Given
\(f(x)=x^2,h(x)=(\frac{1}{6}x)^2\)To find: Which statement best compares the graph of h(x) with the graph of f(x).
Explanation:
It is given that,
\(f(x)=x^2,h(x)=(\frac{1}{6}x)^2\)The graph is shown as,
From, the figure it is clear that, both the graphs have same vertex and the grpah of h(x) lies below the graph of f(x).
Also, h(x) is 5² times less than the value of f(x).
Hence, the graph of h(x) is the graph of f(x) horizontally stretched by a factor of 6.
How do you convert 72 kilograms to pounds? show the mathmatical steps
Find the equation of the line that passes through points A and B.
y.
AA (1,7)
-X
B (-3,-1)
Answer:
y=2x+5
Step-by-step explanation:
start with by stating your formula: y=MX +C
m= Y2-Y1÷X2-X1
m=-1-7÷-3-1
m=-8÷-4
m=2
substitutionUsing A's coordinates
7=2(1)+c
7=2+c
7-2=c
5=c
therefore y=2x+5
Only answer question 2
An oil barrel contains 20.3 gallons of oil. One gallon is equal to 3.8 L. How many liters of oil are in the barrel?
Answer:
77.14L
Step-by-step explanation:
20.3x3.8=77.14L
if f(x)= 1/x+2, what is f(3+h)?
A. 1/ (x+2)(3+h)
B. (3+h)/(x+2)
C. 1/(3+h)
D. 1/ h+5
Answer:
D. 1/h+5
Step-by-step explanation:
f(x)=1/3+h+2
F(x)=1/h+5
Quadrilateral A'B'C'D' is the image of
quadrilateral ABCD under a dilation with a scale
factor of 3. What is the length of segment BC?
By using the concept of dilation factor, length of BC obtained is 3 units
What is dilation factor?
Dilation is a transformation which changes the size of a figure by a certain factor.
That factor is called the scale factor
In the figure, A'B'C'D' is the image of ABCD under dilation with a scale factor of 3
A'B'C'D' is the dilated figure
Length of B'C' = 9 units
Length of BC = \(9 \div 3\) = 3 units
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Complete Question
The figure has been attached here
question 4/3 y=1 what is y?
Answer:
y= 3/4
Step-by-step explanation:
Answer:
y=3/4
Step-by-step explanation:
4/3y=1
divide both sides by 4/3
1 divided by 4/3 is 3/4 so:
y=3/4
What are the 3 types of proofs in math
Answer:
direct proof, proof by contradiction, proof by induction
Step-by-step explanation:
there u go mate
Which equations have infinitely many solutions?
Answer:
your answer is -2
Step-by-step explanation:
x- x/3+2=0
or. (3x -x +6)/3 =0
or. 3x-x+6 =0
or. 2x+6=0
or. 2x= -6
or. x = -6/2
or. x = -2
Answer:
here is the full question
Step-by-step explanation:
How to use Pascal’s triangle to find x^2 using the difference quotient formula
Using Pascal's triangle and the difference quotient formula, we expand (x + h)^2 and simplify the expression to (2hx + h^2) / h. As h approaches 0, the term h becomes negligible, and we are left with 2x, which represents the derivative of x^2.
To use Pascal's triangle to find x^2 using the difference quotient formula, we can follow these steps:
1. Write the second row of Pascal's triangle: 1, 1.
2. Use the coefficients in the row as the binomial coefficients for (x + h)^2. In this case, we have (1x + 1h)^2.
3. Expand (x + h)^2 using the binomial theorem: x^2 + 2hx + h^2.
4. Apply the difference quotient formula: f(x + h) - f(x) / h.
5. Substitute the expanded expression into the formula: [(x + h)^2 - x^2] / h.
6. Simplify the numerator: (x^2 + 2hx + h^2 - x^2) / h.
7. Cancel out the x^2 terms in the numerator: (2hx + h^2) / h.
8. Divide both terms in the numerator by h: 2x + h.
9. As h approaches 0, the term h becomes negligible, and we are left with the derivative of x^2, which is 2x.
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help quick due in 10 minutes you will be reported if you spam Ivan is 75 inches tall if his brother Logan was 5 inches shorter, he would be exactly half Evan's height How tall is Logan? Enter your answer as a decimal in the box,
Answer:
35
Step-by-step explanation:
if not correct I'm very very sorry I tried my best for this</3
If you buy stock for $36.20 per share and sell that stock for $37.90 per share, what was your
return on investment?
Answer:
$1.70 per share
Step-by-step explanation:
37.90-36.20=1.70
what is √ 169 please answer fast and the correct answer please
Answer:
Step-by-step explanation:
Answer:13
Step-by-step explanation:
need the answer thanks!
