Mathematics High School

A tunnel on a bike trail is being designed similar to the picture below. The height of the new bike tunnel, y, in feet, is given by the following equation, where x is the horizontal distance, in feet, from the center line of the opening of the tunnel. Note that negative x-values indicate the distance to the left of the center line, and positive x-values indicate the distance to the right of the center line. Plot the points on the graph where the height of the tunnel is a maximum and where the height of the tunnel is zero feet.

Answers

Answer 1

we have that

[tex]y=-x^2+36[/tex]

we know that

Is the equation of a vertical parabola open down

the vertex is a maximum

step 1

convert the equation of the parabola in the vertex form

[tex]y=-x^2+36[/tex]

[tex]y-36=-x^2[/tex]

the vertex (h,k) is the point (0,36)

Part a) The point on the graph where the height of the tunnel is a maximum is (0,36)

Part b) The points on the graph where the height of the tunnel is zero feet is when y=0

for y=0

[tex]-x^2+36=0[/tex]

[tex]x^2=36[/tex]

[tex]x=(+/-)6[/tex]

the points are (-6,0) and (6,0)

see the attached figure

A Tunnel On A Bike Trail Is Being Designed Similar To The Picture Below. The Height Of The New Bike Tunnel,

Answer 2

Answer:

Step-by-step explanation:

Related Questions

Put in order from greatest to least: -5, -10, -1/2, -2.5, -0.25

Answers

Answer:

-0.25, -1/5, -2.5, -5, -10

Step-by-step explanation:

Answers

The question is an illustration of probability, and the value of P(B|C) is P(B|C) = 9/24 =0.38

How to determine the probability P(B|C)?

The table is given as:

C D Total

A 15 21 36

B 9 25 34

Total 24 46 70

The probability (BIC) is calculated using:

P(B|C) = n(B and C)/n(C)

From the table, we have:

n(B and C) = 9

n(C) = 24

So, the equation becomes

P(B|C) = 9/24

Evaluate

P(B|C) = 0.38

Hence, the value of P(B|C) is P(B|C) = 9/24 =0.38

Answers

The graph that represents the solution of y>x²+2 is given below.

The given inequality is y>x²+2.

We need to identify which graph represents the solution of y>x²+2.

What is an inequality graph?

Inequalities that use ≤ or ≥ symbols are plotted with a solid line to show that the line is included in the region.

For example, this graph shows inequality. This can be seen as there is a dashed line, and the region where the coordinates are less than -1 is shaded.

Graph the inequality by finding the boundary line, and then shading the appropriate area.

Put x=0, 1, 2, 3,....in the inequality and solve for y.

We get y=2, 3, 6, 11,...

The graph that represents the solution of y>x²+2 is given below.

To learn more about the graph of inequality visit:

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Answer:

I did it and got it correct

Step-by-step explanation:

Find the diameter of a circle with a
circumference of 63 ft.

Answers

Answer:

20ft

Step-by-step explanation:

circumference of a circle in terms of diameter has the formular

C = πd

63 = 3.142×d

d= 63/3.143=20.050

diameter= 20ft

Clara visits the aquarium
from her hotel. She walks á mile to the bus stop, takes the bus for
or 1
miles, and walks the rest of the way to the aquarium.
How far did Clara walk after getting off the bus?

Answers

Answer:

The total distance walked to the aquarium is 1/2 miles.

Step-by-step explanation:

What distance did she walk? Distance walked = 2 1/2 - (1/4 + 1 3/4) = 2 1/2 - 2 =1/ 2 miles

Logan has x twenty-dollar bills and 1 fifty-dollar bill. How much money does Logan have? Write your answer as an expression,

Answers

Answer:

Logan has 20x + 50 dollars.

Hope this helps!

Answer:

20x+50

Mark brainliest :)

Ellie missed 76 questions on her multiple choice history final and earned a grade of 62%. How many total questions were on the final exam?

Answers

Answer:

200 questions on the final exam.

Step-by-step explanation:

38% = 76 questions, 100% = 2.63157894737 x 76 = 200

(100/38=2.63157894737 hence this is the answer)

whats the square root of 55

Answers

Answer:

7.4161984871

Step-by-step explanation:

7.4161984871x7.4161984871=55

Answer:

3025

Step-by-step explanation:

A medical sales representative of a certain antibacterial cream ask people who visited their kiosk whether they have tried to use their brand before. What sampling technique was used in this situation?

