Johnny rode his bicycle down a hill. It took him 15 seconds to ride from the top of the hill to the bottom of the hill. The equation h = -3t + 45 models his height, h, in feet, above the bottom of the hill as a function of the time, t, in seconds, after he started riding down the hill. Part A: What is the average rate of change in Johnny’s height? Part B: What is the height of the hill? Part C: How long will it take Johnny to travel 1/3 of the distance down the hill?

Answers

Answer 1

From the height function, we get that:

a) The average rate of change is of -3 feet per second.

b) The height of the hill is of 45 feet.

c) It will take Johnny 5 seconds to travel 1/3 of the distance down the hill.

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

The height, after t seconds, is given by:

[tex]h(t) = -3t + 45[/tex]

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

The height of the hill is [tex]h(t)[/tex] when [tex]t = 0[/tex], thus [tex]h(0) = -3(0) + 45 = 45[/tex]. 45 feet, which means that the the answer for option B is 45 feet.

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

Item a:

The initial height is of 45 feet, at [tex]t = 0[/tex] seconds.The final height is of 0 feet, at [tex]t = 15[/tex] seconds.Thus, the average rate of change is given by:

[tex]A = \frac{0 - 45}{15 - 0} = -\frac{45}{15} = -3[/tex]

The average rate of change is of -3 feet per second.

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

Item c:

One-third of the distance of 45 feet is [tex]\frac{1}{3}45 = 15[/tex] feet, thus, we have to find the time at which he is at 30 feet, that is, t for which [tex]h(t) = 30[/tex]

[tex]h(t) = -3t + 45[/tex]

[tex]30 = -3t + 45[/tex]

[tex]3t = 15[/tex]

[tex]t = \frac{15}{3}[/tex]

[tex]t = 5[/tex]

It will take Johnny 5 seconds to travel 1/3 of the distance down the hill.

A similar problem is given at https://brainly.com/question/20732437


Related Questions

Please put details! I need it! Please and thank you!

Answers

Answer:

.

Step-by-step explanation:

A,0.

B. To plot the three points well, you need to look at where the numbers are. Now, lets says its 1 -1 go to where it says -1 and find 1. For -1 1.25 go to the 1 and now split a line into 1/4 making it 1.25. Last but not least go to -2 and cut a line into 3/4.

Hope this helps<3.

Find the area of the figure at the right in square feet. The figure can be separated into a rectangle and a trapezoid. Find the area of each. (image attached)

Answers

Answer:

Shape 1: Trapezoid

A= h(a+b/2)

A=32

Shape 2: rectangle

A=lw

A=96

32+96=128

Let me know if this helps!

Here is the answers have fun

This shape is made of four congruent kites meeting at a point. Calculate the size of Angle K.

Answers

Answer:

k = 115°

Step-by-step explanation:

Hope it helped.

• • •

90 + 2k + 40 = 360

2k = 360-130

2k = 230

k = 115

Angle K = 115

Answered by gauthmath pls make brainliest and comment thanks

Absolute Value – how far or the
[ Select ] Answer | Counter | Number | or distance
a number is from zero.

Answers

Answer:

The last answer or Distance a number is from zero

Step-by-step explanation:

It's this answer because absolute value is just how far a number is from zero for example | -1 | is equal to 1 because -1 is 1 away from zero. Hope this helps :)

Answer:

The last answer or Distance a number is from zero i think i dont know

Step-by-step explanation:

If f(x) = -3x - 2
find f(-2) + 9

Answers

Answer:

f(-2) + 9 is 19

Step-by-step explanation:

[tex]f(x) = - 3x - 2[/tex]

when x is -9:

[tex]f( - 2) = - 3( - 2) - 2 \\ f( - 2) = 10[/tex]

sum up with 9, f(-2)+9:

[tex]f( - 2) + 9 = 10 + 9 \\ = 19[/tex]

It shluld be 19 i think

HURRY IM TIMED!! which inequality is represented by this graph?

Answers

Answer:

x<6 this is the answer because the circle is hallow (not including) and going left (less than)

Answer:

x<6

Step-by-step explanation:

Look at the way the blue arrow is pointing that means less than and the circle is open so it is not equal to the number 6.

I really need help with this

Answers

Answer:

8/5

Step-by-step explanation:

There are 8 jokers combined, and 5 decks, so the mean is 8/5.

8/5 explanation gut above me

Express each of the following fractions as percentages
12/25
solution for class 7

Answers

Like we did in the previous problem, divide and multiply by 100:
12 / 25 = 0.48
As a percentage, we multiply by 10p;
0.48 *100 = 48

[tex]\\ \sf\longmapsto \dfrac{12}{25}\times 100[/tex]

[tex]\\ \sf\longmapsto \dfrac{12\times 100}{25}[/tex]

[tex]\\ \sf\longmapsto \dfrac{1200}{25}[/tex]

[tex]\\ \sf\longmapsto 48\℅[/tex]

I need help please thank you <:

Answers

Answer:

B

Step-by-step explanation:

We have the following

- 3,210,000

- 420,000

- 1,100,000,000

Now we rearrange the numbers as asked from least to greatest.