Answer:
The sum does not exist, but if you are in a senior math class, it could be - infinity.
Step-by-step explanation:
If the sum does not have an endpoint (and it looks like it does not), then the sum really does not exist.
Consider this question.
Does the sum stop at 0 as in
50 + 40 + 32 + 24 + 16 + 8 + 0
But why not - 8 or - 16 or ...
So it is not that the sum does not exit. It is that we do not know where that stop is. Depending on your grade level, you could answer - infinity, but I doubt that is the expected answer.
Find the distance between the points P and Q shown.
The distance between points P and Q is √73
How to find the distance between the two points?First, remember that the distance between two points whose coordinates are (a, b) and (c, d) is given by:
distance = √( (a - c)² + (b - d)²)
Here we can see that the coordinates of the two shown points are:
P = (-3, 2)
Q = (5, -1)
Replacing that in the distance formula we will get:
distance = √( (-3 - 5)² + (2 + 1)²)
distance = √( (-8)² + (3)²)
distance = √73
So the correct option is the third one.
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Question 6 Which of the following is the graph of f(x) = x² = 5x + 4?
Given: The equation x² = 5x + 4
We have to draw the the graph for the given equation.
Consider the given equation,
x^2 - 5x - 4 = 0
The vertex of the parabola of the form f(x) = ax^2 + bx + c is given by x = -b/2a
Here,
a= 1
b= -5
c= -4
vertex = x = 5/2= 2.5
Also, the y coordinate at x = 2.5 is,
y = (2.5)^2 -5(2.5)-4
y = -10.25
Thus the vertex of parabola is (2.5 , -10.25)
y - intercept is the point where x = 0
put x = 0 in given equation
f(x) = 0 - 0 -4
f(x) = -4
hence y intercept is at (0, -4).
Now, we calculate x- intercept
x- intercept is where y is equal to 0.
Put f(x) = 0
We have,
x^2 - 5x - 4 = 0
by using quadratic formula,
x = -b ±√b² - 4ac/2a
x=5 ±√-5² - 4 (1)(-4)/2
x= 5±√41/2.
Hence with the obtained values the graph of the equation is obtained.
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Let's multiply signed numbers.
Before and After
Where was the girl
1.
5 seconds after this picture was taken? Mark her approximate location on the picture.
2.
5 seconds before this picture was taken? Mark her approximate location on the picture
to find the length of the curve defined by from the point (-3,2136) to the point (3,2238), you'd have to compute
The length of the curve defined by from the point (-3, 2136) and (3, 2238), by use of distance formula is approximately 102.17 units.
The formula for the distance between two points (x1, y1) and (x2, y2) is given by:
\(d = \sqrt{((x2 - x1)^2 + (y2 - y1)^2)\)
In this case, we have:
x1 = -3, y1 = 2136
x2 = 3, y2 = 2238
Substituting these values into the formula, we get:
\(d = \sqrt{((3 - (-3))^2 + (2238 - 2136)^2)\)
\(= \sqrt{(6^2 + 102^2)\)
= \(\sqrt{(10440)\)
≈ 102.17
Therefore, the length of the curve defined by the points (-3, 2136) and (3, 2238) is approximately 102.17 units.
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_____The given question is incorrect, the correct question is given below:
To find the length of the curve defined by from the point (-3,2136) to the point (3,2238), you'd have to compute by using distance formula.
2. The cost of oranges varies directly with the total mass bought. 2 kg of oranges costs $4.50. Describe the relationship between cost and mass in words. You may want to calculate a unit rate first.
Answer:
The relationship between the cost/mass is $2.25/kg.
Step-by-step explanation:
You first need to divide $4.50 / 2, to know what a single kilogram mass costs.
$4.50 / 2 = $2.25
Now that you have this unit rate $2.25, You can multiply/add it.
$4.50 + $2.25 is $6.75, + another $2.25 = $9.00, and so on.
there are 25 student in a class. five of then scored A and 10 of them score B while the other scored C for Biostatistics. if a student is selected at random, calculate the probability that the selected student scored A or B in biostastics.
There is a 60% probability that a randomly selected student from the class scored either an A or B in Biostatistics.
To calculate the probability that a randomly selected student scored either an A or B in Biostatistics, we need to consider the number of students who scored A and B and divide it by the total number of students in the class.
Given that there are 25 students in the class, 5 of them scored an A and 10 scored a B. To calculate the probability, we add the number of students who scored A (5) to the number of students who scored B (10):
Number of students who scored A or B = Number of students who scored A + Number of students who scored B = 5 + 10 = 15.