Cluster Sampling
Volunteer Sampling
Stratified Sampling
Simple Random Sampling

Answers

The answer is Volunteer sampling

The sampling technique that was used in the situation is (d) Simple Random Sampling

How to determine the sampling technique?

From the question, we understand that all people that visited the kiosk were asked the same question.

The people that visited the kiosk have equal chance of being selected.

This type of selection or sampling is a simple random sampling

Hence, the sampling technique that was used in the situation is (d) Simple Random Sampling

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if john has 5 apples in he gives 2 two his friend how many will have in all

Answers

Answer:

5 apples

Step-by-step explanation:

Answer:

3 5-2=3

Step-by-step explanation:

what’s the circumference, to this problem ?

Answers

Answer:

9.42 i think

Step-by-step explanation:

Answer:

The formula to get the circumference of a circle is [tex]C=2*\pi * r[/tex] but in this case we see that a diameter is being used therefore we can get rid of the 2 and the r because that is what the diameter and just replace d into there like this [tex]C=d*\pi[/tex].

We can then input the value and we get that [tex]C=3*\pi[/tex] which then just narrows down to [tex]C=9.425[/tex].

Hope this helps! Let me know if you have any questions

Suppose A< - 1 what must be true about the value of b so that ab< a

Answers

Answer:

b must be positive

Step-by-step explanation:

if a is less than -1

that means to get smaller numbers

b needs to be positive

so that when a is multiplied by b you would have

numbers that are more negative

Answer:

b > 1

Step-by-step explanation:

Given:

a < -1 ab < a

Substituting a = -1 into ab < a

⇒ (-1)b < -1

⇒ -b < -1

⇒ b > 1

If a < -1 then a is negative. If ab < a then ab is also negative.

In order for ab to be negative (when a is negative) b must be positive.

For ab < a then b > 1.

Proof

If b = 0.5 and a = -1.5 then ab = -0.75

As -0.75 > -1.5 then ab > a so this cannot be true.

If b = 1.5 and a = -1.5 then ab = -2.25

As -2.25 < -1.5 then ab < a so this is true.

Therefore b > 1

I NEEED HELP QUICK!!!

Answers

A. Because it has all the numbers organized according to the chart and they are in the correct order :)

The multiplication of two rational numbers results in a _____________

Answers

Answer: rational number

===========================================================

Explanation:

The proof of this is as follows

p, q, r and s are integers

q and s cannot be zero

A = some rational number = p/q

B = some other rational number = r/s

A*B = (p/q)*(r/s) = (p*q)/(r*s)

The result is of some form integer/integer, where the denominator is nonzero. This shows that A*B is rational.

Therefore,

rational*rational = rational

---------------

A few examples:

(1/2)*(3/7) = (1*3)/(2*7) = 3/14(2/5)*(9/8) = (2*9)/(5*8) = 18/40 = 9/20(7/3)*(-1/9) = (7(-1))/(3*9) = -7/27

Side note: any whole number is a rational number. For instance, the number 7 can be thought of as the fraction 7/1 or 14/2 or 21/3 and so on.

In ΔABC, if C is a right angle, what is the measure of x?

Answers

Answer:

x ≈ 72.3°

Step-by-step explanation:

using the cosine ratio in the right triangle

cos x = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{AC}{AB}[/tex] = [tex]\frac{7}{23}[/tex] , then

x = [tex]cos^{-1}[/tex] ( [tex]\frac{7}{23}[/tex] ) ≈ 72.3° ( to the nearest tenth )

The mean of the following data is 509.

{419,450,462,499,520,521,589,612}

What is the mean absolute deviation for the data set?

Enter your answer as a number rounded to the nearest tenth, like this: 42.5

Answers

If the mean value of the data set is 509. Then the mean absolute deviation (MAD) for the data set will be 51.5.

What is the mean absolute deviation?

It is the average distance between each data point and the mean.

The mean of the following data is 509.

{419, 450, 462, 499, 520, 521, 589, 612}

Then the mean absolute deviation (MAD) for the data set will be

[tex]\rm MAD =\dfrac{1}{n}\sum_{i=1}^{n}\left|x_i - \mu \right|[/tex]

We have

μ = 509

n = 8

Then

[tex]\rm MAD =\dfrac{1}{8} \times (|419 - 509| + |450- 509| + ..... + |612 - 509|) \\\\MAD = 51.5[/tex]

More about the mean absolute deviation link is given below.

