The graph shows the quadratic function f(x) . What is the average rate of change for the quadratic function from x = 6 to x = 8? Enter your answer in the box.
Answers
Answer:
The average rate of change for the quadratic function from x = 6 to x = 8 is -1.
Step-by-step explanation:
The average rate of change for the quadratic function from x₁ to x₂ is defined as
[tex]m=\frac{f(x_2)-f(x_1)}{x_2-x_1}[/tex]
From the given graph it is clear that the value of function is 6 at x=6 and the value of function is 4 at x=8.
The average rate of change for the quadratic function from x = 6 to x = 8.
[tex]m=\frac{f(8)-f(6)}{8-6}[/tex]
[tex]m=\frac{4-6}{2}[/tex]
[tex]m=\frac{-2}{2}[/tex]
[tex]m=-1[/tex]
Therefore the average rate of change for the quadratic function from x = 6 to x = 8 is -1.
Related Questions
The graph of a quadratic function touches, but does not cross, the x-axis at x = 4. Which function represents this situation? y = x2 – 16 y = x2 – 4x y = x2 – 8x + 16 y = x2 + 8x + 16
Answers
The quadratic equation is y = x^2 - 8x + 16
How to determine the equation?From the question, we have:
x = 4
Since the graph only touches x = 4 and it does not cross it, then it means that the graph has a multiplicity of 2 at x = 4
The equation is then represented as:
y = (x - 4)^2
Expand
y = x^2 - 8x + 16
Hence, the quadratic equation is y = x^2 - 8x + 16
Read more about quadratic equations at:
https://brainly.com/question/1214333
#SPJ6
Jana wants to navigate page 35 of her report. what is the quickest way to navigate?
Answers
To navigate to page 35 of a report, you can use the 'find' function in a web browser with CONTROL or COMMAND + F, utilize the table of contents with hyperlinks, or enter the page number in a navigator window's spin box, depending on the device and format.
To quickly navigate to page 35 of a report, you have several options depending on the format and the device you are using. If you are viewing the report on a web browser, you can usually press CONTROL or COMMAND and the letter F to open the 'find' function and type '35' to jump to page 35. Alternatively, if the document has a table of contents with hyperlinks, you can click on the relevant section to navigate quickly. For documents with a navigator window, enter '35' in the spin box to jump straight to that page. In a mobile reading environment, you may find a Contents button at the top of the screen; clicking this can allow you to select and jump to the desired page or section.
How would you get the answer??
Answers
20+6=26
6/26
Divide the numerator and denominator by 2
3/13
So, the fraction is 3/13
What is the equation of the line that is parallel to the line 5x + 2y = 12 and passes through the point (−2, 4)? y = – x – 1y = – x + 5y = x – 1y = x + 5
Answers
Answer: The required equation of the line is [tex] y=-\dfrac{5}{2}x-1.[/tex]
Step-by-step explanation: We are given to find the equation of the line that is parallel to the following line and passes through the point (-2, 4) :
[tex]5x+2y=12~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
We know that
the slope-intercept form of the equation of a straight line is given by
[tex]y=mx+c,[/tex]
where m is the slope of the line.
From equation (i), we have
[tex]5x+2y=12\\\\\Rightarrow 2y=-5x+12\\\\\Rightarrow y=-\dfrac{5}{2}x+6.[/tex]
So, the slope of line (i) is given by
[tex]m=-\dfrac{5}{2}.[/tex]
We know that the slopes of two parallel lines are equal. So, the slope of the new line will be
[tex]m=-\dfrac{5}{2}.[/tex]
Since the line passes through the point (-2, 4), so its equation will be
[tex]y-4=m(x-(-2))\\\\\\\Rightarrow y-4=-\dfrac{5}{2}(x+2)\\\\\\\Rightarrow y-4=-\dfrac{5}{2}x-5+4\\\\\\\Rightarrow y=-\dfrac{5}{2}x-1.[/tex]
Thus, the required equation of the line is [tex] y=-\dfrac{5}{2}x-1.[/tex]
If you were given the equation f ( x ) = 3x⁵+6x, what behavior would the ends of the graph have?
