Janell is standing on a set of bleacher and throws a ball in the air at an initial velocity of 35 ft/s. The height of the ball, h, at t seconds is modeled by the equation h=-16t^2+35t+6. How many seconds will it take the ball to reach the ground?

Answers

Answer 1

The time taken by the ball to reach the ground is 0.067 seconds

Given,

The initial velocity of the ball (speed) = 35 feet/second

The height of the ball (distance), h = -16t² + 35t + 6

We have to find the time, (t in seconds) taken by the ball to reach the ground.

Speed = distance/time

So, Time = distance/speed

Here,

Time = (-16t² + 35t + 6) / 35

We have to solve the equation first.

-16t² + 35t + 6 = 0 is in quadratic form. So, we can solve this by using quadratic formula.

Quadratic formula = [tex]\frac{-b(+-)\sqrt{b^{2}-4ac } }{2a}[/tex]

Here,

a = -16, b = 35, c = 6

Now,

[tex]\frac{-b(+-)\sqrt{b^{2}-4ac } }{2a}[/tex]

= [tex]\frac{-35(+-)\sqrt{35^{2}-4(-16)(6) } }{2(-16)}[/tex]

= [tex]\frac{-35(+-)\sqrt{1225 +384} }{-32}[/tex]

= (-35±√1609) / -32

= (-35±40.11) / -32

Now,

Solve for:

(-35 + 40.11) / -32 = 5.11/-32 = -0.15

Solve for

(-35 - 40.11) / -32 = -75.11 / -32 = 2.35

Lets take the height as 2.35 feet.

Now,

Time = distance/speed

Time = 2.35/35 = 0.067

Therefore, the time taken by the ball to reach the ground is 0.067 seconds.

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Related Questions

5÷6?what is it long division picture please

Answers

The solution is ; 5/6 = 0.833... (recurring decimal)

seda 100 soruluk bir sınavda 36 yanlış yapmıştır üç yanlış bir doğruyu götürerek net sayısı hesaplandığına göre seda en çok kaç net yamıştır

Answers

Answer:

Step-by-step explanation:

36÷3=1236+12=48100-48=52EN İYİ SEÇERSEN SEVİNİRİM BAŞARILAR DİLERİM

Dominique paid $15.50 to join an online music service. She purchases 10 songs each month at a cost of $0.99 per song. Dominique thinks that after 8 months, she will have spent around $75.00 total. Is Dominique's estimate reasonable?

Answers

If she thinks that after 8 months, she will have spent around $75.00 total.  Dominique's estimate is not reasonable?

Determining whether the estimated amount is reasonable

We have to make use of the given data to find whether amount of $75 which she estimated that she will spent after 8 months is reasonable

Total cost:

Total cost =$15.50  + 10 × $0.99 × 8

Total cost = $15.50 + 9.9 × 8

Total cost = $15.50 +$79.2

Total cost = $94.7

Hence,

$94.70 ≥ $75.00

Based on the above calculation the amount she estimated is not a reasonable amount because the total cost is greater that the estimated amount.

Therefore we can conclude that the estimate is unreasonable.

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The estimate of the Dominique's is not reasonable.

Given that,
Dominique paid $15.50 to join an online music service. She purchases 10 songs each month at a cost of $0.99 per song. Dominique thinks that after 8 months, she will have spent around $75.00 total. Is Dominique's estimate reasonably is to be justified.

Here,
According to the question,
The total cost of the song for 8 months = 8 (0.99 x 10)
                                                            = $ 79.2
Total cost  = 15.50 + 79.2 = $94.7
Since the total cost exceeds Dominique's estimate so her estimate is not reasonable.

Thus, the estimate of the Dominique's is not reasonable.

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I REALLY NEED HELP PLEASE THIS WORK IS FOR MONDAY.can y’all please help me:(

Answers

hey we can’t help you due to the fact that you didn’t attach any problem or image

Point (2,11.9), (4,13) rise over run so what's the answer ?

