An object is launched from a platform. its height in meters X seconds after the launch is modeled by h(x)=-5x^2+20x+60 how many seconds after launch Will the object land on the ground
Answer:
6 seconds after launch.
Step-by-step explanation:
You should make sure there aren't odd symbols in your question when you post it.
Assuming it is just the equation -5x^2 + 20x + 60, if you graph it you can see the path of the ball. at x=0 this is the starting point It then hits the ground when it touches the x axis. So this is finding zeroes of a quadratic.
You could do this several ways; find a way to factor it, guess and check, the quadratic formula or completing the square. I will complete the square as that is what I am most used to. If you would like to see another let me know.
The first step in completing the square is making sure the x^2 has a coefficient of 1, so now it has -5 so we have to factor out -5 from the equation.
-5x^2+20x+60 = -5(x^2 - 4x - 12)
Now you only really need to focus on the factored expression, but I will continue writing everything. The next step is to find (b/2)^2 where b is the coefficient of the x term. In this case -4. so (b/2)^2 = (-4/2)^2 = 4.
Again, focusing on x^2 - 4x - 12 you want to add and subtract (b/2)^2 from that expression. since you are adding and subtracting you are not changing the value, but we can use this.
-5(x^2 - 4x - 12) = -5(x^2 - 4x - 12 + 4 - 4)
Here you want to rearrange it a bit. Originally c was the constant term, -12, now you want it to be the positive (b/2)^2, which is positive 4. also you can combine the two other constant terms. the original c and -(b/2)^2, but I will hold off for now so I don't do too much at once.
-5(x^2 - 4x - 12 + 4 - 4) = -5(x^2 - 4x + 4 - 12 - 4)
Now you focus on x^2 - 4x + 4. Hope fully you recognize this is the same as (x-2)^2. This always happens at this step of the process. also notice -2 = b/2. Using only variables here are the first steps.
ax^2 + bx + c
a(x^2 + (b/a)x + (c/a))
a(x^2 + (b/a)x + (c/a) + (b/(2a))^2 - (b/(2a)^2)
a(x^2 + (b/a)x + (b/(2a))^2 + (c/a) - (b/(2a))^2)
a((x + b/(2a))^2 + (c/a) - (b/(2a))^2)
Again, being able to make x^2 - 4x + 4 into (x-2)^2 or x^2 + (b/a)x + (b/(2a))^2 into (x + b/(2a))^2 willa lways happen. this is because if you expand (x + b/(2a))^2 you always get x^2 + (b/a)x + (b/(2a))^2.
Now I would combine the -12-4
-5(x^2 - 4x + 4 - 12 - 4) = -5((x - 2)^2 - 12 - 4) = -5((x - 2)^2 - 16)
If you redistribute the -5 you get vertex form, but I am going to stop here because I will just undo that in the next step. So this is the form you want. Finally we can find when it equals 0. So, you set this equal to 0 and use algebra to solve.
-5((x - 2)^2 - 16) = 0
Divide both sides by -5
(x-2)^2 - 16 = 0
add 16 to both sides
(x-2)^2 = 16
Take the square root of both sides, but also count botht he positive and negative version of the answer. the reason is both 2 and -2 squared get you 4.
x - 2 = +/-4
I am using +/- to indicate I am using both positive and negative 4. Now though add 2 to both sides. since you have +/- 4 you are going to get two different results. -4+2 and 4+2
x = -2 and 6.
now, the question wants times after x=0 (the start) so you only get 6. so x=6, or in other words 6 seconds after launch.
Let me know if you have any questions.
Answer:
6
Step-by-step explanation:
sorry no step by step explanation because I’m in a rush please mark me as brainliest bye have a great day !!! :D
Please give real answers with an explaination. 50 points + 5-star rated. No Docs/No Files/No Links only answer with explaination.
Answer:
Te diagonal of a kite will form a parallelogram.
explanation:
Kite properties include (1) two pairs of consecutive, congruent sides, (2) congruent non-vertex angles and (3) perpendicular diagonals. Other important polygon properties to be familiar with include trapezoid properties, parallelogram properties, rhombus properties, and rectangle and square properties.
hope it helps
Mark me as brainlist
Bab isn’t big-brained enough for mafs. Help, please?
Divide using long division! Show your work. As soon as possible!
Answer:
Step-by-step explanation:
if you've any doubt just ask :)
Ava buys a book for 8.58. She pays with a $10 bill. How much change will she get?
