Jack draws a rainbow which is a parabola that has the equation y =-0. 1(x-1) 2+6, where x and y are measured in centimeters. If the height of the rainbow is 6 cm, how far away are the endpoints of the rainbow from one another?

Answers

Answer 1

The endpoints of the rainbow are 2√60 cm apart.

The given equation for the rainbow is in vertex form, which is y = a(x - h)^2 + k, where (h, k) is the vertex of the parabola.

In this case, the vertex is (1, 6), which means that the parabola is shifted horizontally by 1 unit to the right and vertically by 6 units upwards from the standard parabola y = ax^2.

Since the height of the rainbow is 6 cm, this means that the highest point of the parabola is at y = 6, which occurs at the vertex (1, 6).

To find the distance between the endpoints of the rainbow, we need to find the x-intercepts of the parabola. These occur where y = 0. Therefore, we need to solve for x in the equation:

0 = -0.1(x - 1)^2 + 6

-6 = -0.1(x - 1)^2

-6/-0.1 = (x - 1)^2

60 = (x - 1)^2

±√60 = x - 1

x = 1 ± √60

Since we are looking for the distance between the endpoints, we need to subtract the smaller x-value from the larger one:

Distance between endpoints = (1 + √60) - (1 - √60)

Distance between endpoints = 2√60

Therefore, the endpoints of the rainbow are 2√60 cm apart.

The given equation in the question is wrong, the correct equation is:

y = -0.1(x - 1)^2 + 6.

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Related Questions

Please help I will give brainliest.

Please help I will give brainliest.

Answers

Answer:

the answer is (x-1)^2=4

what's the area for 8 in 6 in 4 in in a irregular polygon

Answers

Answer:

192

Step-by-step explanation:

8x6x4

Answer:

192

Step-by-step explanation:

because it is

=
In a recent election Corrine Brown received 12,883 more votes than Bill Randall. If the total number of votes was
119,143, find the number of votes for each candidate.

Answers

Consequently, 119,143 votes were cast in all. Bill received 53,130 votes and Corrine received 66,013 votes.

What is explanation of the problem?

Consequently, 119,143 votes were cast in all.

The result is: 119,143 - 12,883 = 106,260

if we deduct the sum from what Corrine received. The result is 106,260 divided by 2

106,260 / 2 = 53,130

which equals 53,130.

53,130 plus the additional 12,883 votes

Corrine received equals 66,013.

Bill received 53,130 votes and Corrine received 66,013 votes.

For instance, if a property is damaged, three insurers who each provide $60,000 in coverage are each given 50% of the claim. Real estate, workers' compensation, and the distribution of financial advantages are further examples of allocation. Establish the appropriate representational threshold for each representative. Calculate this by dividing the total number of representatives by the combined population of all the states.

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What is the slope of the line that passes through the points (4.2) and (-16, -10)?
Write your answer in simplest form.

Answers

Given:

A line passes through the points (4,2) and (-16, -10).

To find:

The slope of the line.

Solution:

Slope Formula:

\(m=\dfrac{y_2-y_1}{x_2-x_1}\)

A line passes through the points (4,2) and (-16, -10). So, slope of the line is

\(m=\dfrac{-10-2}{-16-4}\)

\(m=\dfrac{-12}{-20}\)

\(m=\dfrac{3}{5}\)

Therefore, the slope of the line is \(\dfrac{3}{5}\).

Which equations have the same value of x as Two-thirds (6 x + 12) = negative 24? Select two options.
4 x + 8 = negative 24
9 x + 18 = negative 24
4 x = negative 16
18 x + 36 over 2 = negative 24
4 x = negative 32

Answers

Answer:

4x+8=-24 and

4x=-32

Step-by-step explanation:

2/3(6x+12)=-24

or,12x+24=-72

or,x=-72-24/12

•°•x=-8

4x+8=-24

or,x=-24-8/4

•°•x=-8

4x=-32

or,x=-32/4

•°•x=-8

Answer:

the guys above me is correct

Step-by-step explanation:

4x+8=-24 and

4x=-32

f(x) = 3(x - 5)(x + 2), then f(5) = and f(-2) =

Answers

Answer:

0

Step-by-step explanation:

Put x as 5 and solve.