Answers

Answer:

0.55

Step-by-step explanation:

( x1, y1 ) = ( 2, 11.9 )

Here,

x1 = 2

y1 = 11.9

( x2. y2 ) = ( 4, 13 )

Here,

x2 = 4

y2 = 13

Formula : -

Rise over run = ( y2 - y1 )/( x2 - x1 )

Rise over run = ( 13 - 11.9 )/( 4 - 2 )

                      = 1.1/2

Rise over run = 0.55

The diagram shows an intersection of roads. Identify all supplementary, complementary, and vertical angles.

Fast please!!!

Answers

Answer:

Supplementary: 2,3

Complementary: 1,4,5

Vertical Angles (VA): 1 is equivalent to 4

Step-by-step explanation:

Supplementary angles are angles that equal up to 180 degrees.

Complementary angles are angles that are 90 degrees.

VA (Vertical Angles) are angles that are basically across from other (take a look at 1 and 4) AND NO, 2,3 or 5 would be considered as Vertical angles as they do not Aline.

Evaluate. Write your answer as a whole number or as a simplified fraction.

Answers

The answer is 121.

Solve by first finding 11 to the 6th power. A simpler way to look at this is just multiplying 11 by itself 6 times. After you do that, multiply 11 by itself 4 times, since the denominator is 11 to the 4th power. Then divide the products.

A new minivan costs $24,897. About how much would 4 minivans cost?

Answers

Answer: about $100,000.

Step-by-step explanation: i gave an estimate because your answer calls for an estimate, not an exact answer. $100,000 is correct because 24,897*4 = 99,588.

99,588 because you would just multiply 24,897 times 4, then if u have to add tax you would multiply that by 99,588, tax is different in every state so you have to look up what ur tax rate is. Then once u have the tax add that to 99,588

I don't know how to simplify this A=[tex]\frac{2\sqrt{x}-9}{x-5\sqrt{x}+6\:}-\frac{\sqrt{x}+3}{\sqrt{x}-2}-\frac{2\sqrt{x}+1}{3-\sqrt{x}}[/tex]

Answers

The most appropriate choice for rationalization will be given by

What is rationalization?

When a surd is present in the denominator of a fraction, the surd has to be removed form the denominator. The process by which surds in the denominator of a fraction can be eliminated is called rationalization.

Here,

let [tex]\sqrt{x}[/tex] = a

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

[tex]\frac{2a-9}{a^2 -5a + 6} - \frac{a + 3}{a-2} - \frac{2a+1}{3-a}[/tex]

[tex]\frac{2a-9}{a^2 -2a-3a + 6} - \frac{a + 3}{a-2} - \frac{2a+1}{3-a}[/tex]

[tex]\frac{2a-9}{a(a -2)-3(a -2)} - \frac{a + 3}{a-2} + \frac{2a+1}{a - 3}[/tex]

[tex]\frac{2a-9}{(a-2)(a-3)} - \frac{a + 3}{a-2} + \frac{2a+1}{a-3}[/tex]

[tex]\frac{2a-9 - ((a + 3)(a-3)) + (2a+1)(a-2)}{(a-2)(a-3)}[/tex]

[tex]\frac{2a-9-a^2+9+2a^2-4a+a-2}{(a-2)(a-3)}[/tex]

[tex]\frac{2a-a^2+2a^2-3a-2}{(a-2)(a-3)}[/tex]

[tex]\frac{a^2-a-2}{(a-2)(a-3)}[/tex]

[tex]\frac{a^2-2a+a-2}{(a-2)(a-3)}[/tex]

[tex]\frac{a(a-2)+1(a-2)}{(a-2)(a-3)}[/tex]

[tex]\frac{(a-2)(a+1)}{(a-2)(a-3)}[/tex]

[tex]\frac{\sqrt{x} +1}{\sqrt{x} -3}[/tex]

[tex]\frac{(\sqrt{x} +1)(\sqrt{x}+3) }{(\sqrt{x} -3)(\sqrt{x} +3)}[/tex]

[tex]\frac{x + 3\sqrt{x} + \sqrt{x} +3 }{x -9}[/tex]

[tex]\frac{x + 4\sqrt{x} +3 }{x -9}[/tex]

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¿Qué es una variable?

