any number is that given number".
We know that every complex number have two parts one is real and other is imaginary.
If a is real number and b is imaginary part then by definition
(a + bi) × 1 = (a + bi).
1. Uses Distributive Property of Multiplication.
2. Zero product property.
3. Commutative property of multiplication
4. Identity property of multiplication.
Hence, equation shows identity property of multiplication is (a + bi) × 1 = (a + bi)
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what is the probability that she randomly picks up a reference book and then, without replacing it, picks up a nonfiction book?
The probability that nadia randomly picks up a reference book and then without replacing it picks up a nonfiction book is 5/136.
Given:
17 total number books out of which 10 are fiction books,2 are reference books , 5 non fiction books.
Number of ways of picking reference book = [tex]2_C_1[/tex]
Probability of picking a reference book = [tex]2_C_1/17_C_1[/tex]
= 2/17
The total number of books left on the shelf is 16.
The number of ways in which a non fiction book can be picked after a reference book is already picked = [tex]5_C_1/16_C_1[/tex]
= 5/16.
Total probability = 2/17*5/17
= 10/272
= 5/136.
Therefore The probability that nadia randomly picks up a reference book and then without replacing it picks up a nonfiction book is 5/136.
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Write 35/3 as a mixed number.
Answer:
Step-by-step explanation:
11 2/3
factor completely 81x^2-4
Answer:
(9x-2)(9x+2) is the correct answer
help asaap
Calculate the area of the pavement surrounding the swimming pool.
Answer:
5x2=10. 7x2=14. 10+14=24.
Step-by-step explanation:
Write the equation of the line in fully simplified slope-intercept form. PLS HELP ME IM FAILING THIS CLASS
Answer:
The answer is: y = x + 7
Step-by-step explanation:
happy learning
A new car is purchased for \$14,000$14,000 and over time its value depreciates by one half every 5.5 years. What is the value of the car 18 years after it was purchased, to the nearest hundred dollars
Answer:
$1400
Step-by-step explanation:
You want the value of a car 18 years on if its initial value was $14,000 and its value is cut in half every 5.5 years.
Exponential modelThe value of the car can be modeled by the exponential equation ...
value = (initial value) × (growth factor)^(t/(growth period))
where "growth period" is the period applicable to the "growth factor."
ApplicationHere, the problem statement tells us ...
initial value = $14,000growth factor = 1/2growth period = 5.5 yearsSo, our exponential model is ...
value = 14,000·(1/2)^(t/5.5)
When t=18 years, this is ...
value = 14,000(1/2)^(18/5.5) = 14000(1/2)^(36/11) ≈ 14000·0.103469 ≈ 1449
The value after 18 years is about $1400.
9x²-12x-5+0
solve quadratic expression
Answer:
(3x−5)(3x+1)
Step-by-step explanation:
Evaluate
9x2−12x−5
Rewrite the expression
9x2+3x−15x−5
Factor out 3x from the expression
3x(3x+1)−15x−5
Factor out −5 from the expression
3x(3x+1)−5(3x+1)
Solution
(3x−5)(3x+1)
Answer:
(3x - 5)(3x + 1)
Step-by-step explanation:
1. Add the numbers
9x² - 12x - 5 + 0
9x² -12x - 5
2. Use the sum-product pattern
9x² - 12x - 5 + 0
9x² + 3x - 15x - 5
3. Common factor from the two pairs
9x² + 3x - 15x - 5
3x(3x + 1) - 5(3x + 1)
4. Rewrite in factored form
3x(3x + 1) - 5(3x + 1)
(3x - 5)(3x + 1)
May I have Brainliest please? My next rank will be the highest one: A GENIUS! Please help me on this journey to become top of the ranks! I only need 15 more brainliest to become a genius! I would really appreciate it, and it would make my day! Thank you so much, and have a wonderful rest of your day!
A closed top box with a square base is to have a volume of 4000 cubic inches. What are the dimensions that will minimize the amount of material used to build the box?.
The minimum dimensions to minimize the amount of material is 15.87 x 15.87 x 15.87 inch.
We need to know about the minimum function to solve this problem. The minimum function can be defined as the minimum value of the variable. It can be calculated by the derivative of the function. The minimum function can be written as
f'(s) = 0
where f'(s) is the derivative function
From the question above, the given parameter is
V = 4000 inch³
The cubic volume can be written as
s² x h = 4000
where s is the length of the base area and h is the height of the box.
the minimum value of the box refer to its surface area, hence
f(s) = 4sh + 2s²
f'(s) = 4h + 4s
4h + 4s = 0
h = s
It means that the length of the base area and the height must have the same dimension. The minimum volume should have a cube shape
V = s³
s³ = 4000
s = 15.87 inch
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A men’s basketball coach would like to know if there is a relationship between how tall a player is and how high he can jump. He collects the following data from every member of the team.
Examine the scatterplots provided in this graphic. Which one correctly displays these data?