a. Both ends will point up
b. Both ends will point down
c. the left end will start down at a large negative and the right end will go upwards
d. the left end will start up at a large positive and the right end will go downwards EXPLAIN ANSWER
Answers
You can know the behavior of the function f(x)=3x⁵+6x by given values to the variable x and plot each point obtained. For example:
If x=-1⇒ f(-1)=3(-1)⁵+6(-1)=9
If x=0⇒ f(0)==3(0)⁵+6(0)=0
If x=1⇒ f(1)=3(1)⁵+6(1)=9
Therefore, as you can see in the graph attached, the correct answer is:
c. The left end will start down at a large negative and the right end will go upwards.
The ends of the graph of the function f(x) = 3x^5 + 6x will display the behavior described in option c. This is due to the highest power of x in the equation being an odd number and the coefficient being positive. As such, the left end of the graph will start down at a large negative and the right end will go upwards.
Explanation:The behavior of the ends of the graph of the function f(x) = 3x^5 + 6x is determined by the highest power of x in the equation, which is 5 in this case. The coefficient of x^5 is positive, so as x approaches positive infinity, f(x) also approaches positive infinity. Conversely, as x approaches negative infinity, the value of f(x) would approach negative infinity. We can describe this behavior as the left end of the graph starting at a large negative and the right end going upwards. Thus, answer c. 'the left end will start down at a large negative and the right end will go upwards' is correct.
Learn more about End behavior of polynomial functions here:https://brainly.com/question/19809669
#SPJ3
A person at the top of a cliff 100 ft. tall sees Gilligan's boat. He sees the boat at an angle of depression of 10. How far is the boat from the base of the cliff.
Answers
or 567.128ft rounded
hope this helps<3
the ordered pairs below represent a relation between x and y.
(-3,0), (-2,4), (-1,8), (0,12), (1,16), (2,20)
could this set of ordered pairs have been generated by a linear function?
A. No, because the distance between consecutive x-value is different than the distance between consecutive x-values.
B. Yes, because the relative difference between y-values and x-values is the same no matter which pairs of (x, y) values you use to calculate it.
C. No, because the y-values decrease and then increase
D. Yes, because the distance between consecutive x-values is constant.
Answers
Answer:
Yes because the relative difference between y-values and x-values is the same no matter what which pairs of (x,y) values you use to calculate it
Step-by-step explanation:
Yes, this set of ordered pairs have been generated by a linear function because the relative difference between y-values and x-values is the same no matter which pairs of (x, y) values you use to calculate it.
The correct option is (B)
What is graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
Given are ordered pairs are: (-3,0) (-2,4)(-1,8)(0,12)(1,16)(2,20).
It can be seen that the there only unit increase in x coordinates and units increase in consecutive y- coordinates.
Now, if we set up the equation of line as:
Here, m =4 and b = 12
So the relationship is linear and represented by the equation
y=4x+12
Hence, the relative difference between y-values and x-values is the same no matter which pairs of (x, y) values you use to calculate it.
Learn more about concept here:
https://brainly.com/question/3433683
#SPJ2
I need help on #9. The help would be grateful appreciated.
Answers
Length = 15
Width = 5
Height = 10
Volume = Length*Width*Height
Volume = 15*5*10
Volume = 750
New Figure
Length = 3
Width = 1
Height = 2
Each dimension has been divided by 5 (eg: 15/5 = 3)
Volume = Length*Width*Height
Volume = 3*1*2
Volume = 6
The old volume was 750 and it changes to 6
Notice how 750/6 = 125
Which can be rearranged to 750/125 = 6
Answer: if you divide the old volume by 125, then you get the new volume
Note: the new volume is 125 times smaller than the old volume
Put another way, the old volume is 125 times larger compared to the new volume
The fact that 125 = 5^3 is not a coincidence. If you divide each dimension by some number k, then you divide the volume by k^3
A bakery sold 115 cupcakes in one day. The head baker predicted he would sell 95 cupcakes that day. What was the percent error of the baker's prediction?
