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

If km and np are parallel lines and m

Answers

Answer:

60 degrees

Step-by-step explanation:

Deon has $600 in his saving account
•He spends $15 per month on Netflix
•He spends $5 per month in Hulu

If he does not make any more purchases, select all of the months that he can continue to have the subscription before he goes into debt.

Answers

Answer:

30 months total

Step-by-step explanation:

15+5=20

600÷20=30

An element's identity is determined by the number of

Answers

Answer:

number of protons

Step-by-step explanation:

The identity of an element is determined by the number of protons. One cannot alter the number of protons without altering the identity of the element. By adding a proton, the atomic number increases by one and the element identity changes. Number of neutrons can be altered to create isotopes.

Markus receives dollar bills from his grandfather for one week. On the first day he received $1; on the second day he received $2, on the third day he received $4, and on the fourth day he received $8. If this continues, how much money will Markus have in total by the end of the week?

(Don't forget your units.)

Answers

Answer:

$127

Step-by-step explanation:

1+2+4+8+16+32+64=127

The second the is doble the first day, the third day is double the second day, the fourth day is double the third day, keep on continuing the patern.

Answer: Markus will receive $64 dollars at the end of the week.

Step-by-step explanation: 1*2=2     2*2=4       4*2=8      8*2=16     16*2=32

32*2=64

PROBLEM I WITHOUT A CALCULATOR)
1. A room is warming up such that the temperature rise, in degrees Fahrenheit, is proportional
to the time the room has been heating. After 4 minutes, the room temperature rose 12 °F.
(a) What is the constant of proportionnlit for the

Please help

Answers

Answer:

12 minutes I think question kinda confusing

CAN YOU PLEASE HELP ME CORRECT ANSWER GETS BRAINLIST !

Answers

Answer:

25

Step-by-step explanation:

7^2+24^2=625 the sqr root of 625 is 25

Answer:

Answer is 25

Step-by-step explanation:

[tex]24x^{2} +7x^{2} =25x^{2}[/tex]

Please help asap
25m^2+30m-30m-36

Answers

Answer:

(5m+6) (5m-6)

Step-by-step explanation:

That's how you factor it since +30 and -30 cancel out

So first of all, 30m and -30m cancel each other out so you are left with 25m^2-36.

You’ll notice that 25m^2-36 is a difference of two squares equation so your answer is (5m-6)(5m+6).

What addition statement does this show?

A. 10 + 3 = 13
B. 10 + (–3) = 7
C. –10 + 3 = –7
D. –10 + (–3) = –13
please answer as soon as you can!<3

Answers

Answer:

I think the answer is A sorry if I am wrong

Step-by-step explanation:

Answer:

The answer is b

Step-by-step explanation:

10 + (-3) = 7

Two shapes with equal perimeter are pictured below.




What is the measure, in units, of CD¯¯¯¯¯¯¯¯?

Answers

Answer:

Measure of CD = 17 units

Step-by-step explanation:

Perimeter of a polygon = Sum of measures of all sides of the polygon

Perimeter of the given rectangle = 2(length + width)

                                                       = 2[(x + 3) + (2x - 1)]

                                                       = 2(3x + 2) units

Perimeter of triangle EFG = EF + FG + GE

                                           = (x - 7) + (4x - 8) + (3x + 1)

                                           = (8x - 14)

                                           = 2(4x - 7) units

Since, perimeters of both the figures are equal,

2(3x + 2) = 2(4x - 7)

3x + 2 = 4x - 7

4x - 3x = 7 + 2

x = 9

Measure of CD = (2x - 1)

                         = 2(9) - 1

                         = 17 units

Judy has 2 3/4 bags of rock that she wants to use in her yard. Each bad will cover 310.2 sq ft. How many square feet will Judy be able to cover if she used all the bags of rocks? Round up your answer to the neatest tenth place.

Answers

Answer:

853.1 sq ft

Step-by-step explanation:

Total bags of rock = 2 3/4

Each bag will cover 310.2 sq ft

How many square feet will Judy be able to cover if she used all the bags of rocks?

Total Square feet covered = number of bags of rock × area covered by each bag

= 2 3/4 × 310.2 sq ft

= 11/4 × 310.2 sq ft

= 853.05 sq ft

To the nearest tenth

= 853.1 sq ft

The average of your 3 quiz grades is 17 points. Two of your quiz grades are 14 points and 19 points. Write and solve an equation to find the score of your third quiz.