Answers

algunos animales adoptan formas y colores

solve for x
3/4=x-4/6
simply as much as possible

Answers

The value of x is 17/12.

Given equation:-

3/4 = x - 4/6

We have to find the value of x from the given equation.

Rearranging the terms to find the solution, we can write,

x = 3/4 + 4/6

Least Common Multiple (LCM) of 4 and 6 = 12

Hence, we can write,

x = (3*3) + (2*4)/12

x = (9 + 8)/12

x = 17/12

Least Common Multiple (LCM)

In arithmetic, Least Common Multiple (LCM) of two or more numbers is the least positive number that can be divided by both the numbers, without leaving the remainder. It is also known as Lowest Common Multiple (LCM), Least Common Denominator, and Smallest Common Multiple.

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INEED HELP NOW PLS HELP IVE GIVEN EXSAMPlES AND I NEED SNSWeRS With work to it

Answers

1) 20 percent of 60 is 12

2) 25 percent of 24 is 6

3) 4 percent of 600 is 24

4) 88 is 110 percent of 80

5) 18 is 20 percent of 90

What is percentage ?

To calculate the proportion of value to the original value, the percentage concept is employed. For calculating a company's profit or loss percentage , percentages are frequently employed in business. Additionally, it's a common way for universities and schools to display the grades that pupils have earned. An estimation of the pupils' grades can be made using a percentage calculation. A ratio of any value to the total value multiplied by 100 is how percentages are typically defined. The percentage is shown as % in symbols.

1) [tex]\frac{20}{100}[/tex]×x=12

x=[tex]\frac{1200}{20}[/tex]

x = 60

2) x ×[tex]\frac{24}{100}[/tex] = 6

x=25%

3)[tex]\frac{4}{100}[/tex]×600 = 24

4) [tex]\frac{110}{100}[/tex]×x = 88

x =[tex]\frac{8800}{110}[/tex]

x= 80

5) [tex]\frac{x}{100}[/tex]×90 = 18

x = 20

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What is the diameter of a circle with a circumference of 62.83185? a. 5 units c. 20 units b. 10 units d. 25 units

Answers

Answer:

i believe it is 20

Step-by-step explanation:

to find the diameter you just deveide the circumference by pi thats it and i got 20.0101433

so i believe its 20

hope this helped :)

A supermarket sells 500g pots of yoghourt. There is a special offer on yoghourt:
Buy 2 pots and get a 3rd one free!
A week later, the price of a single pot of yoghourt is still the same, but the offer changes to:
Buy 1 pot and get a second one half price!
Is the second offer better than the first? Show working to justify your answer.​

Answers

The first offer is better from the perspective of a customer but the second one is better from the perspective of a seller.

Here we have different 2 cases, and to find the answer we have to follow a few steps.

First of all, we should simplify these two cases and will try to give them a proper equation format.

Let's assume the price of each yogurt is $x.

Therefore the total price of 2 pots is (2× x) = $2x.

But the condition is if we buy 2 pots, get the 3rd one for free. So, we can purchase a total of 3 pots at the same cost.

∵ If 3 pots cost $2x, then the average cost for each pot is 2x/3 =$0.67x

( average value of each unit = Total value / total unit )

In the second case, if we buy 1 pot we can get the second one at half price.

Therefore, the total price of two pots is, ( x + 0.5x ) = $1.50x

∵ If 2 pots cost $1.50x, then the average cost for each pot is 1.50x/2 = $0.75x

( average value of each unit = Total value / total unit ).

The price of yogurt per pot in the first case <  The price of yogurt per pot in the second case.

As $0.67 <  $0.75.

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the difference of the squares of two positive integers is 325 and their difference is 3. what are the numbers​

Answers

Answer:

figure it out best of luck tho.

Suppose we are given the following.
Line 1 passes through (0, 4) and (-3, 8).
Line 2 passes through (-4,-2) and (4, 4).
Line 3 passes through (4, 1) and (8, 4).
(a) Find the slope of each line.
Slope of Line 1 = 0
0
Slope of Line 2 =
Slope of Line 3 =
0

(b) For each pair of lines, determine whether they are parallel, perpendicular, or neither.

