The function f(x) = -5x² + 20x + 55 models the height of a ball x seconds after it is thrown into the air. What is the total time that the ball is in the air?

Answers

Answer 1

Answer:

The ball is in the air for about 5.873 seconds.

Step-by-step explanation:

The function:

[tex]f(x)=-5x^2+20x+55[/tex]

Models the height of a ball x seconds after it is thrown in the air.

And we want to find the total time the ball is in the air.

So, we can simply find the time x at which the ball lands. If it lands, its height f above the ground will be 0. Thus:

[tex]0=-5x^2+20x+55[/tex]

We will solve for x. Dividing both sides by -5 yields:

[tex]0=x^2-4x-11[/tex]

The equation is unfactorable, so we can use the quadratic formula:

[tex]\displaystyle x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

In this case, a = 1, b = -4, and c = -11. So:

[tex]\displaystyle x=\frac{-(-4)\pm\sqrt{(-4)^2-4(1)(-11)}}{2(1)}[/tex]

Evaluate:

[tex]\displaystyle\begin{aligned} x&=\frac{4\pm\sqrt{16+44}}{2}\\&=\frac{4\pm\sqrt{60}}{2}\\&=\frac{4\pm2\sqrt{15}}{2}\\&=2\pm\sqrt{15}\end{aligned}[/tex]

Approximate:

[tex]x_1=2+\sqrt{15}\approx5.873\text{ or } x_2=2-\sqrt{15}\approx-1.873[/tex]

Since time cannot be negative, our only solution is the first choice.

So, the ball is in the air for about 5.873 seconds.


Related Questions

When graphing a system of equations with one solution, the slopes of the two lines will be

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Answer:

independent

Step-by-step explanation:

independent

Monica’s retirement party cost two dollars, plus an additional three dollars for every guess she invites. If there are 16 guests, how much will monica’s retirement party cost

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Answer:

TWO BUCKS?? ballin on a budget

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Last one

What is the volume, in cubic centimeters, of the cylinder?

A 602.88

B 150.72

C 50.24

D 301.44

Answers

Answer:

A

Step-by-step explanation:

The base of your cylinder has a radius of 4 cm, its area is 16 × 3.14, or 50,24 square centimeters. If that same cylinder is 12 cm tall, its volume is 50,24 × 12 = 602,88 cubic centimeters.

Hope this helps

Kind Regards

Farah Syed

The answer is A ..........

Mr. Garcia deposited $2,500 in a new account at his bank.

The bank pays 6.5% interest compounded annually on this account.
Mr. Garcia makes no additional deposits or withdrawals.


Which amount is closest to the balance of the account at the end of 2 years?

A.$2,513.00

B.$2,662.50

C.$2,835.56

D.$2,825.00

Answers

Answer:

$2,825.00

Step-by-step explanation:

First, I found out what 6.5% of 2,500 is, so 6.5% x 2,500 = 162.5 . Then I did 162.5 x 2, which equals 325. I then added 325 to 2,500 and got 2,825.

Find the area of a regular octagon with a side length of 5 cm. Round to the nearest tenth

Answers

Answer:

120.7 cm²

Step-by-step explanation:

2( 1 + √2 ) a² = 2( 1+ √2 ) · 5² ≈ 120.7

how to tell if a equation has one solution, no solution, or an infinite number of solutions

Answers

Answer:

no solution

Step-by-step explanation:

Answer:

If the slope is different - always one solution

if the slope is the same but the y intercept is different - no solution

if the slope and y intercept are the same - infinite number of solutions

solve for x and y.
A x=6; y=10
B x=13.5; y=10
C x=6;y=5
D x=13.5; y=5

Answers

Answer:

B x=13.5; y=10

this is answer

Step-by-step explanation:

HELLPPP

Describe in words how to map AABC to its image
AAB'C'.

Answers

Answer:

Reflected across thhe Y-Axis (I think thats what your looking for)

PLEASE HELP Adam has a rectangular swimming pool. He fills it with water to a depth of 5 feet. The water has a VOLUME of 1200 cubic feet.

