Mathematics High School

A stone is thrown straight down from a tall building. The relation h = 150 - 5t - 5t^2
approximates its path, with h in metres and t in seconds.
a) How tall is the building?
b) Factor the right side of the equation fully.
c) When does the stone hit the ground?

Answers

Answer 1

Answer:

a) The building is 150 m tall

b) h(t)=-5(t+6)(t-5)

c) The stone hits the ground at 5 seconds.

Step-by-step explanation:

Function Models

The path of a stone thrown down from a tall building is modeled by the function:

[tex]h(t)=150-5t-5t^2[/tex]

Where h is the height in meters and t is the time in seconds after the stone is thrown.

a) To find the height of the building, we set t=0 because it's the moment when the stone is thrown and has the same height as the building:

[tex]h(0)=150-5*0-5*0^2[/tex]

[tex]h(0)=150[/tex]

The building is 150 m tall

b) The function is

[tex]h(t)=150-5t-5t^2[/tex]

Factoring out -5:

[tex]h(t)=-5(-30+t+t^2)[/tex]

Rearranging:

[tex]h(t)=-5(t^2+t-30)[/tex]

To factor the polynomial in parentheses, we must find two numbers whose product is -30 and sum is 1. We can also use the quadratic formula to find the roots and factor later.

These numbers are 6 and -5, thus the function is:

[tex]h(t)=-5(t+6)(t-5)[/tex]

c) The stone hits the ground when h=0:

[tex]-5(t+6)(t-5)=0[/tex]

The equation has two solutions:

t = -6

t = 5

The only feasible solution is t = 5, thus the stone hits the ground at 5 seconds.

Related Questions

Hi can someone please help me on my homework

Answers

Answer:

8. yes, ASA

9. yes, SAS

10. yes, AAS

11. no

12. no

13. yes, SSS

Step-by-step explanation:

10 POINTS!!!

-12m = 16

explain your thinking

Answers

Answer:

divide -12 from each side

16/-12=-4/3

-4/3, or -1 1/3

Step-by-step explanation:

Answer:

-1.333333333

Step-by-step explanation:

-12(-1.333333333)=16

Whats a line passing
through the
points (0, 0) and
(5,-7)?

Answers

Answer:

y = -7/5x

Step-by-step explanation:

First, we need to use the two points to find the slope.

m = y₁ - y₂ / x₁ - x₂

m = -7 - 0 / 5 - 0

m = -7/5

Now we know that the slope is -7/5. Now we'll substitute the information we've gathered into the point-slope form equation to get an equation.

y - y₁ = m(x - x₁)

y - (-7) = -7/5(x - 5)

y + 7 = -7/5x + 7

y = -7/5x

Therefore, the equation of the line is y = -7/5x.

What is equivalent to 8:5

Answers

Answer:24:15

Step-by-step explanation:I think it's right i did the math

Answer:

I’m pretty sure its 1:6

Step-by-step explanation:


2a + 3b = 5
b = a - 5
What is a and b?

Answers

2a + 3(a-5) = 5, 2a + 3a+15=5, 5a=-10, a=-2, b= (-2) -5, b=-7...a=-2, b=-7

An ice cube is made of 5 fluid ounces of water. About how many milliliters of water does it take to make an ice cube​

Answers

Answer:

[tex]147.868[/tex]

Step-by-step explanation:

1. Lets transfer ounces ⇄ to Millimeters.

[tex]29.5735milliliters[/tex]

2. Lets multiply.

[tex]5 x 29.5735[/tex] is: [tex]147.868[/tex].

Hope this helps :)

Answer:

5 floz = 147.85 ml

Step-by-step explanation:

What your doing is converting floz to ml so if 1 floz = 29.57 ml your going to multiply 5 floz x 29.57 ml which equals 147.85 ml. Hope this helps or is right at least.

b) How many more "dots” would you need to completely fill a 5 by 5 square?

Answers

Answer:

i think 25 or 80

Step-by-step explanation:

i hope i am roght goodluck

what is 0.65×0.11 if you answer first ill make brainlyest

Answers

Answer:

0.0715

Step-by-step explanation:

Not much to explain

What would you do to solve the equation below x/2=15

Answers

Answer: x=30

Step-by-step explanation:

Multiply both sides of the equation by 2 to cancel out the divide by 2.

x=15×2=30

Answer:

x=30

Step-by-step explanation:

2*x/2=15*2

x=30

5x-16<-64-x
pls help

Answers

Inequality Form: x < -8

Interval Notation: (-\infty, -8)

HOPE IT HELPS! can I get brainiest?

math is hard help pls​

Answers

Answer:

60% Hope this helped! :)

Step-by-step explanation:

Write a verbal sentence then solve the equation. The quotient of X and 6 is 8.7

Answers

Answer

6/x = 8.7

Step-by-step explanation:

let x = a number that we will find out

6/x = 8.7 (determinethe defined range)

6/8 = 8.7, x = 0 (multiply both sides)

6 = 8.7x (swap sides)

8.7 x = 6 (divide both sides)

x = 20/29

check

x = 20/29, x = 0

OR x = 0.689655

which is the prime factorization of 24?