Answer:
1.42
Step-by-step explanation:
I need help with this question please
Answer:
angel BAC=CBD
BAC=43°because CBD also 43°
Solve for x and show work
Answer:
6.14 rounded to the nearest hundreth.
Every paralelogram equals 360º. And every oppisite angle is eqaul to each other. So by doing the math we can tell the smaller angles is 80º. Now we solve for x.
80=7x+37 minus 37 from both sides
43=7x. then divide both side by 7 to cancel it out
6.14=x that is the answer rounded
You can check by inputing x's vaule into the equation and getting the angle measurment we solved for which is 80º.
7(6.14)+37
by doing this you get 80, the measure of the angle so the vaule for x is 6.14 rounded to the nearest hundreth.
NEED HELP ASAP skajsjsjjajaja
Answer:
The answer is "3"
Step-by-step explanation:
[tex]\to f(7)=f(5 + 2)=1+f(5)\\\\\to f(5)=f(3+2)=1+f(3)\\\\\to f(3)=f(1+2)=1+f(1)=1+0=1\\\\[/tex]
Therefore
[tex]\to f(7)=1+f(5)=1+1+f(3)=2+1+f(1)=2+1+0=3[/tex]
CAN SOMEONE PLEASE HELP ME I'M STUCK. PLEASE
I don't understand and know how to solve it.
Answer:
7/10
Step-by-step explanation:
red + green = 50 + 20 = 70 marbles
Total marbles = 50 + 30 + 20 = 100 marbles
P(red or green) = 70/100
P(red or green) = 7/10
what is the solution of in(x-2)^2=6
Answer:
22.09
Step-by-step explanation:
Given the expression ln(x-2)^2=6
Take exponent of both sides
e^ln(x-2)^2=e^6
(x-2)² = e^6
(x-2)² = 403.43
x - 2 = √403.43
x - 2= 20.09
x = 20.09 + 2
x = 22.09
Hence the value of x is 22.09
Select all the equations
represented by this tape diagram.
A. 6 + 6 + 6 + 6 + 6 = ?
B. 5 + 6 = ?
C. ? = 6.5
D. ? = 6.6.6.6.6
E. ? = 5 = 6
F.5 = ?= 6
Answer:
D.
is the correct answer
The owner of a small restaurant bought 75 kilograms of rice. Each week, the restaurant uses 4.5 kilograms of rice.
Function r gives the remaining amount of rice, in kilograms, as a function of the number of weeks since the restaurant
owner bought the rice.
Complete the table. Type the answers in the boxes below.
WEEKS
KILOGRAMS OF RICE LEFT
6
12
Answer:
6 weeks = 48 kg
12 weeks = 21 kg
Step-by-step explanation:
6 weeks:
4.5 x 6 = 27 kg
75 - 27 = 48 kg
12 weeks:
4.5 x 12 = 54 kg
75 - 54 = 21 kg
Hope this helps!
Use the Fundamental Counting Principle to find the number of outcomes from tossing a quarter, a dime, and a nickel.
Answer:
aaaaaaaaacvvrcgb
If 6 newborn babies are randomly selected, how many different gender sequences are possible?
a. 720
C. 12
b 36
d. 64
Answer:
D.64
Step-by-step explanation:
im not slow itz simple 2 to the power of 6
Math help please help fast
Step-by-step explanation:
Angle C: 50 degrees
Angle E: 55 degrees
Angle D: 50 degrees
Angle A: 125 degrees
Angle B: 75 degrees
a ball is shot out of a homemade air cannon. It flies through the air such that its height, as a function of time, is given by: h= -16t^2 + 64t + 10. where h is the height of the ball in feet and t is the time since it was fired in seconds. Max estimates that it takes 4 seconds for the ball to hit the ground and Cole estimates it takes 5 second. Algebraically determine who is closer and support your answer.
Answer:
Max
Step-by-step explanation:
the function given that h = -16t³+64t+10
the general function Equation:
h = at²+bt+c
=> t at the highest point is defined by t = -b/2a
= -64/2(-16) = -64/-32 = 2 second
the total times that the ball hits the ground
= 2× 2 seconds = 4 seconds.
so, Max is right
Answer:
Solution given:
Let h=0=when the ball hit the ground,the height=0.
h= -16t^2 + 64t + 10.