Answers

Answer:

The equation would be 14+19+x=51, and the 3rd quiz score would be 18.  

Step-by-step explanation:

To get to the average, you have to add all the quiz scores and divide by the number of quizzes. If you work backwards, you can multiply the average by the number of quiz scores, which is 51. Then you subtract the known test scores, and you get your answer.

Please help me solve this problem

Answers

x=66
subtract 103 degrees from 180 to get 77, then add 77 and 37 together and subtract by 180
First you have to subtract 180 to 103 and you get 77 because a straight line always add up to 180, then you have to add that 77 to the 37 that is inside of the triangle and you get 114 and then you subtract 180 to 114 and you get 66 because the sum of the angles inside of the triangle is 180 degrees
The final answer is x= 66
Hope that helps.
And hope you understand how to do it :)

PLEASE HELP ASAP!!!

OK SO I SOLVED ALL OF THIS: It costs a company $20 per box to make pocket-sized stuffed animals. The company also has a fixed manufacturing cost of $2300. The owners are trying to calculate their cost for making boxes of animals. --Function Rule: c(x) = 20b + 2300.

BUT I NEED HELP WITH THIS!!! Use your function rule to find out how many boxes of stuffed animals can the company manufacture for $5000? SHOW WORK.

basically just show the work to find out what "b" would have to be in order for the
answer to be $5,000 i would appreciate it so much :) please help this is due today :(

Answers

Answer:

The company can manufacture 135 boxes of stuffed animals for $5000

Step-by-step explanation:

To find b, substitute $5000 for c(x), so

5000 = 20b + 2300

Then subtract 2300 from both sides of the equation, so

5000 (-2300) = 20b + 2300 (-2300)2700 = 20b

Finally divide both sides of the equation by 20, so

2700/20 = 20b/20135 = b

To check your answer substitute 135 in as b...

c(x) = 20(135) + 2300c(x) = 5000

:( can sum1 please help me I got 15min till its due and well my grades are due in 5 and I'm really suck at this question

Answers

Answer:

14 is the answer your welcome

Answer: If Noah scored twice as many points as Diego that’d mean Diego scored 5 points, since 10*.5=5, and that’d also mean Andre scored 14 points.

WILL GIVE BRAINLIEST. Will report if answer is absurd What is the trademark of a linear table?

Answers

Answer:

You can tell if a table is linear by looking at how X and Y change. If, as X increases by 1, Y increases by a constant rate, then a table is linear. You can find the constant rate by finding the first difference.

Step-by-step explanation:

Hope this helps!

Vanessa wanted to buy chocolate online. The Chocolatier A offers 2 pounds of chocolate for
$32.50, while the Chocolatier B offers 2 pounds of the same chocolate for $35.00. Which
company is offering the lowest price per pound?
Both companies have the same price
Chocolatier B
Chocolatier A

Answers

Answer:

Chocolatier A has the lower price.

Step-by-step explanation:

32.50 < 35

Dennis is getting balloons for his grandfather's birthday party. He wants each balloon string to be 9 feet long. At the party store, string is sold by the yard. If Dennis wants to get 69 balloons, how many yards of string will he need?

Answers

Answer:

207

Step-by-step explanation:

9ft=3yrds

3x69=207

find the value of 1/2×3/5 +1/2×2/5 by using suitable property.
please answer this friends​

Answers

Answer:

[tex]\frac{1}{2}[/tex]

Step-by-step explanation:

Given

[tex]\frac{1}{2}[/tex] × [tex]\frac{3}{5}[/tex] + [tex]\frac{1}{2}[/tex] × [tex]\frac{2}{5}[/tex] ( perform multiplication before addition )

= [tex]\frac{3}{10}[/tex] + [tex]\frac{2}{10}[/tex]

= [tex]\frac{5}{10}[/tex] ( divide numerator/ denominator by 5 to simplify )

= [tex]\frac{1}{2}[/tex]

Answer:

0.5

Step-by-step explanation:

first put the given below:

1/2 × 3/5 + 1/2 × 2/5 = 0

second take the first and second for the first answer to make the whole answer:

