Answer the questions below about the quadratic function.g(×)=-×^2+10×-27Does the function have a minimum or maximum value? minimum or maximum Where does the minimum or maximum value occur?x=?what is the functions minimum or maximum value?
Answers
To find if this quadratic function has a minimum or a maximum value, we need to see the quadratic coefficient of the function. If the value of this coefficient is negative, the function will have a maximum. If the coefficient is positive, the quadratic function will have a minimum.
Therefore, in this case, we have:
\(g(x)=-x^2+10x-27\)We can see that "in front of x^2, we have that the coefficient is negative. Therefore, this function has a maximum.
To find where this maximum occurs, we can use the formula for the vertex of a parabola (quadratic function):
\(x_v=-\frac{b}{2a},y_v=c-\frac{b^2}{4a}\)We can get a, b, and c from the quadratic function in question:
\(ax^2+bx+c\Rightarrow-x^2+10x-27\)Then, we have that:
a = -1
b = 10
c = -27
Then, to find the value of x when the maximum occurs, we have:
\(x_v=-\frac{10}{2(-1)}=-\frac{10}{-2}=5\Rightarrow x_v=5\)And now, to find the value of y when the maximum occurs, we also have:
\(y_v=-27-\frac{(10)^2}{4\cdot(-1)}=-27-\frac{100}{-4}=-27+25=-2\Rightarrow y_v=-2\)Therefore, the value for x is equal to 5 (x = 5), and the value for y is equal to -2 ( y = -2) when the quadratic function takes its maximum value.
A graph for this function can be seen as follows:
In summary, the function has a maximum value since the quadratic coefficient is negative, and the x-coordinate for this maximum is x = 5, and the y-coordinate for this maximum is y = -2 (and this is the maximum value for the function).
Related Questions
somebody answer, please?
The table displays data collected, in meters, from a track meet.
one fourth 6 2 4
3 two thirds one third nine halves
What is the median of the data collected?
2.5
4.5
2
3
Answers
The median of the data collected from a track meet is 2 meters.
What is median?The median is the middle number in a sorted, ascending or descending list of numbers.
To calculate the median of the given date, we folloe the steps below.
Collected date: 1, 4, 6, 2, 4, 3, 2/3, 1/3, 1/2
Step 1: Rearreange the date in accending order.
1/3, 1/2, 2/3, 1, 2, 3, 4, 4, 6Step 2: Pick the middle of the number in the arranged data
Median = 2 meters.Hence, the median of the data collected is 2 meters.
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Answer:
2.5
Step-by-step explanation:
how many miles could he ride in 3 hr
Answers
In case whereby Jake rides his bicycle 6 miles in 3/5 of an hour. At this rate, the number of miles could he ride in 3 hours is 30 miles
How can the number of miles be calculated?The distance = bicycle 6 miles
number of hours =3/5 of an hour
then the rate = 6/ (3/5)
Then we can calculate the number of miles with the 6milesi n 3/5 hours as;
= (6 * 5/3 )
=30/3
=10
Then the rate will be 10 miles in 1 hour , hence the number of miles he will ride in 3hrs
=10 * 3 hours
= 30 miles
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how many like terms are in the expression 4j^2 +3j^2-9j^2
Answers
Answer: 16j^3+2
Step-by-step explanation:
Select all the expressions that equal 6^-10
Answers
Answer:
we need a list first
Step-by-step explanation:
Allison is choosing between two rental car companies. Countrywide Auto charges $27 plus $0.27 per mile, and Smart Auto charges $45 plus $0.21 per mile.
Use the following system of equations, where y represents total cost and x represents miles, to answer the question:
y = 0.27x + 27
y = 0.21x + 45
At what point would the two lines intersect if graphed? (4 points)
(300, 108)
(108, 300)
(45, 27)
(27, 45)
Answers
The point where the two lines intersect is the solution to the system of linear equations, which is: A. (300, 108).
How to Solve a System of Linear Equations?Given that:
y = total cost
x = miles
We are also given the system of linear equations that models the scenario given as:
y = 0.27x + 27 --> equation 1
y = 0.21x + 45 --> equation 2
To find the value of x, make both equations equal to each other and solve:
0.27x + 27 = 0.21x + 45
Combine like terms
0.27x - 0.21x = -27 + 45
0.06x = 18
Divide both sides by 0.06
0.06x/0.06 = 18/0.06
x = 300
To find the value of y, plug in the value of x into equation 1, and find y:
y = 0.27(300) + 27
y = 81 + 27
y = 108
Thus, the point where the two lines intersect is the solution to the system of linear equations, which is: A. (300, 108).