3(5 - 5)(5 + 2)

3(0)(5 + 2)

3(0)(7)

= 0

Put x as -2 and solve.

3(-2 - 5)(-2 + 2)

3(-7)(0)

= 0

The altitude (i.e., height) of a triangle is increasing at a rate of 2 cm/minute while the area of the triangle is increasing at a rate of 1.5 square cm/minute. At what rate is the base of the triangle changing when the altitude is 12 centimeters and the area is 99 square centimeters

Answers

Answer:

A = 1/2 B H       area = 1/2 base X height

B = 2 A / H = 2 * 99 / 12 = 16.5 cm

dA / d t = 1/2 * (B dH / dt + H dB / dt)

dB / dt = (2 dA / dt - B dH / dt) / H

dB / dt = (2 * 1.5 cm^2 / min - 16.5 cm * 2 cm / min) / 12 cm

dB / dt = (3 - 33) / 12 cm/min = -2.5 cm/min

What is multiplicative property of equality?

Answers

According to this property, when both sides of an equation are multiplied by the same real number, both sides of the equation always remain the same. The formula for this property can be expressed in real numbers a, b and c. If a × c = b × c.

Property of Equality:

The equivalence property describes the relationship between two equal quantities. If you apply a math operation to one side of the equation, you must also apply it to the other side of the equation to maintain balance.

That is, a property that does not change the truth value of an equation or does not affect the equivalence of two or more quantities is called an equality property. These equality properties help solve various algebraic equations and define equivalence or equilibrium relationships.

Multiplicative Property of Equality:

According to this property, when both sides of an equation are multiplied by the same real number, both sides of the equation always remain the same.

The formula for this property can be expressed as for the real numbers a, b, and c.

If a × b, then, a × c = b × c.

In algebra, the multiplicative property of an equation helps extract unknown terms from an equation. Because multiplication and division are opposites of each other.

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The diagram below shows different layers of sedimentary rocks.
Based on the diagram, which of these inferences is most likely correct?
Layer F was formed earlier than Layer A.
Layer B was formed earlier than Layer E.
Layer G was formed more recently than Layer D.
Layer D was formed more recently than Layer C.

Answers

In conclusion, the most likely correct inference based on the given diagram is that Layer D was formed more recently than Layer C.

The diagram below shows different layers of sedimentary rocks, and based on the diagram, the most likely correct inference is that Layer D was formed more recently than Layer C.

Explanation: The layers of sedimentary rocks on the diagram are given as follows: A, B, C, D, E, F, and G. The principle of superposition states that sedimentary layers are older at the bottom than they are at the top of a rock formation.

As a result, we can infer the relative ages of these layers based on their order and position. Layer C is found underneath layer D and the Principle of Superposition applies.

Therefore, we can conclude that Layer D was formed more recently than Layer C.

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Can someone help me pls

Can someone help me pls

Answers

Answer:

Where's the answer?

Step-by-step explanation:

the garden table and a bench cost $582 combined. the garden table costs $68 less than the bench. what is the cost of the bench?​

Answers

Answer:

$325

Step-by-step explanation:

t +b = 582

t = b - 68

b - 68 + b = 582

2b = 582 + 68

2b = 650

2/2 b = 650 / 2

b = 325

What's 1/-9 in decimal form

Answers

-11.1111111111 is the answer

Three spheres each with charge Q uniformly distributed through its volume Rank the spheres according to the magnitude of the electric field they produced at point P (greatest firstl P (1) (2) (3) Select one: a. 3 > 2 > 1 b. all tie c. 1>2>3 d. 1 and 2 tie > 3 e. 2 > 3 >1

Answers

The correct ranking of the spheres according to the magnitude of the electric field they produce at point P (greatest first) is: 1 > 2 > 3. The answer is option C.