Answers

Answer:

slope: -4/3, perpendicular to lines 2 and 3slope: 3/4, parallel to line 3, perpendicular to line 1slope: 3/4, parallel to line 2, perpendicular to line 1

Step-by-step explanation:

Given pairs of points that define three lines, you want to know their slopes, and whether line pairs are parallel or perpendicular.

The lines are defined by point pairs ...

(0, 4) and (-3, 8)(-4, -2) and (4, 4)(4, 1) and (8, 4)

Slope

The slope of a line is given from a pair of points by the formula ...

  m = (y2 -y1)/(x2 -x1)

Lines with the same slope are parallel.

Lines with opposite reciprocal slope are perpendicular.

Application

Line 1 slope = (8 -4)/(-3 -0) = 4/-3 = -4/3

Line 2 slope = (4 -(-2))/(4 -(-4)) = 6/8 = 3/4

Line 3 slope = (4 -1)/(8 -4) = 3/4

The slopes of the lines are ...

-4/33/43/4

Relation of line pairs

Lines 1 and 2 have slopes that are opposite reciprocals (-4/3 and 3/4), so are perpendicular.

Lines 1 and 3 have slopes that are opposite reciprocals (-4/3 and 3/4), so are perpendicular.

Lines 2 and 3 have identical slopes (3/4 and 3/4), so are parallel.

1. Jasmine is 5 years younger than twice her sister's age. If Jasmine is 39 years old, how old is her sister?

Answers

Let J be Jasmine age and S the sister's age. Then, we have

[tex]2S-5=J[/tex]

this equality means Jasmine is 5 years younger than twice her sister's age. Now, we also know that J=39 years then by substituying this value into the last equality, we have

[tex]2S-5=39[/tex]

and now, we can solve this equation for S. First, we must move -5 to the right hand side as 5. It reads

[tex]\begin{gathered} 2S=39+5 \\ 2S=44 \end{gathered}[/tex]

and finally, we obtain

[tex]\begin{gathered} S=\frac{44}{2} \\ S=22 \end{gathered}[/tex]

therefore, Jasmine's sister has 22 years old.

Find the value of x *
80°
Your answer
20x

Answers

Answer:

x = 4

Step-by-step explanation:

80 is equal to 20x because they are alt ext angles

so

80 = 20x

divide to both sides

4 = x

that is your answer

The probability that your raffle ticket is not a winner is 0.9998. What is probability that your raffle ticket is a winner?

Answers

The probability of raffle ticket is a winner is 0.0002.

What is probability?

The ratio of good outcomes to all possible outcomes of an event is known as the probability. The number of positive results for an experiment with 'n' outcomes can be represented by the symbol x. The probability of an occurrence may be calculated using the following formula.

Probability(Event) = Positive Results/Total Results = x/n

Given:

probability that your raffle ticket is not a winner = 0.9998.

Now, we know if we have to find the complement probability we can use

P(E) = 1 - P(not E)

where E is any event.

Here, E = not winner

So, P( raffle ticket is a winner)

= 1- 0. 9998                                                  

= 0.0002

Hence, the probability of raffle ticket is a winner is 0.0002.

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If f(x) = x³ + 15x² +68x + 84, which of the following is not a factor of f(x)?
○ (x+6)
○ (x + 2)
○ (x + 7)
(x+8)
Submit Answer

Answers

I think the answer is D

-6, -10, - 15, 16, 9, 12 least to greastest

Answers

the answer is -15,-10,-6,9,12,16

An amusement park charges an admission fee of 25 dollars per person. The cost, C (in dollars), of admission for a group of p
people is given by the following function.
C (p)=25p
What is the cost of admission for a group of 5 people?

Answers

Answer:

c=125 dollars

Step-by-step explanation:

c=25p

p(people)=5

c=25*5

c=125

How many segments of crown molding should be bought to complete the job?

Answers

Answer:

4.62 segments should be brought to complete the job.

Step-by-step explanation:

I guess you only need the answer so, is it okay with no explanation?

