Eva is jumping on a trampoline. Her height h at time t can be modeled by the equation h=-16t^2+20t+6. Would Eva reach a height of 14 feet?

Answers

Answer 1

Given the equation modeling Eva's height at time,t. To evaluate if she will reach height of 14 ft, we evaluate maximum height that she will reach.
At maximum height h'(t)=0
but
h(t)=-16t^2+20t+6
h'(t)=-32t+20=0
solving for t we get:
-32t=-20
t=20/32
t=5/8
thus the maximum height reached was:
h(5/8)=-16(5/8)^2+20(5/8)+6
h(5/8)=12.25 ft
Thus we conclude that she won't reach the height of 14 ft because her maximum height was 12.25 ft

Answer 2

A function assigns the value of each element of one set to the other specific element of another set. Eva can not reach a height of 14 feet.

What is a Function?

A function assigns the value of each element of one set to the other specific element of another set.

As the function of the height of the jump, Eva is given as h=-16t^2+20t+6. Now, in order to know if Eva will reach 14 feet height, we need to substitute the value of her height of Eva as 14 feet, therefore,

[tex]h=-16t^2+20t+6\\\\14=-16t^2+20t+6\\\\16t^2 - 20t+14-6=0\\\\16t^2 -20t + 8=0[/tex]

If we calculate the discriminant of the given quadratic equation, we will understand that the given quadratic equation has imaginary roots.

Therefore, Eva can not reach a height of 14 feet.

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Related Questions

A farmhouse shelters 10 animals. Some are pigs and some are ducks. Altogether there are 36 legs. How many of each animal are there?

Answers

8 pigs 4 ducks
8x4=32
2x2=4
32+4=36

there are 8 pigs and 2 ducks. 2 ducks equal 4 legs, and 8 pigs equal 32 legs. Then, you do simple math, so 32 plus 4 is 36 legs!

A saving account pays 3.6% per annum simple interest Heidi puts £400 into the account, how much will she have in the account after 5 years?

Answers

One year:
0.036(400)+400
Because it is 5 years:
5(0.036(400))+400
0.18(400)+400
We can make it simpler:
1.18(400)
Multiply
472
SHE WILL HAVE £472

Final answer:

Using the simple interest formula, Heidi will gain £72 in interest on her initial £400 deposit over 5 years at an interest rate of 3.6%. Therefore, she will have a total of £472 in her account at the end of 5 years.

Explanation:

The subject of this question is simple interest calculation which is a topic in Mathematics. It's all about calculating the final amount Heidi will have in her account after 5 years, with a simple interest rate of 3.6% on her initial deposit of £400.

Given the simple interest formula, Interest = Principal × Interest rate × Time, here, the principal is £400, the interest rate is 3.6% (which is 0.036 as a decimal), and time is 5 years.

Using the formula: Interest = £400 × 0.036 × 5 = £72

So, Heidi earns £72 in interest over 5 years.

To find out how much money she will have after 5 years, we will need to add the interest to the initial deposit: Amount = Principal + Interest which gives: Amount = £400 + £72 = £472

So after 5 years, Heidi will have £472 in her account.

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how to graph (-3,4) ;m=6

Answers

[tex]m=6=\dfrac{6}{1}[/tex]

We have the point (-3; -4) in the coordinate system.

From this point we go 1 unit to the right and 6 units to the up.

We get the second point.

Draw a straight line.

Look at the picture.

Hideki throws a baseball ball upward with an initial velocity of 12 meters/sec. When he throws the ball, it is two meters above the ground. How long will it take the ball to hit the ground?

Answers

For this case we have the following kinematic equation that models the problem:
h (t) = (1/2) * (- 9.8) * t ^ 2 + 12 * t + 2
Rewriting we have:
h (t) = -4.9 * t ^ 2 + 12 * t + 2
When the ball hits the ground we have:
-4.9 * t ^ 2 + 12 * t + 2 = 0
Solving the polynomial we have:
t1 = -0.16
t2 = 2.61
We ignore the negative root because it is time.
Answer:
It will take the ball to hit the ground about:
t = 2.61 sec

Answer:

-4.9^2 + 12t + 2 = 0

Step-by-step explanation:

what does it mean if the quotient times the divisor does not equal the dividend? What should you do?

