please help! the approximate path of a projectile launched from 100 m above the ground is given by f(×)= -5×^2+40+100, where f(×) represents the height × seconds after it is released into the air. use the info to answer the questions below. 1. what is the factored form of the equation? 2 how long will it take the projectile to reach the ground?​

Answers

Answer 1

Answer:

Part 1) [tex]f(x)=-5(x-10)(x+2)[/tex]

Part 2) After 10 seconds.

Step-by-step explanation:

We have the function:

[tex]f(x)=-5x^2+40x+100[/tex]

Where f(x) represents the height x seconds after it is released into the air.

Part 1)

First, let's distribute a -5 out of the function:

[tex]f(x)=-5(x^2-8x-20)[/tex]

Now, let's factor. We want to pick two number that multiplies to -20 and adds to -8.

We can use -10 and 2. So:

[tex]f(x)=-5(x^2+2x-10x-20)[/tex]

Factor:

[tex]\begin{aligned}f(x)&=-5(x^2+2x-10x-20) \\ f(x)&=-5(x(x+2)-10(x+2)) \\ f(x)&=-5(x-10)(x+2) \end{aligned}[/tex]

Hence, our factored form is:

[tex]f(x)=-5(x-10)(x+2)[/tex]

Part 2)

We want to find after how many seconds does it take for the projectile to reach the ground.

If it reaches the ground, the height above the ground, f(x), will be 0.

So, we can set f(x) equal to 0 and solve for x. Instead of using the original equation, we can use the factored form. So:

[tex]0=-5(x-10)(x+2)[/tex]

Zero Product Property:

[tex]x-10=0\text{ or } x+2=0[/tex]

Solve for x:

[tex]x=10 \text{ or } x=-2[/tex]

Since x measures time, -2 does not make sense in this context.

Therefore, our solution is x=10.

So, after 10 seconds, the projectile will hit the ground.


Related Questions

WILL GIVE BRAINLIEST NEED DONE ASAP
Write an equation in standard form of the line that passes through the given point
and has the given slope.
1. (2,-4), m= 2/3
2. (5, -3); m = 2
3. (6,0); m = 3/4
4. (-1, 2); m = 7
5. (-3,-5)m= 1/3
6. (4,0); m = -5

Answers

Answer:

y=2/3x-16/3    

Step-by-step explanation:

ok ill show you how to do one question since the rest will take too long so what you do is

equation is y=mx+b right

so you have slope and these points (2,-4) and m=2/3

y=2/3x +b right

now all you do is sub in x and y which are ur given points

-4=2/3 (2) +b

now you solve for b

-4 = 4/3 + b

-4-4/3 = b

-12/3 - 4/3 = b

-16/3=b so therefore

y=2/3x-16/3    

Here is working and answers
Hope it helps :)

Do imaginary numbers follow the rules of algebra?

Answers

Answer:

no

Step-by-step explanation:

No they do not.

Hope this helps!

I need help ill giv3 brainlyness​

Answers

The answer is d hope this helps☺️

Answer:

i think the answer if (-9,-3)

Step-by-step explanation:

Tell me if i got it right so i can see where i made a mistake IF i got it wrong

could someone help me with this ? i need to find m

Answers

the three angles of a triangle always add up to 180 degrees.

So, add the three angles together!

2x - 12 + 2x + 17 + 9x - 7 = 180

Group the similar numbers together.

13x -2 = 180

13x = 182

x = 14

Plug x in to 2x + 17

14*2 + 17 = 45

mX = 45 degrees

Answer:

m∠X = 45°

Step-by-step explanation:

All angles in a triangle add up to 180°

2x - 12 + 2x + 17 + 9x - 7 = 180

13x = 180 - 17 + 12 + 7

13x = 182

x = 14°

m∠X = 2x + 17

sub x = 14° into m∠X

2(14) + 17

m∠X = 45°

What is the equation of the line that passes through the point (-6,3) and has a slope of -2/3

Answers

Answer:

The answer is y=-2/3x-1

Step-by-step explanation:

y-y=m(x-x1)

y-3=-2/3(x-(-6))

y-3=-2/3x-4

+3 +3

y=-2/3x-1

if 6 litres of petrol cover's 60km , how many litres of petrol will a car need to cover 50km​

Answers

Answer:

5 litres

Step-by-step explanation:

60 ÷ 10 = 6

50 ÷ 10 = 5

So 5 litres of petro

I hope this helped, please mark Brainliest, thank you!

2(x2 + 6) – 3 vy when x = 3 and y = 64.

Answers

Answer:

73

Step-by-step explanation:

you would do distributive property we know x= 3 so on the inside would be 32 now since we are doing distributive property you multiply 32x2 and 6x2

then you add them together and after you subtract 3 from 76 which = 73

A cook has 11.64 pints of olive oil before the dinner service. There were 5.2 pints of olive oil used during the dinner service. What amount of olive oil is left after the dinner service, with the correct number of significant digits?

