"A toy rocket is shot vertically into the air from a launching pad 7 feet above the ground with an initial velocity of 72 feet per second. The height in feet, of the rocket above the ground at t seconds after launch is given by the function h(t)=-16 t²+72 t+7. How long will it take the rocket to reach its maximum height? What is the maximum height?
The rocket reaches its maximum height at second(s) after launch.
(Simplify your answer.)
The maximum height reached by the object is feet.
(Simplify your answer.)"

"A Toy Rocket Is Shot Vertically Into The Air From A Launching Pad 7 Feet Above The Ground With An Initial

Answers

Answer 1

Answer:

2.25 seconds ; 88 feet

Step-by-step explanation:

the maximum height of the rocket is the vertex of the parabola

x coordinate = -72/2(-16)

-72/-32 = 2.25 seconds

y coordinate = -16(2.25)^2 + 72(2.25) + 7

-81 + 162 + 7

-81 + 169

88 feet


Related Questions

What is the length of Line segment AC?

3 ft
4 ft
18 ft
12 ft

Answers

it’s either 18 or 12ft but i feel like 12ft I may be wrong might want to ask your math teacher

Consider a function f(x) = x^ 2.
A second function h(x) is the result of reflecting f(x) across the x-axis and translating it 3 units in the positive y-direction (upward). Write the equation of h(x).
Please Help will mark brainliest :)

Answers

Answer:

h(x) = - x² + 3

Step-by-step explanation:

Given f(x) reflected in the x- axis , then

h(x) = - x²

Given h(x) then h(x) + c is a vertical translation

• If c > 0 then a shift up of c units

• If c < 0 then a shift down of c units

Here h(x) is shifted 3 units up , then

h(x) = - x² + 3


i gotchu

Write an equation of the line through (-4,0) and (6,-1). Write the equation in standard form.

Answers

standard form for a linear equation means

• all coefficients must be integers, no fractions

• only the constant on the right-hand-side

• all variables on the left-hand-side, sorted

• "x" must not have a negative coefficient

[tex](\stackrel{x_1}{-4}~,~\stackrel{y_1}{0})\qquad (\stackrel{x_2}{6}~,~\stackrel{y_2}{-1}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-1}-\stackrel{y1}{0}}}{\underset{run} {\underset{x_2}{6}-\underset{x_1}{(-4)}}} \implies \cfrac{-1 -0}{6 +4} \implies \cfrac{ -1 }{ 10 } \implies - \cfrac{1 }{ 10}[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{0}=\stackrel{m}{- \cfrac{1 }{ 10}}(x-\stackrel{x_1}{(-4)}) \implies y -0 = - \cfrac{1 }{ 10} ( x +4) \\\\\\ y=- \cfrac{1 }{ 10}(x+4)\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{10}}{10(y)=10\left( - \cfrac{1 }{ 10} ( x +4) \right)}\implies 10y=-(x+4) \\\\\\ 10y=-x-4\implies {\Large \begin{array}{llll} x+10y=-4 \end{array}}[/tex]

Please answer for brainly and 5 star thanks

Answers

Using the graph given, the rate of change from hour 4 to hour 7 is: -20.

How to Find the Rate of Change of a Graph?

The rate of change of a relationship that is represented on a graph is determined using the formula below:

Rate of change = f(b) - f(a) / b - a.

Given the graph above, we are asked to find the rate of change between the interval x = 4 to x = 7:

a = 4

f(a) = f(4) = 120

b = 7

f(b) = f(7) = 60

Plug in the values:

Rate of change = f(b) - f(a) / b - a = (60 - 120) / (7 - 4)

= -60/3

Rate of change = -20.

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Does the volume of a cone increase more when you double the height of the original or when you double its radius? Explain why.

Answers

The volume of a cone increase more when you double the height of the original or when you double its radius. This is true.

What is a cone?

A cone is a shape formed by connecting a common point, known as the apex or vertex, to all the points of a circular base with a set of line segments. The height of the cone is the distance from the vertex to the base.