- 420,000

- 3,210,000

- 1,100,000,000

They answer should be B

Hii! Please helpppp!! This was due like 3 days ago lol

Answers

Fergus has 3 1/4 cups of oats

= 13/4 cups of oats

Oatmeal bars = 2 2/3

= 8/3 cups of oatmeal used

Therefore cups of oats left = 13/4 - 8/3

= 39/12 - 32/12

= 7/12 cups of oats left

She borrowed 1 cup of oats from neighbour

7/12 + 1/1

= 7/12 + 12/12

= 19/12 cups of oats

Blueberry oats muffin = 1 3/4 cups of oats

= 7/4 cups of oats

Total she will have now = 19/12-7/4

= 19/12 - 21/12

= - 2/12

= -1/6

Which means she needs 1/6 cup of oats more

Therefore its option 4

Must click thanks and mark brainliest

Answer:

she needs 1/6 more so the last option! looking at the pic i dont think you need to show the work :)

Step-by-step explanation:

Express each of these percentages as a fraction
158%
solution for class 7

Answers

Answer: 158% = [tex]\frac{158}{100}[/tex] = [tex]\frac{79}{50}[/tex]

Hope it helps :)

79/50!!!!!!!!!!
!! 79/50!!!!!!!!!!
!!

Where do the slope and y-intercept show up in the tables and graphs?

Answers

Answer:

Solution: The general form of the line on a graph is y = mx+c,

where y is the coordinate of the point along the y-axis,

x is the coordinate of the point along the x-axis,

m is the slope of the line or arc tan of the angle the line makes with the x-axis, and

c is the intercept the line makes on the y-axis.

Suppose we want a line having a slope of 45º with the x-axis and passes through point P (4,6), the equation of the line is

y = mx + c

6 = tan 45 * 4 + c, or

6 = 4 + c, or

c = 6–4 = 2.

Positive side of graph?

I know how to find the distance of two coordinates but not three could someone help me on this??

Answers

Find distance between R and S and then between S and T and add them together
Answer:

12 units

Step-by-step explanation:

Step 1. Find the distance between R(-1, 4) and S(5, 4)

Answer: 6

Reason: from -1 to 5, it’s 6 units.

Step 2. Find the distance between S(5, 4) and T(5, -2)

Answer: 6

Reason: from -2 to 4, it’s 6 units

Step 3. Add the distance between R to S and S to T.

Answer: 12 units

Reason: R to S = 6 units. S to T = 6 units.

6 + 6 = 12 units

Given: UR ∥ ST ∠R, ∠T right angles Prove: ∆RSU ≅ ∆TUS
What you will get:
25 pts
Brainliest

Answers

Here

Angle R = Angle T

UR = ST

US = SU

So using RHS conguerence criteria Triangle RSU conguerent to Triangle TUS

Heres your answer
Hope it helps !

The figure shows a line graph and two shaded triangles that are similar:



Which statement about the slope of the line is true?

A. It is fraction 1 over 2 throughout the line.
B. It is 2 throughout the line.
C.The slope from point O to point A is fraction 1 over 2 time the slope of the line from point A to point B.
D. The slope from point O to point A is two times the slope of the line from point A to point B.

Answers

Answer:

Answer is B

just do your work and proof the work and that will give u the right answer

Answer:

it is B

Step-by-step explanation:

it is just B man, trust

Why are the divisibility rules for 2, 3, and 5 very useful for determining prime and composite numbers

1. They are the smallest odd numbers
2. They add up to 10
3. They are prime numbers with nice divisibility rules
4. They multiply to 30
5. They can be multiplied together to make every number

Answers

Answer:

option 3.

Step-by-step explanation:

alright, ima explain each option.

1. "smallest odd numbers" 2 is an even number. that's out of the playing field.

2. "add up to 10" sure, they do add up to 10, but finding prime and composite numbers are all about division and multiplication.

3. this is true. 2, 3, and 5 are all prime numbers, and they have the nice divisibility rules. [ for 2, it has to be even, for 5, it has to end in 0 or 5, and 3 has to have the sum of its digits being divisible by 3. ]

4. they do multiply to 30, but this does not help break the composite numbers down.

5. we cannot make every number with just these. we can not multiply any other whole number to get 7 for per example, because it's a prime number.

sub to gauthmath sub reddit if ya can !

They are prime numbers with nice divisibility rules

Step by step in how to do this plz

Answers

Answer: a. 5^42 and b 9a^6

Step-by-step explanation:

a. (5^3+4)^6

(5^7)^6 = 5^42

The answer to a is 5^42 and the answer to b is 9a^6

If f(x) = 3x+1, then f(a+h) - f(a) =
1. 03 h
2. h
3. 3 h + 2

Answers

Ok I’m really sorry but I’m not sure if your options are right or my answer is…
But I tried my best ! Hope you understand !!
hey bestieeee the answer is 03 h

Make a list of three rates that describe things that you do. For example, you could describe how many classes you attend in a day. For each example, explain why it is a rate.​

Answers

I tried to make this as vague as possible since this is a question about your personal life.