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Wendy stops running
A.Speed
B.Velocity
C.Acceleration
Answers
Answer:
i think is c tell me if im right
4
0
A
Compare and using the number line.
름
10
A
Which point represents ?
B
B
-|~
2
C
D
1
D
Enter
Answers
The point D represents 1 on the number line.
What is number line ?A number line is a visual representation of numbers arranged in sequential order. It is usually depicted as a horizontal line, with tick marks or hash marks at regular intervals, representing the numbers. Number lines can be used to represent a wide variety of mathematical concepts, such as fractions, decimals, negative numbers, absolute value, and ratios. They are also used to compare numbers and to help visualize the concepts of addition, subtraction, multiplication, and division. Number lines can also be used to explore inequalities, algebraic equations, and graphing.
The point D represents 1 on the number line.
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Which of these is the correct ratio of strawberries to blueberries for the fruit salad?
A. 8 strawberries: 30 blueberries
B. 8 strawberries: 8 blueberries
C. 4 strawberries: 30 blueberries
D. 32 strawberries: 30 blueberries
Answers
The ratio of the strawberries to the blueberries is 32 strawberries: 30 blueberries (option d).
What is the ratio?
Ratio expresses the relationship between two or more numbers. It shows the frequency of the number of times that one value is contained within other value(s). The sign that is used to represent ratio is :.
The ratio of strawberries to blueberries - total number of strawberries : total number of blueberries.
(8 x 4) : 30
32 : 30
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Answer: A. 8 strawberries: 30 blueberries
Step-by-step explanation:
If a dart is thrown and hit inside the square. What is the probability
that it will NOT hit inside the circle? Round your answer to the
nearest percent.
lin
5in
The probability of NOT hitting inside the circle is
percent.
Answers
Answer: 50%
Step-by-step explanation:
An augmented matrix is given. Determine the number of solutions to the corresponding system of equations. 1961-1 0 0 0 0 [ 0 0 0 0 The system has one solution. The system has no solution. The system has infinitely many solutions.
Answers
There is one pivot entry at the first column and the last two rows are zero. So the system has infinitely many solutions.
An augmented matrix is a matrix formed by combining the columns of two matrices to form a new matrix. The given augmented matrix is shown in the image below. It is an important tool in matrices used to solve simple linear equations. The number of rows in the augmented matrix is equal to the number of variables in the linear equation. An augmented matrix is similar in that it, too, is a coefficient matrix, but in addition it is augmented with a column consisting of the values on the right-hand side of the equations of the linear system. As we can see there is one pivot entry at the first column and the last two rows are zero. So the system has infinitely many solutions.
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What is the answer to this?
Multiply
1/4 x -2=
Answers
Answer:
-0.5
Step-by-step explanation:
Answer:
−8x+1 / 4x
Step-by-step explanation:
Help me with this please!
Answers
Equation of the ellipse is x²/4 + y²/1 = 1
Given ellipse has major axis at x- axis i.e it is stretched more in the x- axis or horizontal axis.
When horizontal axis is the major axis the standard form of an ellipse equation is
x²/a² + y²/b² = 1 ( a>b )
a² = square of the x co-ordinate at x- axis.
b² = square of the y co- ordinate at y - axis.
Co- ordinates of x- axis - (-2,0) and (2,0).
Co- ordinates of y- axis - (0,-1) and (0,1).
Substituting the values of a² and b² in the standard form of ellipse equation.
a²= 4
b² = 1
Equation of ellipse = x²/2² + y²/1² = 1
= x²/4 + y²/1 = 1
Hence the required equation of ellipse having x-axis as major axis is
x²/4 + y²/1 = 1 .
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Denise has $10 and wants to buy pens that cost
$0.80 each. How many pens can Denise buy and
have at least $6 left?
Answers
Answer:
5 pens
Step-by-step explanation:
$10 - 6$ = $4
$4/$0.80
she can afford 5 pens
PLEASE HELP ASAP
The diagrams show a polygon and the image of the polygon after a transformation.
Use the diagrams to determine which statements are true. Select all statements that are true.
Answers
The correct statements regarding the transformations are given as follows:
Parallel lines will always be parallel after a reflection.Lines that are not parallel will never be parallel after a translation.What are transformations on the graph of a function?Examples of transformations are given as follows:
A translation is defined as lateral or vertical movements.A reflection is either over one of the axis on the graph or over a line.A rotation is over a degree measure, either clockwise or counterclockwise.For a dilation, the coordinates of the vertices of the original figure are multiplied by the scale factor, which can either enlarge or reduce the figure.Parallel lines are lines that have the same slope, that is, lines that do not intercept, and the transformations do not change whether the lines are parallel or not.