Answers

Answer:

I would prefer 2×2×2×3

Step-by-step explanation:

2×2×2×3

     or

24 = 2³ x 3        

Reed bought 1.8 pounds of green beans. The green beans cost $1.27 per pound. What was the total cost of Reed’s green beans? Round your answer to the nearest hundredth.

Answers

Answer:

2.3

Step-by-step explanation:

Mila buys 1112 pound of almonds and 56 pound of pecans.
Need this fast!
Which answer is the most accurate estimate for how many more pounds of almonds she buys than pounds of pecans?


A. 0 pounds

B. 12 pound

C. 1 pound

Answers

Answer:

B. 12 pounds

Step-by-step explanation:

All of them are off but if I had to choose an answer between those three I would choose B.

If you round 1112 to 1000 and 56 to 60, and do 1000 divided by 60 you get 16.6

Out of all the answers 12 pounds is closest to 16.

This is how I would answer it. Hope this helps!

Convert .25 to a fraction.

Answers

I’m pretty sure the answer is 1/4

Answer:

1/4

Step-by-step explanation:

.25 is a fourth of a dollar, so 1/4 is the answer

Please helppppp my assignment is missing and I need to get it done. pleaseeeeeee

Answers

Answer:

B.

Step-by-step explanation:

perpendicular lines are the reciprocal and opposite of the slopes. the opposite and reciprocal of -4/5 is 5/4. B is the only one with that slope.

ASAP ASAP ASAP ASAP... pls pls pls

Answers

3.7%

hey im just guessing

Answer:

B. 37%

Step-by-step explanation:

There are 37 students out of 100 that prefer pineapples to peaches and a percent is out of a hundred so therefore 37% is correct

Leah just moved and she's looking for a nee dance studio. She gets to list the price from tip top toes charges $300 for 12 classes and groovin amd movin charges $264 11 classes which studio offers the better deal?

Answers

Ansi dont know

Step-by-step explanati dont know

Just help.. please and thank you​

Answers

Answer:

nonlinear

Step-by-step explanation:


{(-5,1),(-3,9), (4,6), (4, -2)}
A) function
B) not a function

Answers

Answer:

Step-by-step explanation:

It is not a function

The 4 in the domain is used more than once

6. All angles in the figure below are right angles. What is the area of the figure? (1 point)

Answers

Answer:

Option (4)

Step-by-step explanation:

Area of the figure given in the picture = Area of large rectangle - Area of rectangle A

Area of rectangle A = Length × Width

                                 = [9 - (2 + 4)] × 3

                                 = 3 × 3

                                 = 9

Area of the large rectangle = Length × Width

                                             = 9 × 5

                                             = 45

Therefore, area of the given figure = 45 - 9

                                                          = 36

Option (4) will be the correct option.

Sam needs a web designer. Designer A is offering her services for an initial
$500 in addition to $100 per hour. Designer B is offering her services for an initial
$600 in addition to $50 per hour. When will the two designers charge the same
amount of money?

Answers

They will charge the same amount of money in the second hour

even betteerrrr u guys like it <3

Answers

Answer:

ummm

Step-by-step explanation:

what's that???

quiet didnt get it lol¿

NEED HELP IM GIVIN BRAINLIEST
Jackson spent 2 of his total money on an antique game. He has $12.50 left. 3
If there was no tax added to the cost, how much did Jackson spend on the
antique game? (Keep in mind that he has 1 of his money left)

Answers

Answer:

$37.50

Step-by-step explanation:

1 money = 12.50

Before spending anything he had 2 money more than this (3 overall)

Therefore we are multiplying-

12.50 x 3 = 37.50

The answer is $37.50

I need help!!
I don’t understand

Answers

Answer:

Step-by-step explanation: the picture is not put correct it is sidewords so i dont understand what it says

You are starting a babysitting business to earn enough money to buy a new iPhone 7 Plus, which costs $769. You already have $240 from last summer. You charge $9.00 per hour for babysitting. Write an inequality that shows how many hours you need to work to earn more than $769.

Answers

Answer:

9 times 59 is 531. 531+240= 771 she needs to work 59 hours.

Step-by-step explanation:

PLZ HELP WILL DO ANYTHING

Answers

Answer:

Help me with my Physics lol

Can somebody plz help answer these questions correctly thanks!! :))

WILL MARK BRIANLIEST WHOEVER ANSWERS FIRST

Answers

1 is A
2 is C
3 is B

hopefully this helps

Zeke has swim club every 2 days and robotics club every 8 days.
This month, he has swim club on the 2nd day of the month and robotics club on the 8th day of the month.
Zeke says that the first time he will have both clubs on the same day is the 16th day of the month because the LCM of 2 and 8 is 16.

Answers

Answer: No. Zeke found the LCM to be the product of two and eight but because eight is a multiple of two the LCM is eight so the first day he will have both clubs is the 8th day of the month

Step-by-step explanation:

All you have to do is fine the least common multiple of 2 and 8 which is eight so obviously zeke is incorrect because they said the least common multiple was 16 and it is not. zeke multiplied 2 and 8 which is not what you’re supposed to do to get the lcm.

No. Zeke found the LCM to be the product of two and eight but because eight is a multiple of two the LCM is eight so the first day he will have both clubs is the 8th day of the month
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