Answers

say just for a example, that you have 400 divided by 20. The correct answer is 20. But say that you got ten. You would say how many times can 20 go into 40? The answer would be twice. Then, you would say, how many times can 20 go into zero. The correct answer would be 0. you should go back to your work and check and ask yourself those problems and see if they match. Hope this helps!

Final answer:

When the quotient times the divisor does not equal the dividend, it means there is a remainder. Depending on the context of the problem, you can round down, express the remainder as a fraction or decimal, or choose another appropriate method.

Explanation:

When the quotient times the divisor does not equal the dividend, it means that the division did not result in an exact whole number. This is called a remainder. For example, if you divide 15 by 4, the quotient is 3 and the remainder is 3. So, 3 times 4 does not equal 15.

If you encounter this situation, you can do a few things. You can round the quotient down to the nearest whole number, or you can express the remainder as a fraction or decimal. It depends on the context of the problem and what is required.

For example, if you are dividing cookies among friends, you may want to express the remainder as a fraction, saying each friend gets 3 and a half cookies. But if you are calculating the number of whole boxes needed, you may round down to 3 boxes.

Plz show work and explain
Haley and Madison are arguing over a math problem. Haley insists that a square with a area of 196 square units is bigger than Madison’s square that has a perimeter of 196 units. Who is correct and why?

Answers

Perimeter of a square is:

4 * s

where s is the side length.

Area is:

s * s

So, we can set both of these values to 196.

4s = 196
s = 49

s * s = 196
s = 14

So, Madison is correct.

Hope this helped!

Food express is running a special promotion in which customers can win a free gallon of milk with their food purchase if there is a star on the receipt so far 147 of the first 156 customers have not received a star in the receipts what is experimental probability of winning a free gallon of milk

Answers

Formula
P(nw) = no wins / total
no wins = 147
Total = 156

Calculation for no wins
P(nw) = 147 / 156 = 0.9423

Calculation for winners.
P(w) = 1 - 0.9423
P(w) = 0.05769

Another way.
You could calculate the winners from the total
156 - 147 = 9

P(w) = 9/156 = 0.05769 Same answer as before. Pick the method you like best.

The equation above can be used to calculate the volume V, of a pyramid with a height h and base with length l and width w. If the volume of a pyramid is 81inches^3, and l=w=3h, what is the length of the base of the pyramid in inches?

Answers

Volume of a pyramid is V= lwh/3
You know
V=81
l=3h
w=3h

h=3
l=9
w=9

So length is 9 inches

Comment
The formula for a pyramid = (1/3) L * W * h The base in this case is square.

Givens
L = W
W =W
L = 3H
H = L/3 = (1/3L)
V = 81 in^3

Solve
V = 1/3 L * W * H
V = 1/3 L * L * 1/3 L
81 = 1/9 L^3 Multiply through by 9
81 * 9 = L^3
729 = L^3 Take the cube root of both sides.
cube root (L^3) = cube root (729)
L = 9 in

Which of the following graphs shows the solution of the inequality
x+1<5
?
A. Graph A
B. Graph B
C. Graph C
D. Graph D

Answers

[tex]x + 1 < 5 \\ x < 4[/tex]

Answer is C. Graph C

Hope this helps. - M

What fraction is equivalent to the repeating decimal 0.18

Answers

18/99 can be reduced, it becomes 2/11

Therefore the answer is 2/11!!

Hope this helps!!! :)

P.S. You can check it if you wish by dividing 2 by 11!

Let's begin by setting x equal to our repeating fraction

x=0.18181818...

The next step is a bit of a trick where we multiply by a power of 10 such that what remains to the right of the decimal is the repeating fraction itself, i.e.

100x=18.1818181818...=18+0.18181818...

which can be re-written

100x=18+x

taking x to the left-hand side we get

99x=18

and finally

x=18/99=2/11

Hope this helps!

In a '20% off' sale, a coat was £220. Work out the original price.