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Equivalent to 28xy+16x

Answers

Answer:

[tex]4x(7y+4)[/tex]

Consider the equation below. n2 3h2 right arrow. 2nh3 what is the mole ratio of hydrogen to ammonia? 1:1 1:2 3:2 5:4

Answers

The mole ratio of hydrogen to ammonia in the equation N₂ + 3H₂ → 2NH₃ is 3:2

How to find mole ratio?

we will balance the equation to find the mole ratio of the hydrogen to ammonia.

Therefore,

N₂ + 3H₂ → 2NH₃

From the equation, Nitrogen has a coefficient of 1 , Hydrogen have a coefficient of 3 and ammonia have a coefficient of 2.

Therefore, the coefficient of the substance is the number of moles.

Hence, the mole ratio of hydrogen to ammonia is 3:2

learn more on mole ratio here: https://brainly.com/question/8170320

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6. At one point, there were only 2,410
black rhinos left on Earth. With the help
of conservation efforts, the black rhino
population then increased by about 130%.
About how many black rhinos were on
Earth then?

Answers

Answer:

5543 rhinos.

Explanation:

present population: total population(100% + increased percentage)

Based on the information, insert following :

Black Rhinos = 2410(100% +130%) = 2410(230%) = 2410(2.3) = 5543

The heights of two groups of students in different grades are shown in the box-and-whisker plot below.

Which statement correctly compares the two data sets?

A.
The range of group A is less than the range of group B.

B.
The median of group A is less than the median of group B.

C.
The interquartile range of group A and group B is the same.

D.
The first quartile of group A is greater than the first quartile of group B.

Answers

Answer:

Step-by-step explanation:

The first quartile of group A is greater than the first quartile of group B.

Joe opened a bank account with $80. He then withdrew $35 and deposited $115. What is his account balance after these transactions?

$__

Answers

Answer

[tex]160[/tex]

Explanation

Based on the given conditions, formulate: [tex]115+80-35[/tex]

Calculate the sum or difference: [tex]195-35[/tex]

Calculate the sum or difference: [tex]160[/tex]

get the result: [tex]160[/tex]

Answer: [tex]160[/tex]

Answer:

$ 160

Step-by-step explanation:

80 -35 +115 = 160

7. What is the surface area of the triangular prism shown?

Answers

Answer:

1120 yd²

Step-by-step explanation:

Surface area =

(Perimeter of the base × Length of the prism) + (2 × Base Area) =

(S1 + S2+ S3)L + bh

(17 + 15+ 8)25 + 15*8

40*25+120

1000+120 =

1120

cuemath

what’s the value of x

Answers

Answer:

x = 11

Step-by-step explanation:

282/2 = 141

180 - 141 = 39

4x - 5 = 39

4x = 44

x = 11

The company is going to choose three rows in each section to win the hats. There are 46 rows in a
section. If you are sitting in a winning section, what is the probability that you are not sitting in a winning
row?

Answers

Answer:

[tex]\frac{43}{46}[/tex]

Step-by-step explanation:

3 out of 46 rows are going to win, meaning that 43 out of 46 rows are not going to win

Make that a fraction:

[tex]\frac{43}{46}[/tex]

what’s the area and the perimeter and of the triangle?

Answers

Perimeter=22.9 m
Step by step explanation
4.4+8.7=13.1+9.8=22.8

Area=19.14
Step by step explanation
4.4x8.7=38.28 divided by 2 = 19.14

Triangle DEF is simialar to triangle ABC

Answers

Step-by-step explanation:

This is false as you do not what type of triangle that it is

Which expression is equivalent to
(
3
4
7
5
)
3
?

Answers

I would say that the answer would have to be 23

If angle b measures 25°, what is the approximate perimeter of the triangle below? a right triangle is shown. angle a is 90 degrees and angle b is 25 degrees. side a b has a length of 4. 10.3 units 11.8 units 22.1 units 25.2 units

Answers

Answer:

Step-by-step explanation:

I think the answer is 10.48 or 10.3, It was a little difficult because I solved this multiple ways but I do believe 10.48 is more accurate, I apologize however if I am wrong.

Answer:

10.3

Step-by-step explanation:

its right

PLEASE HELP ME

Select the correct answer. Which stem and leaf plot represents the given data set?

Answers

Answer:

i think its x

Step-by-step explanation:

it looks simple yet intimidating

A 3% fee is taken out of an initial amount of $3,460, and then a $100 fee is taken after that, leaving a new amount of

Answers

Answer:

turn 3% into decimal by diving 3 by 100

3/100=0.03

0.03X3460=103.80

3460-103.80=3356.20

3356.20-100=3256.2

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