A cone always contains a right angle. To solve for the volume of a cone, we need to get the radius of the cone and its height. radius is the line from the center of the circle of the cone going to the edge of the circle. height is the measurement of the cone from its pointy tip going downward.

The volume of a cone is 1/3πr²h, so if you double the radius the volume would quadruple. So, when the height is doubled, the volume is also doubled.

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My brain has gone blank and I forgot how to do these

Answers

Answer:

Step-by-step explanation:

x= 80 degrees

I think that's the answer

113-33= 80

Answer:

133+33+x=180

X=180-133-33

X=14

Graph the solution to this inequality on the number line.

35z>34

Answers

Answer:

see the attached image.

Step-by-step explanation:

First, divide by 35 on both sides to isolate 1 multiple of z.

[tex]35z > 34\\\overline{\ 35\ } \ \ \ \: \overline{35}[/tex]

[tex]z > \dfrac{34}{35}[/tex]

See the attached image for a graph.

The values of z stop at an open circle at the point 34/35.

3 + 5 to the power of 2 - 6 • 4

Answers

Answer: The correct answer is 4

Step-by-step explanation:

You welcome have a great day

What is the perimeter of this triangle?

Answers

The triangle has a perimeter of 48 units.

How to determine the perimeter of a triangle

Triangles are figures with three sides, the perimeter is the sum of the lengths of the three sides. The length of each side is determined by Pythagorean theorem:

l = √(x² + y²)

Where:

l - Side lengthx - Horizontal length of the side.y - Vertical length of the side.

First, determine the horizontal and vertical length of each side:

Side 1

x = 18, y = 0

Sides 2, 3

x = 9, y = 12

Second, determine the side lengths:

Side 1:

l = 18

Sides 2, 3

l = √(9² + 12²)

l = 15

Third, calculate the perimeter of the triangle:

p = 18 + 15 + 15

p = 48

The perimeter of the triangle is equal to 48 units.

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Write three and seven eighths as an improper fraction and as a mixed number.
A 17/8, 3 7/8
B 31/8, 3 7/8
C 31/8, 7 3/8
D 59/8, 7 3/8

Answers

The answer is B because if u multiply 8•3 you get 24 + 7

Solve for m.

m+15<−123
Responses

m>−11315
m is greater than negative 1 and 13 over 15

m>−1715
m is greater than negative 1 and 7 over 15

m<−1715
m is less than negative 1 and 7 over 15

m<−11315
help

Answers

The solution to the value of m in the inequality m + 1/5 < - 1 2/3 is "m is less than negative 1 and 13 over 15".

The correct answer option is option D

How to solve inequality?

Inequality is a statement that is of two quantities I'm which one is specifically less than (or greater than) another. The symbols of inequality are;

Greater than >Less than <Equal to =Greater than or equal toLess than or equal to

m + 1/5 < - 1 2/3

substract 1/5 from both sides

m < -5/3 - 1/5

m < (-25-3) / 15

m < -28/15

Therefore, from the inequality m + 1/5 < - 1 2/3, m is less than negative 1 and 13 over 15.

Complete question:

m + 1/5 < -1 2/3

Responses

A. m > −1 13/15

m is greater than negative 1 and 13 over 15

B. m > −1 7/15

m is greater than negative 1 and 7 over 15

C. m < −1 7/15

m is less than negative 1 and 7 over 15

D. m < −1 13/15

m is less than negative 1 and 7 over 15

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find the greatest perfect square that is a factor of 495

Answers

Answer:

1, 3, 5, 9, 11, 15, 33, 45, 55, 99, 165, and 495 are the factors of 495. Additionally, the highest perfect square on this list is 9, and 3 is 9's square root. So, A is equal to 3.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

The factors of 495 are:

1, 3, 5, 9, 11, 15, 33, 45, 55, 99, 165, and 495.

The greatest perfect square that is a factor of 495 is 9.

What is an expression?

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

495

The factors of 495 are:

1, 3, 5, 9, 11, 15, 33, 45, 55, 99, 165, and 495.