Therefore, the probability that a randomly selected student scored A or B
in Biostatistics is:
Probability = Number of students who scored A or B / Total number of students = 15 / 25 = 0.6 or 60%.
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help please!!!!!!!!
Which of the following is equal to the expression listed below?
27 + 36
A.
9 + (3 × 4)
B.
(9 + 3)(9 + 4)
C.
9(3 + 4)
D.
(9 × 3)(9 × 4)
I really need help with this omg
Answer:
its d kkkkkkkkkkkkkkkkkkkkkk
Southside High School found that 80% of last year's sold-out plays occurred
during weekend performances. Based on this information, the drama teacher
decided to add another performance time on Saturday. This decision is a
result of
OA. describing data
OB. making an inference
OC. creating involvement
D. collecting data
Answer:
B. making an inference.
Step-by-step explanation:
The drama teacher's decision to add another performance time on Saturday is a result of making an inference based on the information that 80% of last year's sold-out plays occurred during weekend performances. By observing this pattern, the drama teacher infers that adding another performance on Saturday will likely attract a larger audience and increase the chances of having a sold-out show.
i dont know the answer please help me
what is the diameter of a circle with a radius of 4.375"? 2.187" or 2.375" or 8.375" or 8.750"
Find the times (to the nearest hundredth of a second) that the weight is halfway to its maximum negative position over the interval 0<_t<_0.5. Solve algebraically, and show your work and final answer in the response box. Hint: Use the amplitude to determine what y(t) must be when the weight is halfway to its maximum negative position. Graph the equation and explain how it confirms your solution(s).
Answer:
0.20 and 0.36
Step-by-step explanation:
y(t) = 2 sin (4π t) + 5 cos (4π t)
We wish to convert this to:
y = A sin(ωt + φ)
We know that ω = 4π. We also know the following:
5 = A sin φ
2 = A cos φ
Divide the first equation by the second equation:
5/2 = tan φ
φ = tan⁻¹(5/2)
Now, square the two equations and add them together.
5² + 2² = (A sin φ)² + (A cos φ)²
29 = A²
A = √29
The equation of the wave is therefore:
y = √29 sin(4π t + tan⁻¹(5/2))
The maximum negative position is -√29. And half of that is -½√29.
-½√29 = √29 sin(4π t + tan⁻¹(5/2))
-½ = sin(4π t + tan⁻¹(5/2))
7π/6 + 2kπ or 11π/6 + 2kπ = 4π t + tan⁻¹(5/2)
7 + 12k or 11 + 12k = 24t + 6 tan⁻¹(5/2) / π
t = (7 + 12k − 6 tan⁻¹(5/2) / π) / 24 or (11 + 12k − 6 tan⁻¹(5/2) / π) / 24
Trying different integer values of k, we find there are two possible values for t between 0 and 0.5, both when k = 0.
t = (7 − 6 tan⁻¹(5/2) / π) / 24 or (11 − 6 tan⁻¹(5/2) / π) / 24
t ≈ 0.20 or 0.36
This equation for y(t) can be expressed as follows:
\(\to \bold{y(t) = \sqrt{29} \cdot \sin(4\pi t +\ arc \tan(\frac{5}{2}))}\)
\(-\frac{1}{2}\) was its value of the given equation for angles \(\bold{\frac{7\pi}{6}} \ and \ \bold{\frac{11 \pi}{6}}\).
The weight will be midway between its equilibrium point and its maximum negative position if...
\(\to \bold{4\pi t +\arc \tan(\frac{5}{2}) = \frac{7\pi }{6}\ or\ \frac{11\pi}{6}}\\\\ \to \bold{t = \frac{(\frac{7\pi}{6} -\ arc \tan(\frac{5}{2}))}{(4\pi)} \approx 0.196946 \ seconds}\)
and
\(\to \bold{t = \frac{(\frac{11\pi}{6} - \ arc \tan(\frac{5}{2})) }{(4\pi)} \approx 0.363613 \ seconds}\)
The weight would be halfway from equilibrium towards the maximum negative position around–approximately \(\bold{0.20\ seconds \ and \ 0.36\ seconds}\), and that every half-second subsequently.
Therefore the final answer is "0.20 second and 0.36 second".
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Please Help me
Fred's account balance is -$13.37, and Hank's account balance is $11.17. Which of the following is true?
A.
Fred's account balance = Hank's account balance
B.
Fred's account balance > Hank's account balance
C.