A. 6.44 pints

B. 16.84 pints

C. 6.4 pints

D. 17 pints ​

Answers

Answer:

c

Step-by-step explanation:

a truck weighs 9,000 pounds. a repair shop sends a tow truck that can pull 5 tons.can the tow truck tow the truck? explain.

Answers

Yes! A ton is 2000 pounds and the tow truck can pull 5 tons, so you multiply 5 by 2000. That is 10,000 pounds and is more than 9,000 pounds which is how much the truck weighs. So the tow truck can tow the truck

Hope this helps

If you have 6 pieces of plywood
that are 4'x8', how many total
1xl pieces can you get out if
you use all of them?

Answers

Answer:192

Step-by-step explanation:

Calculate the area l*w or s*s

Divide the two areas to get the number of 1*1 from 1 plywood then multiply by their number which is 6 here

4*8=32/1=32*6=192

Nothing but slope.................

Answers

Answer:

1. 1

2. 3

3. 4

Step-by-step explanation:

Question
Help me -.8+ 2X = .3 - x

Answers

Step-by-step explanation:

2x+x=.3+.8

3x= 1.1/:3

x=0.366

Answer:

x = -2.566667

Step-by-step explanation:

simplify both sides

8 + 2x = 0.3 - x

8 + 2x = 0.3 + - x

2x + 8 = - x + 0.3

add x to both sides

2x + 8 + x = - x + 0.3 + x

3x + 8 = 0.3

subtract 8 from both sides

3x  + 8 - 8 = 0.3 - 8

3x = -7.7

divie both sides by 3

3x/3 = -7.7/3

x = -2.566667

due 7:59 am est. Faith is saving up to buy a new bicycle. She already has $40 and can save an additional $6 per week using money from her after school job. How much total money would Faith have after 8 weeks of saving? Also, write an expression that represents the amount of money Faith would have saved in w weeks.

Answers

Answer:

After 8 weeks, Faith would have $88. money saved = 40+6w

Answer:

$88 saved in 8 weeks

Step-by-step explanation:

Part 1:

You would first set up the equation 40 + (6 x 8) = t. T would be the total money saved. You would then do 6 times 8 first, as they're in parenthesis. You would get 48. You now have 40 + 48 = t. You would now add like terms, and you would get 88 = t. You would save $88 in 8 weeks.

Part 2:

40 + 6w = t

w would represent the number of weeks, t would represent the total number of money saved.

what is the answer to (x+3)^2 +(y-6)^2

Answers

Answer:

1the answer is 1! hope this helps.

The answer is x^2+ y^2-27

8. If b(x) = -2(x-50), what is the value of
b(20)? Request

Answers

-2(20-50)

60 is your answer

5.
For each equation, determine if x = 2 is a solution. Explain or show your reasoning.
a.
-2(x – 4) = 4
b.
26
= 13
C.
-3.8x = -7.4
4(x - 1) – 3(x - 2) = -8
d.

Answers

A. Yes because -2(2-4) does equals =4
B. Yes because 26/2 does equals = 13
C. No because -3.8(2) equals -7.6 and not -7.4
D. No because 4(2-1)-3(2-2) equals 4 and not -8

x=2 is a solution of equations -2(x – 4) = 4 and 26/x=13

What is Equation?

Two or more expressions with an Equal sign is called as Equation.

-2(x-4)=4

-2(2-4)=4

4=4

Hence, x=2 is the solution

26/x=13

Now x=2

26/2=13

13=13

Hence, x=2 is the solution

-3.8x=-7.4

Now x=2

-3.8×2=-7.4

-7.6=-7.4

x=2 is not a solution of -3.8×2=-7.4

4(x - 1) – 3(x - 2) = -8

4(2-1)-3(2-2)=-8

4=-8

x=2 is not a solution of -3.8×2=-7.4

Hence, x=2 is a solution of equations -2(x – 4) = 4 and 26/x=13

To learn more on Equation:

https://brainly.com/question/10413253

#SPJ2

G
Mr. Chang's class has 28 students, 7 of whom are girls. Which equation shows how to determine the number of girls in
Mr. Chang's class?
o 28-4-49
0 28 x 7 - 16
017-28 - 11
o 1-28-

Answers

Answer:

Girls in Mr. Chang's class: 28 - 21 ; # girl students = # total students - # boy students ; 7 girl students.

Boys in Mr. Chang's class: 28 - 7 ; # boy students = # total students - girl students ; 21 boy students.

The amount of money that Jacob earns based on the number of hours he works is shown in the table. Find the constant of proportionality.