Now,

The perfect squares from the factors of 495 are 1 and 9.

9 is the greatest perfect square of 495.

Thus,

The greatest perfect square that is a factor of 495 is 9.

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Kylie makes $8.50 an hour at a local restaurant. Her paycheck shows she worked 20.88 hours last week. how much money did Kylie make?

Answers

If Kylie's hourly wage at a nearby restaurant is $8.50. She worked 20.88 hours last week, according to her paycheck. Kylie's salary is $177.48.

What is an arithmetic operation?

It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has basic four operators that are +, -, ×, and ÷.

It is given that, Kylie makes $8.50 an hour at a local restaurant. Her paycheck shows she worked 20.88 hours last week.

We have to find the money did Kylie make,

We can utilize multiplication for a number of common tasks, such as figuring out how much it will cost to buy several identical things, calculating sales tax, and figuring out area and other geometric measurements.

Suppose the money did Kylie make is x,

x = 8.50 ×  20.88

x=$ 177.48

Thus, if Kylie's hourly wage at a nearby restaurant is $8.50. She worked 20.88 hours last week, according to her paycheck. Kylie's salary is $177.48.

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I need help with this ! Anything helps.

Answers

No.5
X=85

No.6
X=80

No.7
X=10

No.8
X=6

No.9
X= -9

No.10
X=29

No.11
X= -6

No.12
X= -7

Hope this helps

The temperature T°C of a cup a tea t minutes after being poured is modelled by the exponential decay function:
T=18+68e^-t/8, t>/= 0

a) What is the initial temperature of the tea the moment it was poured?

b) When will the temperature of the tea reach 35°C?

c) Explain why the tea will never reach an ambient temperature of 15°C.

Answers

Using the exponential function T = 18 + 68e^(-t/8), the initial temperature is 86°C, the time the temperature will reach 35°C is 11.1 minutes

Exponential Function

An exponential function is a mathematical function in the form f (x) = ax, where “x” is a variable and “a” is a constant which is called the base of the function and it should be greater than 0.

An exponential function is defined by the formula f(x) = aˣ, where the input variable x occurs as an exponent. The exponential curve depends on the exponential function and it depends on the value of the x.

The exponential function is an important mathematical function which is of the form f(x) = aˣ

In the question given, the exponential function given shows an exponential decay

T = 18 + 68e^(-t/8)

a) The initial temperature when the tea was poured would be (t = 0)

T = 18 + 68e^(-0/8)

T = 16 + 68 = 86°C

b) The temperature of the tea at 35°C

35 = 18 + 68e^(-t / 8)

T = 11.1

c) The reason why the the tea will never reach 15°C is because there's no solution for the expression.

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The sales tax rate on a new vehicke is 6.5 percent. If the vehicle is priced at 12,000, how much will you be charged for sales tax?

Answers

If sales tax rate on a new vehicle is 6.5 percent. If the vehicle is priced at 12,000, then 780 will be charged for sales tax

What is Percentage?

percentage, a relative value indicating hundredth parts of any quantity.

Given,

The sales tax rate on a new vehicle is 6.5 percent.

The price of the vehicle is 12000

We need to find the how much will you be charged for sales tax

Let us convert 6.5 percent to the decimal value by dividing it with 100

6.5/100×12000

0.065×12000

780

Hence, 780 will be charged  for sales tax.

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Point P was rotated about the origin (0, 0) by - 15°.

Answers

Answer:

the answer is d.

Step-by-step explanation:

Jordan went swimming for 7/8 hour in the morning and 5/6 hour in the afternoon. What is the best estimate for the total time Jordan went swimming?

Answers

The total time for Jordan went swimming will be;

⇒ 41/24

What is Addition?

The process of combining two or more numbers is called the Addition.

Given that;

Jordan went swimming for 7/8 hour in the morning and 5/6 hour in the afternoon.

Now,

Since, Jordan went swimming for 7/8 hour in the morning and 5/6 hour in the afternoon.