Fred's account balance < Hank's account balance
Answer: i think its c, hope this helps
Step-by-step explanation:
Raffle tickets will be sold at an event. The graph shows the amount of revenue, in dollars, the event will raise if different numbers of tickets are sold. 100 How much revenue will the event raise for each raffle ticket sold? 90 А $4.00 80 B $2.00 70 С $1.50 D $0.75 60 Revenue (5) SO 40 30 20 10 4 8 12 16 28 32 20 24 Tickets Sold 36 40
9514 1404 393
Answer:
C. $1.50
Step-by-step explanation:
The graph is a straight line through the origin, so the revenue is proportional to the number of tickets. The ratio of revenue to tickets will tell you the money raised for each ticket sold. Pick any point on the graph and divide the revenue value by the number of tickets.
The division can be easy if the number of tickets is 10. We see that the revenue for 10 tickets is $15, so the amount raised for each ticket is ...
$15/10 = $1.50 . . . . raised per ticket sold
solve this one problem 1X13 and only this problem the problem that says 1x13 no other problem.
11111111111111111111111111111111111111111+23333333333333333+000000000000999999999999999999999999999999=
Answer:
13
Step-by-step explanation:
because...math
Question 3: Mathematical proficiency and the construction of mathematics ideas. To answer this question, you need to understand paragraphs 2.12 and 2.13 in your study guide: Key to note the following concepts: constructivism and behaviourism. inductive and deductive thinking or reasoning. instrumental and relational understanding conceptual and procedural knowledge; and ● elements of mathematics proficiency. . e . (10 marks) ● 3.1 Create an activity where procedural and conceptual understanding co-exists. Revisit your content areas and choose a problem to solve and demonstrate how procedural and conceptual knowledge can be linked to the teaching and learning process. (6) 3.2 Provide an example to explain the difference between conceptual knowledge and procedural knowledge.
Given statement solution is :- Math Proficiency conceptual knowledge involves understanding the fundamental concept of division and its relationship to fractions, enabling flexibility in solving division problems with different fractions. Procedural knowledge, on the other hand, focuses on following a specific set of steps to achieve a correct solution without necessarily comprehending the underlying concept.
3.1 Activity: Procedural and Conceptual Understanding in Action
Content Area: Fractions
Problem: Comparing Fractions
Objective: Students will demonstrate both procedural and conceptual understanding of comparing fractions.
Activity Steps:
Begin by introducing the concept of fractions and reviewing the basic procedures for comparing fractions (e.g., finding a common denominator, cross-multiplying).
Provide students with a set of fraction comparison problems (e.g., 2/3 vs. 3/4, 5/8 vs. 7/12) and ask them to solve the problems using the traditional procedural approach.
After students have solved the problems procedurally, engage them in a group discussion to explore the underlying concepts and relationships between fractions. Ask questions such as:
What does it mean for one fraction to be greater than or less than another?
Can you explain why we need a common denominator when comparing fractions?
How can you visually represent and compare fractions to better understand their relative sizes?
Introduce visual aids, such as fraction bars or manipulatives, to help students visualize the fractions and compare them conceptually. Encourage students to reason and explain their thinking.
Have students revisit the fraction comparison problems and solve them again, this time using the conceptual understanding gained from the group discussion and visual aids.
Compare the students' procedural solutions with their conceptual solutions, and discuss the similarities and differences.
Conclude the activity by emphasizing the importance of both procedural and conceptual understanding in solving fraction comparison problems effectively.
By incorporating both procedural and conceptual approaches, this activity allows students to develop a deeper understanding of comparing fractions. The procedural approach provides them with the necessary steps to solve problems efficiently, while the conceptual approach helps them grasp the underlying principles and relationships involved in fraction comparison.
3.2 Example: Conceptual Knowledge vs. Procedural Knowledge
Conceptual knowledge refers to the understanding of underlying concepts, principles, and relationships within a domain, whereas procedural knowledge focuses on knowing the specific steps or procedures to perform a task without necessarily understanding the underlying concepts.
Example: Division of Fractions
Conceptual Knowledge: Understanding the concept of division as the inverse operation of multiplication, and recognizing that dividing fractions is equivalent to multiplying by the reciprocal of the divisor. This understanding allows for generalization and application of division concepts to various fractions.
Procedural Knowledge: Following the specific steps to divide fractions, such as "invert the divisor and multiply" or "keep-change-flip" method. This knowledge involves applying the procedure without necessarily grasping the underlying concept or reasoning behind it.
In this example, Math Proficiency conceptual knowledge involves understanding the fundamental concept of division and its relationship to fractions, enabling flexibility in solving division problems with different fractions. Procedural knowledge, on the other hand, focuses on following a specific set of steps to achieve a correct solution without necessarily comprehending the underlying concept.
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