Answers
======================================================================
% error=
actual value-estimated value
Then divide that by actual value
The baker's prediction had a 17.39% error.
To calculate the percent error of the baker's prediction, we use the formula:
Percent Error = (|Actual Value - Predicted Value| / Actual Value) * 100%
In this case, the Actual Value is the number of cupcakes actually sold, 115. The Predicted Value is the number the baker predicted to sell, 95.
So, the computation will be:
Percent Error = (|115 - 95| / 115) * 100%
Percent Error = (20 / 115) * 100
Percent Error = 0.1739 * 100%
Percent Error = 17.39%
The graph shows the number of copies a copier can make. What is the unit rate?
A)
1
25
B) 5
C) 15
Eliminate
D) 25
Answers
Answer:
25
Step-by-step explanation:
Which is a monthly recurring cost associated with renting a house?
utility bills
property tax
insurance
Answers
If side a has a length of 3 and side b has a length of 4, use the Pythagorean Theorem to find the length of side c. Round the answer to the nearest tenth.
Answers
[tex]a {}^{2} + b {}^{2} = c[/tex]
when you put the numbers in for the variables given it will look like this
[tex]( {3})^{2} + ( {4})^{2} = c[/tex]
3 squared equals 9 and 4 squared equals 16:
[tex]9 + 16 = 25[/tex]
so side c is 25 units
Solve the equations to find the number and type of solutions. The equation 8 − 4x = 0 has real solution(s).
Answers
Answer:
The number of solution is, 1 and the type of solution is, Integer solution.
Step-by-step explanation:
Given the equation:
[tex]8-4x=0[/tex]
Add 4x to both sides we have;
[tex]8 = 4x[/tex]
Divide both sides by 4 we have;
[tex]2 = x[/tex]
or
x = 2
Solution for this equation is, 2
Therefore, The number of solution is, 1 and the type of solution is, Integer solution.
The equation has a single real solution, x = 2.
The equation 8 − 4x = 0 can be solved as follows:
8 − 4x = 0
4x = 8
x = 2
The equation has one real solution, x = 2.
A real solution is a solution that is a number. The number 2 is a real number, so the equation has one real solution.
Here is a more detailed explanation of the solution:
We subtract 8 from both sides of the equation.
We divide both sides of the equation by -4.
We simplify both sides of the equation.
The answer is x = 2, which is a real number. So, the equation has one real solution.
To learn more about equation here:
https://brainly.com/question/29657992
#SPJ3
Indicate a general rule for the [tex] n^{th}[/tex] term of this sequence.
-6a, -3a, 0a, 3a, 6a. . .
A.] [tex] a_{n}=3an+9a[/tex]
B.] [tex] a_{n}=-3an-9a[/tex]
C.] [tex] a_{n}=-3an+9a[/tex]
D.] [tex] a_{n}=3an-9a[/tex]
Answers
Justification:
1) That is an arithmetic sequence which you prove by determining the difference between two consecutive terms (which shall be constant if it indeed is an arithmetic sequence):
2)
Second term - first term = -3a - (-6a) = -3a + 6a = 3a
Third term - second term = 0a - (-3a) = 3a
Fourth term - third term = 3a - 0a = 3a
Fith term - fourth term = 6a - 3a = 3a
Therefore, it is an arithmetic sequence with difference d = 3a.
3) the general rule for the nth term of an arithmetic sequence is given by the formula:
An = Ao + d (n - 1)
Where Ao = -6a and d, as determined above, is 3a
=> An = -6a + 3a (n - 1)
Expand the parenthesis (distributive property) =>
An = -6a + 3an - 3a = -9a + 3an = 3an - 9a = option D. <------- answer.
Solve for x where a is an integer less than 0
Answers
So to do this, simply change the sign for a to -a in the original equation and solve for x.
-ax > -12
X < 12/a.