Hence, The total time for Jordan went swimming will be;

⇒  7/8 + 5/6

⇒ (21 + 20) / 24

⇒ 41/24

Thus, The total time for Jordan went swimming will be;

⇒ 41/24

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There is a store that is having a 25% sale off of everything.Lin is buying a jacket that costs $40. What is the cost of the jacket after the discount?

Answers

Answer:

30

Step-by-step explanation:

Given m || n, find the value of x.

Answers

Answer:

x=11°

Step-by-step explanation:

Because line t is 180°, (9x-5)°+(6x+20)°=180°

Simplify:

(9x-5)°+(6x+20)°=180°

9x-5+6x+20=180

15x-5+20=180

15x+15=180

15x=165

x=11

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(04.06A) Which of the following does not describe slope?

Answers

The option that doesn't describe slope is A. A line joining points.

What is a slope?

Slope is determined by dividing the vertical change by the horizontal change between two distinct points on a line.

It is defined as the difference in y coordinate divided by the difference in x coordinate between two distinct points on the line.

A line's slope is a number that describes both its direction and its steepness. Slope is a measure of change or a constant rate of change between two points.

As a result, from the options given, slope is not a line segment connecting two points, but rather the change in a line segment between two points.

It should be noted that the correct option is A.

The complete question is given below.

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Complete question

Which of the following does not describe slope?

A. A line joining points.

B. A constant rate of change

C. A proportional relationship

D. A measure of change

Use the distributive property to simplify: 5(4x - 7)
Group of answer choices

20x-35

5x-5

35-20x

4x-35

Answers

Answer:

the answer is 20x -35

Step-by-step explanation:

5 x 4x = 20x

5 x -7 = -35

The answer options for exercise 5(4x-7) are:

A) 20x-35

B) 5x-5

C) 35-20x

D) 4x-35

To solve this exercise 5(4x-7), we organize the expression with the distributive law.

The distributive law is: a(b+c)=ab+ac.

5(4x - 7) = 5 × 4x - 5 × 720x - 35

Therefore, the correct option is alternative "A".

floor of a classroom is 38 feet in length and 34 feet in width. A scale drawing of the floor has a length of 19 inches.

Answers

Answer:

38 i think i hope this helps

A clothing store buys a sweater for $15 before marking it up by 1/5 before selling it for a profit. What is the markup on the sweater?

Answers

The markup amount on the sweater of cost price $15 is $3.

What is a fraction?

A fraction is written in the form of p/q, where q ≠ 0.

Fractions are of two types they are proper fractions in which the numerator is smaller than the denominator and improper fractions where the numerator is greater than the denominator.

Given, A clothing store buys a sweater for $15 before marking it up by 1/5.

So, the markup amount can be obtained if we multiply the cost price by the fraction of mark up which is,

= 15×(1/5).

= 3.

The markup price is $3.

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find the paramater 1/2x-7 x

Answers

Answer:

-13/2x

Step-by-step explanation:

1/2x +(−7x)

Combine Like Terms:

12x +(−7x)

(1/2x +−7x)

−13/2x

3) A
a
Square with an area of 25m² and
perimeter of 20 is reflected across line
L, then translated 20m right, and then
rotated 20 degrees clockwise, what is
area and perimeter after these transformations?
the

Answers

Answer:

Area =25m²

Perimeter = 20m

Step-by-step explanation:

None of the transformations described change the size or shape of the original object, only position and orientation are changed

What 3 parts are needed to show a number in scientific notation?

1. A whole number and a decimal, a multiplication symbol, a power of 10

2. An exponent to the 2nd power, a multiplication symbol, a whole number from 1 to 10

3. A decimal or whole number, a multiplication symbol, a power of 10

4. A decimal between 1 and 10, a multiplication symbol, a power of 10​

Answers

2 I think…. Numbers in scientific notation are made up of three parts: coefficient, base and exponent.

Since 2009 the number of smartphones shipped from manufacturers to stores around the world has increased exponentially. The growth from 2009 through 2015 can be modeled using the function G (t) = 174 . 1.67^t where t is the number of years singe 2009 and G (t) is measured in millions of smartphones.