2k-3/5k-6 = 2/3 what does k equal to

Answers

Answer:

100/21

Step-by-step explanation:

k = 3/4

Steps to solve

3(2k - 3) = 2(5k - 6)

6k - 9 = 10k - 12

6k - 10k = -12 + 9

-4k = -3

k = 3/4

Can someone help me please?

Answers

[tex]Answer:\ \boxed {-n+3}[/tex]

Step-by-step explanation:

                            y=mx+b

1.

To find m, choose any two coordinates from the table: (1,2) and (0,3)

and use the formula for the slope of the line:

                            [tex]\displaystyle\\\boxed {The\ slope\ m=\frac{y_2-y_1}{x_2-x_1} }[/tex]

[tex]\displaystyle\\m=\frac{3-2}{0-1} \\\\m=\frac{1}{-1} \\\\m=-1\\\\Hence,\ y=-x+b\ \ \ \ (1)[/tex]

2.

To find b, choose any coordinate from the table: (2,1) and substitute its values into the formula (10):

[tex]2=-(1)+b\\\\2=-1+b\\\\2+1=-1+b+1\\\\3=b\\\\Thus,\ b=3\\\\Hence, \ y=-x+3[/tex]

what number groups contain the number -2.22.​

Answers

-2.22 can be identified as Rational and Real
Rational and Real numbers

3x+[tex]\frac{1}{5}[/tex]y=7

Answers

I got x=(35-y)/15 Attached is the work

at a certain college there are twice as many english majors as history majors and three times as many english majors as mathematics majors. what is the ratio of the number of history majors to the number of mathematics majors?

Answers

The ratio of the number of history majors to the number of mathematics majors is 3 to 2.

When two objects are related using numbers or amounts, the relationship is known as a ratio.

Let E be the number of English majors, H be the number of history majors, and M is the number of math majors.

Now,

There are twice as many English majors as history majors.

E = 2 × H

There are three times as many English majors as mathematics majors.

E = 3 × M

Now, let's assume E = 6.

Then,

6 = 2 × H

H = 3 and,

6 = 3 × M

M = 2

Therefore, the ratio of the number of history majors to the number of mathematics majors will be:

H: M = 3 : 2

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A farmer needs to enclose three sides of a garden with a fence (the fourth side is a river). The farmer has
30 feet of fence and wants the garden to have an area of 108 sq-feet. What should the dimensions of the
garden be? (For the purpose of this problem, the width will be the smaller dimension (needing two sides);
the length with be the longer dimežision (needing one side). Additionally, the length should be as long as
possible.)

Answers

length×width = 108

length + 2×width = 30

length = 30 - 2×width

using that in the first equation

(30 - 2×width)×width = 108

-2×width² + 30×width - 108 = 0

the general solution to such a quadratic equation like

ax² + bx + c = 0

is

x = (-b ± sqrt(b² - 4ac))/(2a)

so,

width = (-30 ± sqrt(30² - 4×-2×-108))/(2×-2) =

= (-30 ± sqrt(900 - 864))/-4 =

= (-30 ± sqrt(36))/-4 = (-30 ± 6)/-4

width1 = (-30 + 6)/-4 = -24/-4 = 6 ft

width2 = (-30 - 6)/-4 = -36/-4 = 9 ft

for width = 6 ft

length = 30 - 2×width = 30 - 12 = 18 ft.

for width = 9 ft

length = 30 - 2×width = 30 - 18 = 12 ft

given the request that the length sound be as long as possible,

width = 6 ft

length = 18 ft

is our solution.

The graph of an exponential function has a y-intercept of 9 and contains the point (2,144). Construct the function that describes the graph.

Answers

The graph of an exponential function has a y-intercept of 9 and contains the point (2,144). the function that describes the graph.

y=9(4)^x

This is further explained below.

What is the function that describes the graph.?

Generally, the Standard form of an exponential function

y=a b^x

Where

y= is the y component of the graph

x=  is the x component of the graph

a and b are equation vaiables

Given the y-intercept (0,9) and the point (2,144) Applying both.

a=9,

144=9 b^2

Solve further by making b the subject of formular

b^2=144/9

b^2=16

b[tex]= \sqrt{ 16}[/tex]

Therefore  b=4

So, y=9(4)^x

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