Answers

80% of p = 220 (We know this as the sale price is 20% off, so there is still 80%)

0.8p = 220

p = 220/0.8 (This is because we are making p the subject of the formula)

p = 275 (If you are not allowed to use a calculator for this, then: 220/0.8 is the same as 2200/8 because we are just simply multiplying both the numerator and denominator by 10. This can be simply worked out by long division)

80% is equal to 220

1) Set up a proportion:
80/100=220/x

2) Simplify:
4/5=220/x

3) Solve by cross-multiplying:
4x=1100
x=275

Original Price: 275

What is the true solution on 2 in e ^in 5x=2 in 15

Answers

2In (e^(In5x))= 2 ln15

In(e^x)=x

2(ln5x)=2ln15

In 5x=In 15

5x= 15

x= 3

genius

What is the measure of X

Answers

Answer:

we can know the answer by using phorem therom so

Step-by-step explanation:

all are 90 degree so x angle will also be 90 degree

now h^2 =p^2+b^2 so

NEED HELP ASAP!!! Susan makes $5 per hour babysitting and $7 per hour as a life guard. Her goal is to make at least $140. which of the following represents three possible solutions to the problem?

Answers

Number of hours Babysitting: x
Number of horus Lifeguard: y

Susan makes $5 per hour babysitting
Money she makes Babysitting: 5x

Susan makes $7 per hour as a life guard
Money she makes as a life guard: 7y

Total money she mahes: 5x+7y

Her goal is to make at least $140:
5x+7y>=140

Answer: First option
5x+7y>=140

A hose fills a hot tub at a rate of 3.45 gallons per minute. How many hours will it take to fill a 280 -gallon hot tub?

Answers

For this case we must use the following definition:
Q = V / t
Where,
Q: flow
V: volume
t: time
Clearing the time we have:
t = V / Q
Substituting the values:
t = (280) / (3.45)
t = 81.16 minutes
In hours we have:
t = (81.16) * (1/60)
t = 1.35 hours
Answer:
it will take to fill to 280 -gallon hot tub about:
t = 1.35 hours

It will take approximately 1.35 hours to fill the 280-gallon hot tub.

We have,

A hose fills a hot tub at a rate of 3.45 gallons per minute.

This can be written as an expression:

3.45 gallons = 1 minute

Now,

Multiply 280/3.45 on both sides.

280/3.45 x 3.45 gallons = 280/3.45 minutes

280 gallons = 81.16 minutes

Now,

81.16 minutes can be converted into hours.

Divide 81.16 by 60.

So,

81.16/60 = 1.35 hours

Therefore,

It will take approximately 1.35 hours to fill the 280-gallon hot tub.

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What must you do if you multiply one number in a ratio by n?

Answers

Hi there!

From what I know, when you multiply one number in a ratio, you must also multiply the other number by the same number. This allows for the ratio to stay the same, thus keeping it correct. If both terms were not multiplied by n, the ratio would no longer be the correct ratio.

Hope this helps!! :)
If there's anything else that I can help you with, please let me know!

English has 6 letters that can be vowels. This includes Y, which can be either a consonant or a vowel; for this problem, we'll consider Y a vowel. The other 20 English letters are always consonants. How many two-letter "words" can we make from these letters if we are required to use at least one vowel? (We aren't limited to words that have an actual meaning in English. Thus, for this problem, we'll include nonsense "words" like QO, XY, and UZ.)

Answers

I think this should be posted in English instead of Math... but you can make lots of words.

as
my
he
we
me
by
hi
so
go
to

These are just a few.

The vanishing point of the picture is represented by point B.

A) The measure of angle ABD is is 6.2 times greater than the measure of angle CBD. Find the measure of angle CBD.

B) Angle FBE and angle EBD are congruent. Find the measure of angle FBE.

Answers

A) Angles ABD and CBD are supplementary, so you have ...
∠ABD + ∠CBD = 180°
6.2(∠CBD) + ∠CBD = 180°
7.2(∠CBD) = 180°
∠CBD = 180°/7.2
∠CBD = 25°

B) Angles EBD and CBD are complementary, so you have ...
∠FBE = ∠EBD = 90° - ∠CBD
∠FBE = 90° - 25°
∠FBE = 65°

Final answer:

To solve this, we use the fact that angles around a point add up to 360 degrees and angles on a straight line add up to 180 degrees. This allows us to find angle CBD to be 50 degrees and angle FBE to be 130 degrees.

Explanation:

The subject of this question is geometry, specifically it deals with the properties of angles around a point. In the first part of the question, we are told that angle ABD is 6.2 times greater than angle CBD and we are asked to find the measure of angle CBD. As the total angle around a point is 360 degrees, we can set up the equation ABD + CBD = 360. Given that ABD = 6.2 * CBD, we can replace ABD in our equation, resulting in 6.2* CBD + CBD = 360, solving this gives us CBD = 360/7.2 = 50 degrees.