Use this information and your knowledge of exponential and logistic growth to explore the mathematical concepts in the questions below.

Answers

The y-intercept indicates that 174 million smartphones were shipped to stores in 2009. This implies that after two years, in 2011, smartphone manufacturers shipped 500 million smartphones to stores worldwide.

Since 2009 the number of smartphones shipped from manufacturers to stores around the world has increased exponentially.

What is the exponential function?

The mathematical expression f(x)=exp or ex denotes the exponential function. The word, unless specifically stated differently, normally refers to the positive-valued function of a real variable, though it can be extended to the complex numbers or adapted to other mathematical objects like matrices or Lie algebras.

The growth from 2009 through 2015 can be modeled using the function G(t) = 174 * 1.67^t where t is the number of years since 2009 and G(t) is measured in millions of smartphones.

The required graph of the exponential function G(t) has been attached below

Now, finding the y-intercept

G(t) = 174· 1.67^t...(i)

Substitute the value of t = 0 in the above function,

G(t) = 174* 1.67⁰

G(t) = 174(1)

G(t) = 174

The meaning of the y-intercept is that 174 million smartphones are being shipped to stores in years 2009.

Substitute the value of G(t) =500 in the exponential function(i),

500 = 174 * 1.67^t

500/174 = 1.67^t

2.8735 = 1.67^t

In(2.8735 ) = t In (1.67)

t = In (2.8735 ) / In (1.67

t = 2.05827 ≈ 2

Hence, This means after 2 years i.e. in 2011, smartphone manufacturers were shipping 500 million smartphones to stores around the world.

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6,370 x 30 find the products
How do I show my thinking or ideas
Example
637•3 6370•30
=1911 =(6370•3)• (10•10)

Answers

Answer:

Product: 191,100

Step-by-step explanation:

Show your work:

(It should look something like this)

6370                                                                                                                              x   30

First: 0 x 0 = 0 (so you put):

6370                                                                                                                              x   30

      0

(everything else times 0 just equals 0 so you'd get this):

6370                                                                                                                              x   30

0000

Next: 3 x 0 = (so you put):

6370                                                                                                                              x   30

0000

    0

Next: 3 x 7 = 21 (so you put):

6370                                                                                                                              x   30

0000

  10

(carry the 2)

Next: 3 x 3 = 9 (so you put):

 2

6370                                                                                                                              x   30

0000

 1 10

(add the number you carried to 9: giving you 11 so you also have to carry a 1 again)

(the first number: 0 of 110 goes under the third 0 of 0000)

(the spacing is just to make sure that the placement is correct: the first 1: of 110 goes under the first 0 of 0000)

Next: 3 x 6 = 18 (so you put):

1 2

6370                                                                                                                              x   30

  0000

191 10

(you add the 1 that you carried to 18 to give you 19)

(again: I only moved the zeros over so that the placement is correct)

Next: Now you add(this is why the placement of the numbers is important):

1 2

6370                                                                                                                              x   30

     0000

+ 191 10

  191,100

(you will put imaginary zeros over 19 because you know that there is already nothing there. You will also add an imaginary zero under the last zero that is hanging there because you know there is nothing there either.)

(Hope this helps! I know its really confusing, if you have any further questions or if the way I explained confused you please tell me or ask me those questions.) :)

Christopher has $780 to spend at a bicycle store for some new gear and biking outfits. Assume all prices listed include tax.
He buys a new bicycle for $446.45.
He buys 2 bicycle reflectors for $16.82 each and a pair of bike gloves for $24.60.
He plans to spend some or all of the money he has left to buy new biking outfits for $43.70 each.

Write and solve an inequality which can be used to determine oo, the number of outfits Christopher can purchase while staying within his budget.

Answers

The required inequality for number of outfit is n ≤  6.3  and Christopher can purchase 6 biking outfits.