Answers

Step-by-step explanation:

Given that,

The depth of the pool is, h = 5 feet

Volume of the pool, V = 1200 cubic feet

We need to find the possible values for the dimensions of the pool. We know that the volume of a rectangle is given by :

[tex]V=lbh[/tex]

Where

l and b are length and breadth

So,

[tex]lb=\dfrac{V}{h}\\\\lb=\dfrac{1200}{5}\\\\lb=240[/tex]

The first possibillity for dimension is (10×24). Another can be (12×20).

I need help I'm confused!

Answers

Answer:

I think you need to find the area of bottom part hope this helps im confused two but try that

Answer:

ok queen

Step-by-step explanation:

What is the value of the expression below? ( 3 + 1 × 5 ) 2

Answers

Answer:

(3+ 5)2=8*2=16

Step-by-step explanation:

Answer:

16

Step-by-step explanation:

(3+1*5)2

B- brackets

I- indices

D- division

M- multiplication

A- addition

S- subtraction

1*5=5

5+3=8

8*2=16

Please answer this. I would greatly appreciate it
No links, no fake answers or your getting reported.

Answers

Answer:

11.1 feet

Step-by-step explanation:

When you are given a right triangle with a given angle and side, you can use

trigonometric functions to calculate missing side lengths or inverse functions for angles based on this information.

These ratios can be remembered by the mnemonic:

SOH CAH TOA.

S O H → Sin (Sine) = Opposite / Hypotenuse

C A H → Cos (Cosine) = Adjacent / Hypotenuse

T O A → Tan (Tangent) = Opposite / Adjacent

______________________________________

The Opposite side is the side directly across from the angle, The adjacent (next to) side is the side other than the hypotenuse or opposite side, and the hypotenuse is the longest side.

Given that we are trying to find the adjacent side, we must use the cos (cosine) function because that can be multiplied by the hypotenuse to give us the adjacent side we are looking for.

Therefore, 36 [Hypotenuse Side] × cos(72°) = Adjacent Side.

Because: 36 = Hypotenuse Side.

cos(72)° = Adjacent Side / Hypotenuse Side.

36 × cos(72°) =

36 × 0.309016994374... = 11.12461179749... ≈ 11.1

A box in the shape of a triangular prism is painted for a project. Which formula would be used to find the lateral surface area of the triangular prism?

Answers

Answer:

LSA = (a+b+c)×h

Step-by-step explanation:

The formula that would be used to find the lateral surface area of the triangular prism = perimeter of base(P) × Height of prism(H)

Let us assume that three side of triangle are a, b, c and height of prism is h

Then lateral surface area of the prism can be LSA = (a+b+c)×h

A triangle has one side that is 31 inches long and a second side that is 44 inches long. The least possible length of the third side is_____ in. The greatest possible length of the third side is____in. (Please write the answer in whole numbers only)
BRAINLIEST!!!!!!!

Answers

Answer:

The lowest length on the third side is less that 30 and the largest is between 40 and 30

Step-by-step explanation:

If there are 48 oranges then how many apples are there?

Answers

If this is a actual question then you are missing parts of it! Please leave a comment with the full question and I would be glad to help you out! If looking at what is given then 0 apples as all that is stated is only 48 oranges and no apples.

Equations and Expressions 1

Calculate if the value given for the variable is the solution or not.

6x-13=5 x=3


⅓(x+4)=20 x=48



4x+5.25=13.25 x=2



Solve

x/7=11


x-5=4



4x=20



x+3=5

Answers

DONT GO TO THE LINK IT MIGHT BE VIRUS OR SCARY OR TACKING THING BE SAFE

HEKEIAINF AIUOSF AOFNK IO:SAB AIOSFBJK ASMEHELPPP

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Answer:

Ummm give me a second let me solve this

PLEASE HELP I WILL MARK BRAINLIEST

Answers

Answer:

I think 96° but not fully sure sorry if wrong

please help asap!!!!!

Answers

Answer:

RQ = RS = 3

Step-by-step explanation:

Since RQ and RS are radii of the circle then they are congruent

let RQ and RS be x , then

Using Pythagoras' identity in right triangle QRS

x² + x² = (3[tex]\sqrt{2}[/tex] )²

2x² = 18 ( divide both sides by 2 )

x² = 9 ( take the square root of both sides )

x = [tex]\sqrt{9}[/tex] = 3

Thus RQ = RS = 3

A club has members from three grades.
It has 36 members from sixth grade, 24 members from seventh grade, and 30 members from eighth grade.