In the second part of the question, we're told that angle FBE and angle EBD are congruent. This means they have the same measure. Since angle EBD is adjacent to angle CBD and they form a straight line together, their measures add to 180 degrees. Since we already found angle CBD to be 50 degrees, thus angle EBD (or FBE) is 180 - 50 = 130 degrees.

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Jeremy is making a trail mix containing raisins and peanuts. Raisins cost $1.50 per pound. Peanuts cost $2.50 per pound. Jeremy spends $10.50 to make 5 pounds of trail mix. He uses the table below to organize this information. Which equation can Jeremy use to determine the amount of raisins in the trail mix?
a.r + 1.50 = 1.5r
b. r + (5 – r) = 5
c. 1.5r + 2.5(5 – r) = 10.50
d. 1.5r + 2.5(5 – r) = 5

Answers

Answer:

Option C.

Step-by-step explanation:

Let Jeremy mixes "r" pounds of raisins to make a trail mix.

As the total weight of trial is = 5 pounds

So weight of peanuts in the trail mix will be = (5 - r )

Now cost per pound of raisins = $1.50

so cost of r pounds of raisins = $1.50(r)

Cost of the peanuts = $2.50 per pound

so cost of (5 - r) pounds peanuts = $2.50(5 - r)

Jeremy spends total amount = $10.50

So expression will be

Cost of Raisins + cost of peanuts = cost of trail.

1.5r + 2.5(5 - r) = 10.50

Option C. is the answer.

Write an inequality involving the variable x that describes the set of numbers graphed.

Answers

Since it does not include 0 in the inequality, nor does it include any numbers below 0, it must be [tex]\boxed{x\ \textgreater \ 0}[/tex].

A small refrigerator is a cube with a side length of 14 inches. Use the formula S = 6s2 to find the surface area of the cube.

Answers

Formula = 6s²

Surface area = 6 (14)² = 1176 in²

Answer: 1176 in²

2. Savannah recorded the average rainfall amount, in inches, for two cities over the course of 6 months. Put the numbers in order from least to greatest. Show your work! City A: {4, 3.5, 5, 5.5, 4, 2} City B: {5, 6, 3.5, 5.5, 4, 6} (a) What is the mean monthly rainfall amount for each city? (b) What is the mean absolute deviation (MAD) for each city? Round to the nearest tenth. (c) What is the median for each city? Answer: a) Mean of City A: 24 Mean of City B: 30 b) Find the MAD for each city. City A Absolute Deviation MAD for City A City B Absolute Deviation MAD for City B 4 5 3.5 6 5 3.5 5.5 5.5 4 4 2 6 c) Median of City A: 4 Median of City B: 5.25

Answers

City A: {2, 3.5, 4, 4, 5, 5.5}
City B: {3.5, 4, 5, 5.5, 6, 6}

Mean is the average.
Average of City A = 4 (2+3.5+4+4+5+5.5 = 24 and 24/6 = 4)
Average of City B = 5 (3.5+4+5+5.5+6+6 = 30 and 30/6 = 5)

Mean Absolute Deviation
Mean Absolute Deviation of City A = 0.8
Mean Absolute Deviation of City B = 0.8

Median is the middle (after putting it in order least to greatest)
Median of City A = 4
Median of City B = 5.25 (5+5.5 = 10.5 and 10.5/2 =5.25)

Solve for x
X3=1/27
Solve in fraction simplest form

Answers

x³ = 1/27
x=³√1*1*1/3*3*3
x= 1/3

Factor using difference of cubes and set each factor equal to 0.

[tex]x= [/tex] [tex] \frac{1}{3} [/tex], [tex]- \frac{1-i \sqrt{3} }{6} [/tex], [tex]- \frac{ 1+i \sqrt{3} }{6} [/tex]

Hope i was of some help ^.^

spining a spinner that has 5 equal section marked 1 through 5 and landing on an evean number

Answers

Judging on how the only even numbers between 1 and 5 are 2 and 4. You would use a calculator and do 2÷5 and it will come out as .40 meaning 40%! So there is a 40% chance of landing on a even number! Hope I helped!

A rectangular bathtub is 5 1/2 feet long, 1 1/2feet wide, and 3 feet high. Daniel fills the tub to a depth of 2feet.What is the volume of the water in the tub?

Answers

To find the volume of the water that is in the tub, you will multiply the length by the wet by the height/depth of the water.