What is inequality?

Inequality shows relation between two expression which are not equal to each others.

Given that,

Maximum amount that Christopher can spend = $780.

The price of new bicycle = $446.45.

Also, Christopher buys 2 bicycle reflectors for $16.82 each.

And a pair of bike gloves for $24.60.

Let Christopher buys n outfits.

The price of 1 outfit is $43.70.

The price of n outfits = $43.70n

Since,  Price of 1 bicycle reflectors = $16.82

Price of 2 reflectors = $16.82 x 2 = $33.64

The inequality to determine the number of outfits can be written as,

43.70n + 446.45 + 24.60 + 33.64 ≤ 780.

43.70n + 504.69 ≤ 780.

43.70n ≤ 780 - 504.69

43.70n  ≤ 275.31

n ≤  6.3

The maximum number of outfit Christopher can purchase is 6.

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which form of government form takes on military rule? Rank the compounds below from lowest to highest viscosity based on their structures. (Hint: hydrogen bonds formed between molecules with N-H groups are weaker than those formed between molecules with O-H groups.)1-propanol, CH3CH2CH2OHpropane, CH3CH2CH3propanal, CH3CH2CH=O1-propanamine, CH3CH2CH2NH2Please help me out! I've been stuck on this problem for ages! an article reported that, in a study of a particular wafer inspection process, 356 dies were examined by an inspection probe and 201 of these passed the probe. assuming a stable process, calculate a 95% (two-sided) confidence interval for the proportion of all dies that pass the probe. (round your answers to three decimal places.) , in the past decade, there have been many volcanic eruptions. after an eruption, the lava flow leaves behind only bare rock, providing a surface for primary succession. which statement describes an important function provided by the first organisms to colonize the area that facilitates colonization by other organisms in later stages of succession? Pythagoras theorem How do i find the n calculate the braking distance traveled as the speed of the car is reduced from 21 m/s to 0m/s Lola puts $150 into a bank account The account pays 4% per annum simple interest work out the total amount of mo Laurence was just asked to be the main speaker at a data science conference in LasVegas. He'll deliver a 30-minute presentation for the crowd of 500 data scientists.What would you call his speech? one morning, ms. simon drove directly from her home to her workplace in 242424 minutes. what was her average speed, in miles per hour, during her drive that morning? If the inflation rate in an economy is 5 percent and the income earned by workers increases by 5 percent, then _____.nominal income increases by 5 percent and real income is unchangednominal income increases and real income declinesboth nominal income and real income increase by 5 percentboth nominal income and real income decrease by 5 percentnominal income declines and real income increases johnny was quick to criticize bert for being dependent and lazy, but johnnie actually worried that he (himself) is lazy. what refers to the computer chip performance per dollar doubles every 18 months? multiple choice question. which of the following is a true statement? multiple choice most economists believe that the recent rise in the average rate of productivity growth implies an end to the business cycle. mainstream economists disagree as to whether the rate of productivity growth was higher between 1995 and 2010 or between 1973 and 1995. economists who support economic growth say that it is the most practical route to the higher standards of living that the vast majority of people desire. most economists believe that increases in real gdp actually produce decreases in overall economic well-being because of spillover costs. Read the question and type your response in the box provided. Your response will be savedautomatically.What is the central idea of the two sources? Use evidence and reasoning to support your claim. Why did it take 4 billion years of Earth history for multicellular organisms to evolve and diversify to the point of the Ediacara biota? What is the purpose of the ISOO CUI Registry? The colorless, odorless and poisonous gas from the exhaust is called:A) Carbon PeroxideB) Carbon DioxideC) Carbon MonoxideD) Carbon Hydroxide the term for common elements of everyday life? 1. the term for common elements of everyday life? secular mundane philosophy banal Which powers are not specifically detailed in the u. S. Constitution but inferred as necessary to achieve the objectives of government?. what were results of the federal government deregulating the airline industry in 1978, known as the airline deregulation act? (select all that apply.)