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which fraction is equevleint to 12/21
Answers
Answer:
4/7
Step-by-step explanation:
They can be simplified by 3 12 divided by 3 is 4 and 21 divided by 3 is 7 so it's 4/7.
What is the volume of the rectangular prism?
Answers
Answer:
7m^3
Hope you have a good day lad!
Write an equation of the line that passes through point P and is parallel to the line with the given equation. P(3,5); y=2x-6
Answers
Answer:
y = -(5/2)x + 3 is a line perpendicular to y = (2/5)x + 2. This line is also perpendicular to y = (2/5)x + 9 because it has the same slope.
Step-by-step explanation:
A) So the line you are given is written in slope intercept form y = mx + b meaning that the slope of the line is m = 2/5 and the intercept b = 9 (so the line hits the y axis at 0,9). A line that is parallel has to have the same slope so we know our m is the same. So we have y = (2/5)x + b. We need b. It passes (0, 2) since the x coordinate is 0 you know the y intercept is 2 but you can verify this using the point slope formula:
y - y1 = m(x - x1) plug in values
y - 2 = (2/5)(x - 0) now simplify
y - 2 = (2.5)x last solve
y = (2/5)x + 2 see how when the x coordinate is 0 you can automatically use the point slope intercept formula? Neato!
B) Now we want a line perpendicular to y = (2/5)x + 2 and that passes through 0,3. What are the properties of a line perpendicular to a line of the form y = mx + b and passes through (0, 3)? We know that the slope of this new line will be the reciprocal and have the opposite sign of m. So the new slope we will call it mnew = -(1/m) so plug in for m and you get mnew = -(1/[2/5]) if you simplify you get that the mnew = -(5/2). So we have half of our equation for the perpendicular: y = -(5/2)x + b. If you look at (0, 3) you see that the y intercept is 3 so b = 3. So:
The equation of the line that passes through given point and is parallel to the line with the given is y = 2x-1
What is an equation?An equation is a mathematical statement that shows that two mathematical expressions are equal.
Given that, we need to find the equation of a line passing through the point (3, 5) and is parallel to y = 2x-6,
Comparing the given equation with the general equation of line y = mx+c
m = 2 (the slope)
We know that the two parallel lines have equal slope.
Therefore, the required equation is =
y = 2x+c
To find the value of c, put x = 3 and y = 5,
5 = 2(3) + c
c = -1
Therefore,
The required equation is =
y = 2x-1
Hence, the equation of the line that passes through given point and is parallel to the line with the given is y = 2x-1
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Which of the following equations represents F(x)= x4 reflected across the line
y = x?
OA. F(x)=√x
OB. F(x)=√x
OC. F(x)=-4x
OD. F(x) = ±**
Answers
The reflection of F(x) = x⁴, across the line y = x, results in the function \(y = F(x) = \pm \sqrt[4]x\), making option A the right choice.
For any function f(x), the reflection across the line y = x, gives the inverse of the function f(x).
In the question, we are asked for the equation, representing the reflection of f(x) = x⁴, across the line y = x.
The function can be shown as:
y = f(x) = x⁴,
or, x⁴ = y,
or, \(x = \pm\sqrt[4]{y}\)
Changing the variables to general form, that is, y as the dependent variable and x as the independent variable, we get the inverse function as, \(y = F(x) = \pm \sqrt[4]x\).
Thus, the reflection of F(x) = x⁴, across the line y = x, results in the function \(y = F(x) = \pm \sqrt[4]x\), making option A the right choice.
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The complete question is:
"Which of the following equations represents F(x) = x⁴ reflected across the line y = x?
A. \(F(x)= \pm\sqrt[4]{x}\)
B. \(F(x)= \sqrt[4]{x}\)
C. \(F(x)= \pm x^4\)
D. \(F(x)=- \sqrt[4]{x}\) "
2 + 2. what is the sum
Answers
Answer: 4
Step-by-step explanation:
Answer:4
2+2=4 if I have two apples and pick up two more I now have 4 total
The elevation of Desert Shores, California, is less that -55 meters. Which of the following best describes Desert Shores.
A. Desert Shores is lower than 55 meters below sea level.
B. Desert Showers is lower that 55 meters above sea level
C. Desert Shores is higher than 55 meters below sea level.
D. Desert Shores is higher than 55 meters above sea level.
Answers
The option that best describes the elevation of Desert Shores is; A. Desert Shores is lower than 55 meters below sea level.
What is the Elevation below sea level?We are told that the elevation of Desert Shores, California, is less than -55 meters.
Now, an elevation of a natural landmass like this is usually given with reference to the sea level. If above sea level, it is positive but if below sea level, it is negative.