Answers

Answer:

Y=7.5x

Step-by-step explanation:

8-5=3 and 60-37.5 is 22.5 divide 22.5 by 3 and you get 7.5 which is the rate that he earns an hour

the length of a rectangle is 8 units greater than its width . find the dimensions when its area is 105 square units.

Answers

I hope this helps ;)

Find the distance between the two points in simplest radical form.
(1,8)(6,-4)

Answers

Distance in simplest radical form is 13

Or root 169

A recent survey by the alumni of a major university indicated that the average salary of 10,000 of its 300,000 graduates was $125,000. What is the Population?

Answers

Answer:

The population is the total number of the universities  graduates  i.e [tex]N = 300,000[/tex]

Step-by-step explanation:

From the question we are told that

  The number of students that are consider is  n = 10,000

   The total number of graduates is  [tex]N = 300,000[/tex]

  The mean is [tex]\= x = \$125 , 000[/tex]

Here the population is The total number of graduates with value  [tex]N = 300,000[/tex], this is because a population is the pool from with a sample is drawn and in this case the pool is [tex]N = 300,000[/tex] while the sample with is drawn is  n = 10,000

 

is y=x/4 a proportional relationship

Answers

Answer:

yes

Step-by-step explanation:

The function f(x) = x/4 represents a proportional relationship.

What is a proportional relationship?

Proportional relationships are relationships between two variables where their ratios are equivalent.  A straight line represents a proportional relationship. Mathematically -

y = mx + b

(y - b)/x = m       [m is constant]

or

y = mx

m = y/x               [m is constant]

Given is the following function -

y = x/4

We have -

f(x) = x/4

Now, we know a straight line represents a proportional relationship. The general form of equation representing the proportional relationship is -

y = mx

where -  [m] is constant

y = x/4

y = (1/4)x

On comparing, we get -

m = 1/4

Hence, the function f(x) = x/4 represents a proportional relationship.

Therefore, the function f(x) = x/4 represents a proportional relationship.

To solve more questions on proportional relationship, visit the link below-

brainly.com/question/19306970

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Can someone help explain how I get the answer for this? S=R-rR solve for R

Answers

Answer:

s/(1-r)=R

Step-by-step explanation:

S=R-rR

S=R(1-r)

s/(1-r)=R

Use the graph below to answer the question. Quadrilateral PQRS will be rotated 90° clockwise about the origin resulting in quadrilateral P'Q'R'S'. Which statement is true

Answers

Answer: it’s D

Step-by-step explanation:

HELP NOW 15 Points!!!!!!!
Which expression is not equivalent to the other three?
2x + 2+ 2x + 3x – 8
4 + 7x – 2
–2 + 5x + 2x – 4
8x – x – 6

Answers

4 + 7x - 2
That is the different one.

Answer:

4+7x-2

Step-by-step explanation:

i dont know how nit is the anwser put i got it right

Witch fraction is not in simplest form 5/15 or 5/12

Answers

5/15, it can still be divided by 5
5/15 in simplest form is 1/5

Select all the expressions that can be used to find the price of a $400 telescope after a 32% markup. A)400 • 0.32 B) 400 • 3.2 C)400 • 1.32 D)400 + 400(0.32) E)400 • 400(1.32)

Answers

Answer:

(D) 400 + 400(0.32)

Step-by-step explanation:

We need to find the price of a $400 telescope after a 32% markup.

32% markup means increase in the cost of telescope by 32%. It can be calculated as follows :

[tex]P=400+32\% \ of\ 400\\\\=400+\dfrac{32}{100}\times 400\\\\=400+0.32(400)[/tex]

Hence, the correct expression is option (d).

Answer:

(D) 400 + 400(0.32)

Step-by-step explanation:

We need to find the price of a $400 telescope after a 32% markup.

32% markup means increase in the cost of telescope by 32%. It can be calculated as follows :

Step-by-step explanation:

what is the input value other than -7 for which h(x)=3

Answers

Answer:jrntker,fgv;rmjhnopgykjpftg.l/;[]ref

Step-by-step explanation:

wem,yk6iotfkmmkgjjjkdlmeruijtnmgjhudjmv n

Jake has $100 dollars in his wallet. He spends $15 at Tastee Sub and $10 at Wawa. As he is walking home, Jake finds a $20 bill on the ground. Then Brandon comes along and borrows $40 from jake. That night jake decided to do some chores at home and earns $35. How much does jake end up with at the end of the day

Answers

Answer: $75

Step-by-step explanation:

PLS HELP!!!!!!!!!!!!!

Answers

First, multiply the top equation by 2 and bottom by -3.
60x+60y=900
-60x-75y=-1035
————————
-15y=-135
—————-
-15=-15
y=9

So the answer should be 9.
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