What is the ratio of the club's seventh graders to eighth graders?

Answers

The ratio of seventh graders to eighth graders is 24:30 or 24/30. I hope I helped!

Can somebody plz help answer these questions correctly (only if u done this before) thx :3

WILL MARK BRAINLIEST WHOEVER ANSWER THESE FIRST :DDD

Answers

Answer:

Shown Below

Step-by-step explanation:

WPT = 90

WPV =  30

VPT =  60

VPS = 90

RPS = 60

WPS = 120

QPS =  150

qual é a raiz quadrada de 841?

Answers

Answer:

29

Step-by-step explanation:

Convert 189 To A Decimal And Then Round Your Answer To The Nearest Whole Number (29) Is Already Rounded To The Nearest Whole Number So Your Answer Is 29

Someone please help me?!?!

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Answer:

30 is correct answer. ... ...........

PLEASE HELP!!!! will give brainliest points to whoever answers first!!!! only going on for 30 minutes.

One way to name a transformed figure is to place a _________________________ after each letter in the
name of the original figure. For example, a reflection of ΔABC is named __________.

Answers

Answer:

Is to place a ' or a prime

ΔA'B'C'

Answer:

One way to name a transformed figure is to place a apostrophe after each letter in the

name of the original figure. For example, a reflection of ΔABC is named ΔA'B'C' (pronounced A prime B prime C prime).

Step-by-step explanation:

Jim rented a truck for one day. There was
base fee of $17.95, and there was an additional charge of 87 cents for each mile driven, Jim had to pay $153.67
when he returned the truck. For how many miles did he drive the truck?

Answers

Make an equation
Y = 17.95 + 0.87x
Y = total cost, x = miles
153.67 = 17.95 + 0.87x
135.72 = 0.87x
x = 156 miles

Answer:

Jim drove the truck 156 miles

Step-by-step explanation:

Represent the number of miles driven with x.

Then the formula for the total rental cost is C(x) = $17.95 + ($0.87/mile)x, and this comes to $153.67.  Solve for x:

$153.67 - $17.95 = ($0.87/mile)x, or

$135.72 = ($0.87/mile)x

Dividing both sides by ($0.87/mile), we get:

x = 156

Jim drove the truck 156 miles

In Juan's coin bank there are nickels (n),
dimes (d), and quarters (q). The number of
quarters is one-quarter the number of dimes, and
the number of nickels is twice the number of
quarters. The total value of the coins is $6.00.
Find the number of each type of coin. [Show all
work.]

Answers

Answer:

The answer is 8 quarters, 16 nickles, and 32 dimes

Step-by-step explanation:

First, the equation would be (2/4d) x 5 +d x 10 +1/4d x 25= 600 (Don't put 6.00, that's dollars. We put 6 dollars into cents to make it easier.) Then we slowly start to solve: 10/4d + 10d + 25/4d = 600 10d+40d+25d/4 = 600 (Put all of that over 4, not first 25d) 75d= 600 x 4 d=600 x 4/75 (same here put everything over 75) d=32 So then n= 2 x 32/4 = 16 Then n would be equal to : 1/4d= 1/4 x 32 = 8 So your answer would be 8 quarters, 16 nickles, and 32 dimes.

Hope this helped :)

If you know the answer please help

Answers

The answer is 330. 67x5=335. Now round it.

GIVING BRAINLIEST HELP ASAP! please tell me how you did it so I can learn it

Answers

Answer:

Ok since u want to learn ill teach you :)

Get your 3 points and then your do this

Example= 3 power of 2 plus 5 power of 2

Then ur gonna add and get your answer hope this helps

(if u still don't get it ill just give u the answer)

7.2

Step-by-step explanation:

Hope u kinda got a good start on this :)

Someone please help me on this question please. Don’t put a link. Please help me.

Answers

9514 1404 393

Answer:

  34 < x < 74

Step-by-step explanation:

Assuming we're concerned with a triangle, the third side must have a length between the difference and the sum of the two given sides.

  54 -20 < x < 54 +20

  34 < x < 74

NEED HELP I WILL BE GIVING BRAINLIEST:)

Answers

Answer:

mathematics

Step-by-step explanation:

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