Now, the elevation is negative as we can see that it is given as -55 meters. Thus, we can easily conclude that Desert Shores is lower than 55 meters below sea level.
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Select the number that round to 387.4 when rounded to the nearest tenth.
A. 387.461
B. 387.344
C. 387.309
D. 387.352
E. 387.779
Answers
Answer:
D
Step-by-step explanation:
When rounding, the number 5 is rounded up. So the number 387.352 will be rounded up 387.4. Other options are not suitable. Correct answer is "D"
If you think my answer is the best, please mark it as the Brainliest.
Thank you! :))
HELP!! ILL MARK BRRAINLIST
Answers
Answer:
I think answer is D but it could be wrong not sure
Solve using elimination.
- 9x + 2y = 5
-9x + y = -2
Answers
Answer:
(1 , 7)
Step-by-step explanation:
(X,y)=(1,7)
Identify the number of solutions of the system of linear equations.
x=y+3z=6
x-2y = 5
2x - 2y + 5z = 9
no solution
exactly one solution
infinitely many solutions
Solve the system. If there are infinitely many solutions, write the ordered triple in terms of z. If there is no solution, lea
The solution is (x, y, z)
-1.2
3
Answers
The solution to the system of linear equations is (x, y, z) = (64/11, 37/11, 9/11). The system has exactly one solution.
Let's solve the system of linear equations correctly.
The given system of linear equations is:
x = y + 3z = 6
x - 2y = 5
2x - 2y + 5z = 9
To determine the number of solutions, we can analyze the system using the method of elimination or substitution. Let's use the method of elimination:
From equation 1, we have:
x = y + 3z
Substituting this value of x in equation 2:
(y + 3z) - 2y = 5
y + 3z - 2y = 5
-z + 3z = 5 - y
2z = 5 - y
Now, let's substitute the value of x in equation 3:
2(y + 3z) - 2y + 5z = 9
2y + 6z - 2y + 5z = 9
11z = 9
Simplifying the equation, we find:
z = 9/11
Now, substituting this value of z back into the equation 2z = 5 - y, we get:
2(9/11) = 5 - y
18/11 = 5 - y
18/11 - 5 = -y
18/11 - 55/11 = -y
-37/11 = -y
y = 37/11
Finally, we can substitute the values of y and z into equation 1 to find the value of x:
x = y + 3z
x = 37/11 + 3(9/11)
x = 37/11 + 27/11
x = 64/11
Therefore, the solution to the system of linear equations is (x, y, z) = (64/11, 37/11, 9/11).
The system has exactly one solution.
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a water snake in a well is 30 M below the ground level its lights 20 m upward and then slips down 10 M how far it is from the ground level
\( - 30 - + 20 - - 10\)
Answers
If the water snake is initially 30 meters below the ground level and then climbs 20 meters upward, it will be 30 - 20 = 10 meters below the ground level. However, if it then slips down 10 meters, it will be 10 + 10 = 20 meters below the ground level.
students were asked to choose a city if 4/7 of them chose new york and 1/7 chose los angeles what fraction chose either new york or los angles
Answers
Answer: 5/7 of the kids chose New York or L.A.
Step-by-step explanation:
All you need to do in this problem is add the fraction of people that chose New York and the fraction of people that chose L.A:
4/7 + 1/7 = 5/7
Some people believe there are too many taxes and that tax rates
are too high. They refuse to file tax returns or pay taxes because
they disagree with how the government spends the money. Do you
agree with these arguments? Why or why not?
Answers
Answer:
Step-by-step explanation:
(This is technically a personal opinion question) In MY opinion all government run things from libraries to schools to the military come from taxes. If you don't agree with how the government spends the money that you pay in taxes yet enjoy/use government facilities then you have no room to complain and not pay your taxes.
Can someone pls im begging help me with this!!
Answers
Answer:
31
Step-by-step explanation:
9(2n+1) help please brooooooo
Answers
Answer:
18n + 9
Step-by-step explanation:
Distribute 9 into the expression.
9*2n = 18n
9*1 = 9
18n + 9
What is the shape of the cross section of the figure that is perpendicular to the triangular bases and passes through a
vertex of the triangular bases?
A
a parallelogram that is not a rectangle
O a rectangle
O a triangle that must have the same dimensions as the bases
O a triangle that may not have the same dimensions as the bases
Answers
Answer:
a triangle that may not have the same dimensions as the bases
Step-by-step explanation:
The cross section of the figure that is perpendicular to the triangular bases and passes through a vertex of the triangular bases would be a triangle that may not have the same dimensions as the bases.