V = lwh
5 1/2 x 1 1/2 x 2
V = 16 1/2 ft.³

how many 1 cup servings can be poured from 1 gallon of milk?

Answers

There are 16 cups in a gallon.

16 cups Can be poured from 1 gallon of milk

79+b=159
b=
send help pls... :)

Answers

Subtract 79 from both sides to isolate variable b.

b = 159 - 79
b = 80

B=80 simple as that

Please help me!!!!!

Question: Kara and Steven are biking around a 1,800 kilometer path. They start biking from the same place, at the same time, and in the same direction. Kara bikes at a speed of 15 km/h and Steven bikes at a speed of 30 km/h. How long will it take before Steven and Kara will be at the same place of the path next time?

Answers

Answer: 120 hours

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

Explanation:

The path is 1800 km. Kara's speed is 15 km/h. If this speed is held the same throughout the path, then it will take her d/r = 1800/15 = 120 hours to travel the entire path until she gets back to her starting point.

For Steven, it takes him d/r = 1800/30 = 60 hours to make the same journey.

The LCM of 60 and 120 is 120

Every 120 hours, both Kara and Steven will be back at the starting point together.

Note: this is a very very large time value, and this is not considering the fact that the bikers slow down or stop to take a break.

Yo I just need to get this right so help me out

Answers

Answer:

1) yes--first term is -48, common ratio is -2

2) no--no common ratio

3) yes--first term is 3, common ratio is 3

4) yes--first term is 5, common ratio is 2

5) no--arithmetic sequence

6) no--arithmetic sequence

A research company produced a study to find out what percentage of people in the state of Mississippi would purchase a new product being developed. Out of the 24 participants polled, 12 stated that they would buy the new product. The research company concluded that about 50% of the residents of Mississippi would purchase the new product. Identify a problem with the study.

Answers

The sample size is too small. The company is trying to determine the percent of people in Mississippi that would purchase the product. To make a prediction for the entire state of Mississippi, they should survey more than just 24 people. A random survey should be created and given out across the state.

The conclusion is based on a small sample.

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Barbara and jeffrey are both psychologists. barbara believes that biology is the sole cause for psychological disorders. jeffrey believes that while biology plays a large role, psychological and social factors should also be considered. barbara practices from the _____ perspective, whereas jeffrey practices from the _____ perspective. Consider the following set of equations: Equation A: y = x + 5Equation B: y = 6x 2Which of the following is a step that can be used to find the solution to the set of equations? x = 6x + 2 x 2 = 6x + 5 x + 5 = 6x 2 x + 5 = 5x Need help on this please 27.3 less than k is -57.7. What is the value of k ? According to maslow's humanistic theory of motivation, what must people do before they can strive for the realization of their personal potential and creative abilities You are reading a book with 120 pages if you want to read the same number of pages each night how many would you have to read each night to finish in 10 days Solve 4/7=x+3/21 need help ASAP Tasha went on a trekking exposition to a mountain range during her vacation when she reached a particular height it started taking heavily which sphere is responsible for this sudden weather change A store purchases an item wholesale for 60$ and marks it up by 70 percent if there is a 7 percent tax on the item how much will the item cost Franklin Roosevelts presidency was the longest in U.S. history. He is famous for the fireside chats that informed and encouraged the American people through the Great Depression and World War II. Suppose you were asked to give your own fireside chat about Roosevelts presidency. What would you say? Many activists who oppose the trend toward globalization claim that It Which statement best describes an advantage of using the Subtotal dialog box?1)Only one function, Add, can be used to combine data quickly.2)Data from multiple workbooks can be combined in a single step.3)An option is available that can customize any function available in Excel.4)Data can be summarized using a single step rather than by writing multiple formulas. What is a common side effect of both chemotherapy and radiation therapy? loss of limbs bouts of nausea vitamin overdose damage to healthy cells Q # 13 please Graph the image. of AMOP for the translation What does the author mean by the following quote, "It is a mystery where it originated from, though many people believe that China began the tradition of the piata"?a)Only a few people believe that China is where the piata originated.b)China is most definitely where the tradition of the piata began.c)t is possible that the piata originated somewhere other than China.d)Piata is a Chinese word, so the tradition must have begun there. which has the smallest value 11 , 0.675,1.23,0.42,1.011 Can someone help me solve this ?? the slope of a learning curve will _____ Which expressions result in a rational number? Please need help on this