This is the solution.
If you were going to represent the top view of the figure, stated which boxed should be shaded.
Answers
The height of a stack of dimes varies directly with the number of dimes in the stack. A stack of 4 dimes is 5.4 mm tall. How many millimeters tall is a stack of 15 dimes?
Answers
Simplify each expression. K(k^3) that means to the third power btw
Plz help!
Answers
helppppppppppppppppppppppppppppp
Answers
What scale factor was applied to the first rectangle to get the resulting image
Help me plsssssssssssssssssssssssssssssssssssssssssss!
Answers
.5 x 5 = 2.5
scale factor should be 5.
The perimeter of a square must be greater than 188 inches but less than 198 inches. find the range of possible side lengths that satisfy these conditions. (hint: the perimeter of a square is given by p=4s, where s represents the length of a side).
Answers
The range of possible side lengths for the square is from slightly more than 47 inches to slightly less than 49.5 inches. This is found by dividing the given perimeters by 4, using the formula p=4s.
Explanation:In this problem, we need to find the range of possible side lengths of a square where the perimeter is more than 188 inches but less than 198 inches. Remember that the perimeter of a square is found by multiplying the length of one side by 4 (p=4s).
First, let's find the side length for a square with a perimeter of 188 inches. We do this by dividing the perimeter by 4: 188 / 4 = 47 inches. So, any square with side lengths greater than 47 inches would have a perimeter more than 188 inches.
Next, we find the side length for a square with a perimeter of 198 inches. Similarly, we divide the perimeter by 4: 198 / 4 = 49.5 inches. So any square with side lengths less than 49.5 inches would have a perimeter less than 198 inches.
Therefore, the range of possible side lengths that satisfy these conditions is from slightly more than 47 inches to slightly less than 49.5 inches.
Learn more about Perimeter of a Square here:https://brainly.com/question/29192128
#SPJ11
Marcus has a total of 10 nickels and dimes in his pocket. he has a total of 70 cents. how many dimes does he have in his pocket?
Answers
1 nickel = $0.05
1 dime = $0.10
4 dimes = $0.40
6 nickels = $0.30
4 dimes + 6 nickels = 10 coins
$0.40 + $0.30 = $0.70
The answer is: He has a total of 4 dimes in his pocket.
Round 8.414 to the nearest hundredth
Answers
Jason sold half of his comic books and then bought 8 more. he now has 13. how many did he begin with ?
Answers
so 5+5=10
Yu-Xi draws a triangle with two angles measuring 79 degrees and 23 degrees.What is the measure, in degrees, of the third angle?
Answers
180-102=78
the third angle is 78 degrees
Answer:
The Triangle Drawn by ,Yu-Xi,has measure of two angles ,79° and 23°.
All the Basic Learners who knows Math ,that,sum of Measures of three Interior angles of Triangle is 180°.
→79°+23°+Third Angle =180°
→102°+Third Angle =180°
→Third Angle =180° -102°
Third Angle =78°
helpppppppppppppppppppppppppppppppppppp
Answers
First, lets factor 8:
[tex]8=2 ^{3} [/tex]
Now we can divide the power of the term, 3, by the index of the radical 2:
[tex] \frac{3}{2} [/tex] = 1 with a remainder of 1
Next, lets do the same for our second term [tex] x^{7} [/tex]:
[tex] \frac{7}{2} [/tex] = 3 with a remainder of 1
Again, lets do the same for our third term [tex]y^{8} [/tex]:
[tex] \frac{8}{2} =4[/tex] with no remainder, so this term will come out completely.