((1/2 × 3)/5) = 0

( 1/2 ) × 3 = 1.5

1.5/5 = 0.3

FIRST SOLVATION ( ANSWER ): 0.3

third , after we take the first solvation the second is we need to compute the remaining given or number:

((1/2 × 2)/5) = 0

( 1/2 ) × 2 = 1

1/5 = 0.2

SECOND SOLVATION ( ANSWER ): 0.2

and the last but not the list , the last is add the first solvation and second solvation and you will see what is the answer:

0.3 + 0.2 = 0.5

FINAL ANSWER: 0.5

Select the step in the solution that FIRST shows an error.
Step 1: 4x – 10 = 10
Step 2: 4x = 20
Step 3: 4x = 5
Step 4: X = 1.25
Step 1
Step 2
Step 3
Step 4

Answers

Answer:Step 3

Step-by-step explanation:

Can u guys PLEASE ANSWER THIS QUESTION ASAP URGENTLY

Find the equation of the parabola in general form

Answers

Answer:

x^2-4x+3

Step-by-step explanation:

Since the zeroes of the quadratic are 1 and 3, we can set up an equation in factored form:

(x-1)(x-3)

=x^2-4x+3

We can further check that this is the right answer by evaluating it at the vertex:

(2)^2-4*2+3=-1

Since that corresponds to the graph, the answer is x^2-4x+3

Anthony says that the expression abc has three terms because it uses three different variables. Critique Anthony's reasoning and explain whether he is correct.

Answers

Answer:

Anthony's reasoning is incorrect

Step-by-step explanation:

The expression abc is not made up of three terms because it is just an entity. For the expression to be called a three term expression, each of the variables must be separated using mathematical signs. For example, the expression a + b + c can be referred to as three terms because each variables are separated by a plus sign. In this case they are different entity.

From the above explanation, we can conclude that Anthon's reasoning is incorrect. The expression abc is just one term not three terms.

Which figure has the largest shaded region?

Answers

Answer:

is A

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Both the others have 3/4 shaded c has less

0.409 +0.681
can you add this with the repeating decimals?

Answers

Answer:

Yes, you can and the answer would be 1.09.

Step-by-step explanation:

The answer is 1.09 I believe

Albie's total income is $695.25 in a week
where his sales are $2870. If he earns a
commission of 7.5% of his sales, what is
his retainer? can you tell me how to work it out aswell please​

Answers

Answer:

Step-by-step explanation:

7.5/100= .075

$580000 x .075 = $43,500 commission

Is 5.1 times 10 to the power of 9 a scientific notation?

Answers

Answer:

yes

Step-by-step explanation:

hope it helps

it will be written as 5.1×10^9

Answer:

yes

Step-by-step explanation:

A number in scientific notation consists of the product of a number from 1 to under 10 and an integer power of 10.

5.1 is a number from 1 to under 10.

10^9 is an integer power of 10.

Therefore, 5.1 * 10^9 is a number written in scientific notation.

Ms. Pitt went to dinner with her family. The bill came to $55 left a 20% tip. How much money did Ms. Pitt spend in all?

Answers

$66
Tip = 55 x .2 = 11
Total = 55+ 11 = 66

What is the solution to the system of equations?
y= 1/3x-10
2x + y = 4

Answers

34756Step-by-step explanation:

Noah pays $7.65 for a cappuccino on days he's running late to work. One week, he was late on Monday, Wednesday, and Friday. How much did he spend (in $) on cappuccinos that week? $

Answers

Answer:

Amount Noah spent on cappuccino for that week = $22.95

Step-by-step explanation:

Noah pays $7.65 for a cappuccino on days he's running late to work

Cost of cappuccino per day = $7.65

One week, he was late on Monday, Wednesday, and Friday.

That is 3 days in a week

How much did he spend (in $) on cappuccinos that week? $

Amount Noah spent on cappuccino = cost of cappuccino per day × 3 days

= $7.65 × 3

= $22.95

Amount spent on cappuccino for that week = $22.95

two intersecting lines cannot be both parallel to the same line ?
True or false​

Answers

Answer:

true it is true two inter

FOR A TEST!! HELP! Complete the similarity ratio for the similar triangles.

Answers

Answer:

add them up

Step-by-step explanation:

add 8 10 10 and 80 25 20

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