Since all three spheres have the same charge Q and radius, the magnitude of the electric field at point P due to each sphere is proportional to 1/d^2, where d is the distance between the center of the sphere and point P. Therefore, the sphere closest to point P will produce the greatest electric field at that point.

Assuming that the three spheres are arranged in a straight line with sphere 1 being the closest to point P and sphere 3 being the farthest, we can rank the spheres according to the magnitude of the electric field they produce at point P as follows:

Sphere 1 produces the greatest electric field at point P since it is the closest to it.

Sphere 2 produces the second greatest electric field at point P since it is farther away from point P than sphere 1 but closer than sphere 3.

Sphere 3 produces the smallest electric field at point P since it is the farthest from it.

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92 Points!Please help me and if you can explain how you got it.

92 Points!Please help me and if you can explain how you got it.

Answers

Answer: 15 = A 12 = B

Step-by-step explanation: 25 - 10 = 15   6 + 9 = 15 ( by 3's )

Determine if the expression 9y5 – 10y3 is a polynomial or not. If it is a polynomial,
state the type and degree of the polynomial.

Answers

I am going to assume that the equation was supposed to be  \(9y^{5}\)\(-10y^{3}\)

Answer:

It is a polynomial. It is a binomial and it has a degree of 5.

Step-by-step explanation:

A polynomial is an expression consisting of variables and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables so \(9y^{5}\)\(-10y^{3}\) will be considered a polynomial.

A binomial is a polynomial with 2 terms.

The degree of a polynomial is the highest exponent in it which in this equation is 5.

Does anybody know 5.4.7: Teenagers CodeHs. Please help I am stuck in this

Answers

Answer:

The program in Python is as follows:

age = int(input("Age: "))

if age>=13 and age <=19:

   print("Teenager")

else:

   print("Not a teenager")

Step-by-step explanation:

This gets input for age

age = int(input("Age: "))

This checks if age is between 13 and 19 (inclusive)

if age>=13 and age <=19:

If yes, the age is teenage

   print("Teenager")

If otherwise, the age is not teenage

else:

   print("Not a teenager")

A. write the ratio of girls to boys in the class with 12 girls and 15 boys. reduce to the lowest terms.
B. use the information from part A to estimate the number of girls in the school if there are a total of 1350 students in the whole school and in part A is representative of all classes in the school
WILL GIVE BRAINLIEST

Answers

Answer:

A. 4:5

B. 600 girls

Step-by-step explanation:

A. g : b = 12 : 15 = 4 : 5

B. the numbers of girls = 4/(4+5) × 1350

= 4/9 × 1350 = 600

HELP PLEASEEEEEEEEEEEEEEEEEEEEEEEE
13. Write an equation of the graph in slope-intercept form.

14. If misty has been traveling for 9 hours, how many miles of the trip does she have remaining?

15. If there are 50 miles in the trip remaining, how many hours has misty been traveling?

HELP PLEASEEEEEEEEEEEEEEEEEEEEEEEE13. Write an equation of the graph in slope-intercept form.14. If misty

Answers

The Equation of the graph in slope-intercept form is 3y = 1350 - 100x

Misty will travel 150 miles after 9 hours

It will take misty 12 hours to cover 50 miles

What is a linear equation?

A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. The standard form of a linear equation in one variable is of the form Ax + B = 0. Here, x is a variable, A is a coefficient and B is constant. The standard form of a linear equation in two variables is of the form Ax + By = C. Here, x and y are variables, A and B are coefficients and C is a constant.