Scatterplot A
Scatterplot B
Scatterplot C
Scatterplot D
Answer:
Either a or d
Step-by-step explanation:
Because they show the data correctly it is A trust me
Answer: Scatterplot A
Step-by-step explanation:
edGE 23
Ms. Takata has $480 to spend on redecorating her room. She bought 3 sets of curtains that cost $48. 25 each and a dresser that cost $234. 99. How much money does ms. Takata have left to spend?.
The amount that Ms. Takata has left to spend is $100.26 .
In the question ,
it is given that ,
total amount that Ms. Takata can spend on redecorate her room = $480
the cost of 1 curtain is = $48.25
the cost for 3 curtain = 3*48.25 = 144.75
the cost of dresser = $234.99
the amount left to spend can be represented by
the amount left to spend = total amount - ( cost of 3 curtain + cost of dresser)
= 480 - (144.75 + 234.99)
= 480 - 379.74
= 100.26
Therefore , The amount that Ms. Takata has left to spend is $100.26 .
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evaluate (49/64)^1/2
Answer:
Exact Form:
7/8
Decimal Form:
0.875
14. 2x² - 9x - 5≥0
Solve each of the quadratic inequalities.
Answer: x > _5
Step-by-step explanation:
QUICKKK PLEAZZEWrite two different expressions to represent the perimeter of this square. What can you conclude from the two expressions? Express your answer in two or more complete sentences.
The perimeter of the square can be expressed as either S+S+S+S or 4×S
How to write two different expressions to represent the perimeter of a square?
Perimeter is the distance around the edge of a shape. It can be found by adding up the side lengths of the shapes
Given: a square with a side length of S. Thus, the perimeter can be expressed as:
Perimeter = S + S + S + S = 4S
Since there are 4 equal sides each having a length of S. Thus, we can also write perimeter as:
Perimeter = 4 × S = 4S
Therefore, we can conclude the same expression are the same since they both have the same value of 4S
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Please help will mark brainiest!!!
2.) These students want to make more money at their job which pays hourly. If they want their hourly wages to increase, what is an appropriate transformation to accomplish this task? Why? Use a complete sentence.
The appropriate transformation to increase the hourly wage is a vertical stretch of the function.
What is the definition of the payment function?The payment function, as a function of the number of hours worked, is a linear function with definition given as follows:
P(h) = mh + b.
In which the coefficients of the payment function are listed as follows:
m is the slope of the linear function, which is equivalent to the hourly pay of the students.b is the intercept of the linear function, which is equivalent to the fixed pay of the students.To increase the hourly pay, the slope needed to be increased, meaning that the slope m has to be multiplied by a constant k, and this multiplication is a transformation called a vertical stretch by a factor of k.
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The appropriate transformation to increase the hourly wage is a vertical stretch of the function.
What is the definition of the payment function?
The payment function, as a function of the number of hours worked, is a linear function with definition given as follows:
P(h) = mh + b.
In which the coefficients of the payment function are listed as follows:
m is the slope of the linear function, which is equivalent to the hourly pay of the students.
b is the intercept of the linear function, which is equivalent to the fixed pay of the students.
To increase the hourly pay, the slope needed to be increased, meaning that the slope m has to be multiplied by a constant k, and this multiplication is a transformation called a vertical stretch by a factor of k.
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hospital records show that 16% of all patients are admitted for heart disease, 26% are admitted for cancer (oncology) treatment, and 8% receive both coronary and oncology care. what is the probability that a randomly selected patient is admitted for something other than coronary care? (note that heart disease is a coronary care issue.)
0.86 is the probability that a randomly selected patient is admitted for something other than coronary care.
What is probability ?
The likelihood that something will occur is the foundation of it. The justification for probability serves as the basic foundation for theoretical probability.A coin is tossed, for instance, and the theoretical likelihood of receiving a head is 1 in 2.Let H denotes the patients are admitted for heart disease.
Let C denotes the patients are admitted for cancer treatment.
We are given:
P(H) = 0.16
P(C) = 0.26
P( H ∩ C ) = 0.8
P(Hc ) = 1 - P(H) = 1 - 0.16 = 0.86
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Please help with explanation thank you!
The required equation of the line is y = (7/4)x + 2.
What is the Linear equation?A linear equation is defined as an equation in which the highest power of the variable is always one.
The given coordinate of the point on the line is ; (-4, -5) and the slope is 7/4
Let the required equation of the line is
⇒ y - y₁ = m [x -x₁]
x₁ = -4, y₁ = -5 and m = 7/4
Substitute values in the equation, we get
y - (-5)= (7/4)(x - (-4))
y + 5 = (7/4)(x + 4)
y + 5 = (7/4)x + (7/4)4
y = (7/4)x + 7 - 5
y = (7/4)x + 2
Therefore, the required equation of the line is y = (7/4)x + 2.
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You take a new job as a tutor and you get paid $100 whether students come or
not. What type of pay is this?
Salary
Vacation Pay
Piece Rate
Hourly Pay
This year, the Calgary stampede boasts it will offer a Ferris Wheel with a diameter of 150 feet. What is the circumference of the Ferris Wheel in meters?
Answer:
a take 2 hour to plant so flower bulbs if they are working together how long should it takes to plant 150 bulb? solving the question