Finally, lets take our terms out of the radical:
[tex] \sqrt{8x^{7} y^{8} }= \sqrt{ 2^{3} x^{7} y^{8} } =2 x^{3} y^{4} \sqrt{2x} [/tex]
We can conclude that the correct answer is the third one.
root (8x ^ 7y ^ 8)
(8x ^ 7y ^ 8) ^ (1/2)
Properties of exponents:
(8 ^ (1/2) x ^ (7/2) y ^ (8/2)
We rewrite:
(8 ^ (1/2) x ^ (7/2) y ^ 4
(2 * 2 ^ (1/2) x ^ 3y ^ 4x ^ (1/2)
(2 * x ^ 3 * y ^ 4 * (2x) ^ (1/2)
Answer:
(2*x^3*y^4*(2x)^(1/2)
option 3
Given that (6,5) is on the graph of f(x), find the corresponding point for the function-2f(x)
Answers
The point of interest is (6, -10).
Answer:
the person up is wrong
Step-by-step explanation:
i got it wrong on the test rn
The area of square abcd is 36 square units and the area of triangle ebf is 20 square units. if line eb is perpindicular to line bf and line ae is equal to 2 find the length of line cf
Answers
Final answer:
The length of line CF is 20 units.
Explanation:
Let's analyze the given information step by step:
The area of square ABCD is 36 square units, so each side of the square measures √(36) = 6 units.The area of triangle EBF is 20 square units.Line EB is perpendicular to line BF.Line AE is equal to 2 units.Since line EB is perpendicular to line BF, triangle EBF is a right triangle. Let's assume the length of line BF is x units. Using the area of a triangle formula, we have:
Area of triangle EBF = (1/2) * base * height
20 = (1/2) * x * 2
Simplifying the equation, we get:
20 = x
Therefore, the length of line BF (or CF) is 20 units.
AB=2y+1, BC=y+1,CD=7x-3,DA=3x what is x and y
Answers
Answer:
x = 2
y = 5
Explanation:
ABCD is a parallelogram. This means that each two opposite sides are equal.
This means that:
1- AB = CD
2y + 1 = 7x - 3 ...........> equation I
2- AD = BC
3x = y + 1
This can be rewritten as:
y = 3x - 1............> equation II
Substitute with equation II in equation I and solve for x as follows:
2y + 1 = 7x - 3 ...........> equation I
2(3x - 1) + 1 = 7x - 3
6x - 2 + 1 = 7x - 3
6x - 1 = 7x - 3
7x - 6x = -1 + 3
x = 2
Substitute with x in equation I to get y as follows:
y = 3x - 1
y = 3(2) - 1
y = 6 - 1
y = 5
Hope this helps :)
Given the segments of a quadrilateral, the steps show that for it to be closed, the expression 3y + 10x + 1 = 0 must hold. Additional information would be needed to find unique values for x and y.
Given the segments AB, BC, CD, and DA of a quadrilateral:
AB = 2y + 1BC = y + 1CD = 7x - 3DA = 3xFor a quadrilateral to be closed, the perimeter equations must be equal. Thus, we set up the equality:
AB + BC + CD + DA = 0
Substituting the given segment expressions:
(2y + 1) + (y + 1) + (7x - 3) + (3x) = 0
Simplifying this equation:
3y + 4 + 10x - 3 = 0
Combine like terms:
3y + 10x + 1 = 0
This represents a linear equation involving x and y.
Assuming the quadrilateral is closed, another equation or condition is needed to solve for x and y simultaneously. If additional geometric or numeric information is provided about the quadrilateral, it can help solve the system.
here is complete question-Find the values of x and y in ABCD. 9. AB=2y,BC=y+3,CD=5x-1,DA=2x+4 10. AB=2y+1,BC=y+1,CD=7x-3,DA=3x (6.3) Determine whether the quadrilateral must be a parallelogram.
Which transformation shows a reflection of ΔDEF?
Answers
The answer is B or the purple one
Answer:
The image B with purple figures is correct.
Step-by-step explanation:
We are given the figure DEF and we are required to find the figure which is obtained after reflecting it.
Now, reflection of a figure means to flip the figure over a line.
In the green figure, the points D and E are interchanged which is not possible in reflection.
In the blue figure, there is no change.
In the purple figure, the triangle is flipped over the line DE and so it is the correct answer.
Hence, the purple figure is obtained after reflecting the figure DEF.