Equation of line in slope-intercept form is y = mx + c

let y be the distance in miles and x be the time in hours.

from the graph when x = 0, y = 450

substituting into the equation,

450 = 0(m) + c

c = 450 which is the intercept

Also from the graph, taking the point (3, 350)

when x = 3, y = 350

350 = 3m + 450

3m = 350 - 450

3m = -100

m = -100/3

SO the equation of straight line becomes

y = -100x/3 + 450

multiply through by 3

3y = -100x + 1350

if misty travel 9 hours that is x = 9, then y =

3y = -100(9) + 1350

3y = 450

y = 450/3

y = 150 miles

If there are 5o miles remaining,

y = 50, x =

3(50) = -100x +1350

100x = 1350 -150

100x = 1200

x = 1200/100

x = 12 hours.

The Equation of the graph is 3y = 1350 - 100x

Misty will travelled 150 miles after 9 hours

It will take misty 12 hours to cover 50 miles

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helpppppopppppoppppppp

helpppppopppppoppppppp

Answers

answer : A
write as improper fraction,
5/4 / 39/8
5/4 x 8/39 = 40/156
40/156 = 10/39
I did an assignment wit this question and I’m almost positive it’s a :))

How do I solve this question please explain
4n -3 ≥ 105

Answers

Answer:

x>=27

Step-by-step explanation:

You have to remove the -3 from the left side by adding 3 to both sides, 4x=108 then 108/4 to get x. x=27

Cole is an urban planner. He wants to create a small scale drawing of a city block. The block is a square with sides of length 100\text{ m}100 m100, start text, space, m, end text.
Draw the city block such that 111 unit on the grid below represents 5\text{ m}5 m5, start text, space, m, end text.

Answers

Answer:

Make all sides 3.0

Answer:3.0

Step-by-step explanation:

Write 565,000 in scientific notation.AnswerX10

Answers

The given number is

\(565000\)

The scientific notation of the number is,

\(5.65\times10^5\)

WHAT IS THE OPPSIT OF 0

Answers

Answer:

0

Step-by-step explanation:

The zero is in the middle.it is a special number by being its opposite because it doesn't have it's partner.

The answer here is 0

what line is parallel to y=3x-6 and passes through the point 2,-4

Answers

Y+4=3(x-2)
Y+4=3x-6
Answer: Y=3x-10

Kary needs 54 licks for every 3 lollipops she eats. Which option below will complete the table?
Licks 96, Lollipops 1
Licks 108, Lollipops 2
Licks 72, Lollipops 5
Licks 84, Lollipops 4

Answers

Answer:

The second one is correct as 108 is double 54

Step-by-step explanation:

Therefore since 54 licks gets one lollipop gone 108 would get 2 lollipops gone

Susan had four bags of candy, each weighing 6 ounces. Isabel had one bag of candy weighing 1 pounds. Which girl has the more candy in weight? Your work will justify your answer.​

Answers

Susan has more candy in weight compared to Isabel.

To compare the candy weights between Susan and Isabel, we need to ensure that both weights are in the same unit of measurement. Let's convert Isabel's candy weight to ounces for a fair comparison.

Given:

Susan: 4 bags x 6 ounces/bag = 24 ounces

Isabel: 1 bag x 16 ounces/pound = 16 ounces

Now that both weights are in ounces, we can see that Susan has 24 ounces of candy, while Isabel has 16 ounces of candy. As a result, Susan is heavier on the candy scale than Isabel.

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c. if a significance level is to be used to test the claim that , what confidence level should be used?

Answers

There is no direct conversion between significance level and confidence level in hypothesis testing.

What is the relationship between significance level and confidence level in hypothesis testing?

The significance level is the threshold that you set to determine the level of evidence required to reject the null hypothesis. It represents the probability of rejecting the null hypothesis when it is actually true.

Commonly used significance levels are 0.05 (5%) and 0.01 (1%).

On the other hand, the confidence level is the complement of the significance level and represents the level of confidence you have in the estimation or inference made from the sample data.

It is often expressed as a percentage and is used in constructing confidence intervals. Commonly used confidence levels are 90%, 95%, and 99%.

Therefore, if you want to test a claim using a specific significance level, such as α = 0.05, there is no direct conversion to determine the corresponding confidence level.

The choice of the confidence level depends on the level of certainty or precision you desire in your estimation or inference.