1. sleep to hours in a day, 8:24

2. cans of soda to bottles of water, 1:2

3. meals to snacks, 3:2

Choose a number line to model the following situation:

The temperature outside rose 15° and then dropped 15°. (4 points)

a
A vertical number line is shown with labels at 0 and 15. A red arrow (labeled dropped 15 degrees) begins at 15 and ends at 0. A purple arrow (labeled rose 15 degrees) begins at 0 and ends at 15.

b
A vertical number line is shown with labels at negative 15, 0, and 15. A red arrow (labeled dropped 15 degrees) begins at 0 and ends at negative 15. A purple arrow (labeled rose 15 degrees) begins at 0 and ends at 15.

c
A vertical number line is shown with labels at negative 15, 0, and 15. A red arrow (labeled dropped 15 degrees) begins at 15 and ends at 0. A purple arrow (labeled rose 15 degrees) begins at negative 15 and ends at 0.

d
A vertical number line is shown with labels at 0, negative 15, and negative 30. A red arrow (labeled dropped 15 degrees) begins at 0 and ends at negative 15. A purple arrow (labeled rose 15 degrees) begins at negative 15 and ends at negative 30.

Answers

Answer: A

Step-by-step explanation: It is showing that the temp Atari is raising by 15 ( +15) then dropping by 15 (-15)

Hope this Helps :))

Hxjs sis siss is ais sis sis sisw is

Choose the equation that represents the graph.

Answers

Answer:

y = 1x + 3

Step-by-step explanation:

the slope is 1 and the y intercept is 3

Extra points for this question if you just use me for the points I will red flag you with no regrets/ Please help me.

Answers

Answer:

Step-by-step explanation:

The answer is the 2nd one

Gina wants to solve the following proportion.


a / 5/8 = 3/5 / 2/3


A. explain how to solve the problem.

B. solve the proportion. show your work.

Answers

Step-by-step explanation:

please don't understand the question. will be happy if you take a shot of it.

Thanks

a/5/8 = 3/5 / 2/3

We can take the reciprocal of the denominator, since the denominator itself is a fraction

The above equation can be rephrased as,
(a) / (5/8) = (3/5) / (2/3)

Taking reciprocal

8a / 5 = 3*3 / 5*2

8a / 5 = 9 / 5*2

a = 9 * 5 / 5*2*8

5’s get canceled, 2 and 8 gets multiplied in the denominator.

We will then be left with,

a = 9 / 16


I have also verified it and got the right answer.

A parking lot is 4/5 full. There are currently 80 cars in the parking lot. How many cars need to leave the parking lot to make the lot 1/5 full?

A. 100
B. 60
C. 40
D. 20
E. 10

Answers

Answer:

60

Step-by-step explanation:

60........................................

Please Help Me! I will give brainly!!


The distance from your front door to the mailbox is 18 4/5 meters. The distance from your front door to your basketball hoop is 13 7/10 meters. How much farther from your front door is the mailbox than the basketball hoop?

Answers

Answer:

5 1/10 meters

Step-by-step explanation:

18 4/5 can be changed to 18 8/10 so

18 8/10 - 13 7/10 = 5 1/10 meters

5 1/10 meters ahhhhhhhhhhhh

Write two equivalent ratios using four different types of music in the data table showing. How do you know the ratios are equivalent? ​

Answers

The ratio is equivalent because 1/20 is 5 which means 9/10 is equal
wheres the data table ?

Are the ratios 5:4 and 8:2 equivalent? yes or no

Answers

Answer:

no

Step-by-step explanation:

no its no

Answer:

I believe no

Step-by-step explanation:

I believe it is no but I could be wrong...if I am wrong I am very sorry and hope you can forgive me

Find the surface area of the square pyramid shown below.

Answers

Answer: Area = 160 unit^2

Explanation:

Area of square:

8 x 8 = 64

Area of the 4 triangle:

4(8 x 6/2) = 96

Area of pyramid:

96 + 64 = 160

Answer:

179.38 sq.units

Step-by-step explanation:

answer is in the pic

Evangeline is making snake bags for her class. If she can fill 5/8 of her snack bags with 1 1/3 cups of pretzel, how many cup of pretzels are needed to fill all of the snake bags? Write a multiplication equation and a division equation for the situation, then answer the question.

Answers

Answer:

8/3

Step-by-step explanation:

8/3
ik this bec im in hs

Please multiply 6c(4)

Answers

Answer:

24c

Step-by-step explanation:

6 * c * 4 = 6 * 4 * c = 24c

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

Answer:

24c

Step-by-step explanation:

6c * 4 is 24c. You multiply normally and make it c :)

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