In practice, the confidence level is often chosen independently based on the specific requirements of the study or the context in which the hypothesis test is conducted.

It is not determined by the significance level but rather reflects the desired level of confidence in the results.

If you can provide more details about the specific claim or scenario you are referring to, I can help you further in determining an appropriate confidence level.

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A point charge of magnitude q is at the center of a cube with sides of length ᴸ Part A: What is the electric flux phi through each of the six faces of thecube? Use ᴱ⁰ for the permittivity offree space Phi¹ = Part B: What would be the flux Phi¹ through a face of the cube ifits sides were of length ᴸ¹? Use Eo for the permittivity offree space Phi¹=

Answers

a) The electric flux through each face of a cube with a point charge at its center is given by Φ = qL² / ε₀, where q is the magnitude of the charge, L is the side length of the cube, and ε₀ is the permittivity of free space.

b) If we have a cube with a different side length L1, the flux through a face of that cube would be Φ1 = qL1² / ε₀.

a) Electric flux through each face of the cube:

To calculate the electric flux through a surface, we use Gauss's Law, which relates the electric flux (Φ) to the enclosed charge (q_enc) by the equation Φ = q_enc / ε₀, where ε₀ is the permittivity of free space.

In this case, since the point charge is at the center of the cube, it is enclosed by each face of the cube. Therefore, the flux through each face will be the same. Let's calculate it.

The charge enclosed by each face is the magnitude of the point charge, q, since it is located at the center of the cube. Therefore, q_enc = q.

The area of each face of the cube is A = L², where L is the side length of the cube.

Now, substituting the values into the equation Φ = q_enc / ε₀, we get:

Φ = q / ε₀ * (1 face area)

= q / ε₀ * L²

Therefore, the electric flux through each face of the cube is Φ = qL² / ε₀.

b) Electric flux through a face with a different side length:

If we have a cube with a side length L1, we can use the same formula to calculate the flux through one face of the cube.

Using the equation Φ = qL² / ε₀, we substitute L1 for L:

Φ1 = qL1² / ε₀

So, the flux through a face of the cube with side length L1 is Φ1 = qL1² / ε₀.

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Complete Question:

A point charge of magnitude q is at the center of a cube with sides of length L.

a- What is the electric flux Φ through each of the six faces of the cube?

b- What would be the flux Φ1 through a face of the cube if its sides were of length L1?

what is integral of cos?

Answers

The indefinite integral of cos(x) is sin(x) + C, and we can find the definite integral of cos(x) between two limits by evaluating sin(x) + C at the upper and lower limits and subtracting the results.

The integral of cos(x) is sin(x) + C, where C is the constant of integration.

The notation for the integral of cos(x) is ∫cos(x) dx, where the symbol ∫ represents the integral sign, cos(x) is the function being integrated, and dx represents the variable of integration, which in this case is x.

The antiderivative of cos(x) is sin(x), meaning that if we take the derivative of sin(x), we get cos(x). The constant of integration, C, is added because the derivative of a constant is always zero.

Therefore, the indefinite integral of cos(x) is sin(x) + C, and we can find the definite integral of cos(x) between two limits by evaluating sin(x) + C at the upper and lower limits and subtracting the results.

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The table shows the amount of flour
used to make waffles. What is the unit
rate for the amount of flour per waffle?

The table shows the amount of flourused to make waffles. What is the unitrate for the amount of flour

Answers

Answer:

⅛ cups per waffle

Step-by-step explanation:

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Help solve. The people on Coral Island buy only juice and cloth.The CPI basket contains the quantities bought in 2019 The average household spent $32 on juice and $15 on cloth in 2019 when the price of juice was $2 a bottle and the price of cloth was $5 a yard. In the current year, 2020, juice is $7 a bottle and cloth is $3 a yard. Calculate the CPI and the inflation rate in 2020 The CPI in 2020 is >>>Answer to 1 decimal place 9. During the past week, Mr. Hamilton gave one quiz and one exam to his high school algebra class.It takes Mr. Hamilton of an hour to grade one student's exam and of an hour to grade onestudent's quiz. If x represents the number of students that took the quiz and exam, whichequation below could be used to find the y, the total amount of time, in hours, spent grading?a) y = 6xb) y = -X45c) y = -x101d) y = x Solve for the remaining angles and side of the one triangle that can be created. Round to the nearest hundredth: A = 50. c = 6,0 = 6.5 Answer: C=______ B=_______ b=___________ tawney company invests in a piece of equipment that is expected to generate cash inflows of $60,000 per year over its life of 6 years. the equipment cost $240,000 and has no residual value. what is the average annual operating income from asset? Kelly has 138.26 in her bank account.She purches a new table for 124, plus 8% sales tax.How much is in her bank account after the purchase The functions f(x) = x^2 3 and g(x) = x^2 + 2 are shown on the graph.The graph shows f of x equals x squared minus 3, which is an upward-opening parabola with a vertex at 0 commas negative 3 and a point at negative 1 comma negative 2, and a point at 1 comma negative 2. The graph also shows g of x, which is a downward opening parabola with a vertex at 0 commas 2 and a point at negative 1 comma 1, and a point at 1 comma 1.Explain how to modify the graphs of f(x) and g(x) to graph the solution set to the following system of inequalities. How can the solution set be identified?y x^2 3y > x^2 + 2 We return to the olympic1500m.txt data set one more time. (a) Do speed skaters have an advantage in the 1500m race if they start in the outer lane? Formulate null and alternative hypothesis. (b) In Question 2(b) you (should) have established that the data are normally distributed. Use this information to test the null hypothesis at significance levels a = 5% and 2% using the appropriate test. (c) Given your answers in Question 2(d), was it really necessary to conduct the hypothesis tests in Question 7(b)? Am Oro - - Race Inner Outer Diff 1 107.04 105.98 1.06 2 109.24 108.20 1.04 3 111.02 108.40 2.62 4 108.02 108.58 -0.56 5 107.83 105.51 2.32 6 109.50 112.01 -2.51 7 111.81 112.87 -1.06 8 111.02 106.40 4.62 9 106.04 104.57 1.47 10 110.15 110.70 -0.55 11 109.42 109.45 -0.03 12 108.13 109.57 -1.44 14 105.86 105.97 -0.11 15 108.27 105.63 2.64 16 107.63 105.41 2.22 17 107.72 110.26 -2.54 18 106.38 105.82 0.56 19 107.78 106.29 1.49 20 108.57 107.26 1.31 21 106.99 103.95 3.04 22 107.21 106.00 1.21 23 105.34 105.26 0.08 24 108.76 106.75 2.01 What is an angle that is complementary to _1? how many moles of hydronium are present in 0.85 l of a 5.25 x 10-5 m solution? Use the image to answer the question. Which effect of the central governments expanded power is shown in this image 10 + 9(9v + 2) simplify FIND THE DOMAIN:h(theta) = 2 sin ( theta + pi/2)PLEASE SHOW HOW YOU GOT THE DOMAIN WITH SHOWING HOW-TO STEPS WITH TI-84 CALCULATOR OR SHOW MATH WORK WITH HOW-TO STEPS. I NEED TO MEMORIZE HOW TO FIND DOMAIN WHEN IT HAS THETA. I tried doing it on a calculator but the correct answer kept coming up wrong. When did the FBI establish? How are gene-environment interactions are critical for the expression of physical and psychological characteristics? the size of the device that collects radiation (such as light) is called a telescope's Find the largest domain of f(x)=x+1 The base of a right rectangular prism is 20 cm2. If the height of the prism is 9.2cm, what is its volume? Calcium has six naturally occurring isotopes: 40Ca, 42Ca, 43Ca, 44Ca, 46Ca, and 48Ca. Complete the following table: What were the ''border states'' of the civil war simplify plzzzzzzzzzzzzzzz