0=16t²-64t-10
8t²-32t-5=0
∆=[tex] \frac{32±\sqrt{32²+4*5*8}}{2*8}=\frac{8±\sqrt{74}}{4}[/tex]
taking positive
t1=[tex] \frac{8+\sqrt{74}}{4}=4.15seconds[/tex]
t2=[tex] \frac{8-\sqrt{74}}{4}(t2<O)(neglected)[/tex]
So
t=4.15seconds closer to 4seconds.So
Max is closer.
got it wrong help a girl out please thank you
Calculate the volume of a cone with: 11cm height and 6cm radius
Answer:
volume=1243.44 cm^3
Step-by-step explanation:
volume of a cone=πr^2h
=3.14*(6)^2*111
=3.14*36*11
=1243.44 cm^3
Answer:
V=414.69cm³
Step-by-step explanation:
use v=πr²h/3
pie is 22/7 so when you fix in your values you will get the answer
please help me I will mark as a brainliest
Answer:
think that this might help you
Help me! PLEASE! help help help help help help help help help help help help!!!!!!
Sara's results probably do have a higher mean, if we take into account how William is way more willing to pay 20 dollars. Honestly, I think you got your chosen answers right! Just my opinion, as someone inexperienced.
hrs 45 min 67+ hrs 3. min 67
Answer:
hrs 50 min 14
Step-by-step explanation:
hrs 45 min 67 = hrs 46 min 7
hrs 3. min 67 = hrs 4 min 7
Total
hrs 46 min 7
+ hrs 4 min 7
————————
hrs 50 min 14
Figure ABCD is a kite. Find the
value of x.
B
A 2x + 10
С
2x
D
x = [?]
Enter
Answer:
x = 20
Step-by-step explanation:
The diagonals of a kite are perpendicular to each other, so the 4 angles at the intersection are right.
The sum of the 3 angles in a triangle sum to 180° , then
2x + 2x + 10 + 90 = 180
4x + 100 = 180 ( subtract 100 from both sides )
4x = 80 ( divide both sides by 4 )
x = 20
Answer:
20 is the answer
Step-by-step explanation:
Correct for Acellus!
Tonya's dog walking service charges a flat rate of $20 per month, plus $3 Per mile that each dog is walked. Beth does not charge a monthly fee for her dog walking service, but she charges five dollars per mile that each dog is walked.
pls helppp!
Answer:
A) 20+3m = 5m
Step-by-step explanation:
20+3m = 5m
20 = 2m
m = 10
after each girl has walked dogs for 10 miles, their amount they charge would be equal
Tonya would charge: 20+3(10) = 20+30 or $50
Beth would charge: 5(10) or $50
the sixth graders rasied money to fund a feild trip. the five classes raised $42, $51, $38, $49, and $40. what is the median on the ammount of money raised?
a. $36
b. $42
c. $40
d. $13
Answer:
The median is $42, or B.
Step-by-step explanation:
Our numbers are :
42, 51, 38, 49, and 40.
The first step to finding the median is ordering the numbers from least to greatest.
38, 40, 42, 49, 51.
Now we find the number perfectly in the middle - that's 42, between 49 and 40. The median is $42, or B.
Please mark brainliest!
I also need help with this lol
Answer:
Luca
Step-by-step explanation:
Juan 566/734 = 0.7711
Luca 7/9= 0.7777
Luca has a greater percentage
Mr sharma can do 1/15part of piece of work in 1 day he worked for 3 days and left if Vishnu finished the remaining work how much work is done by bishnu?
Answer:
12/15
Step-by-step explanation:
if in one day mr sharma did 1/5 part of piece of work and he worked three days he did 3/15, if vishnu finished the remaining work then he did 12/15 parts, they did 15/15
HELP ASAP
Answer:
it think it is 26
Step-by-step explanation:
as angle on a straight line add up to 180
so 180-64-90=26
hope this helps :)
Grant is working at a veterinarian's office, and he needs to give a dose of medicine to a
25 kg dog. If a 10 kg dog needs 18 mL of the same medicine, how many milliliters of
medicine does the 25 kg dog need?
Answer:
45ml
Step-by-step explanation:
10 kg needs 18mL
So, 1kg = 1.8ml
25kg needs = 1.8kg/ml x 25 kg
25 kg dog would need 45ml.
Answer:
45 ml
Step-by-step explanation:
Weight of the dog and quantity of medicine is in Direct proportion.
Let the quantity required for 25 Kg dog =x
10 : 18 :: 25 : x
Product of extremes = product of means
10 * x = 18 * 25
[tex]x = \frac{18 * 25}{10}\\\\x = 9 * 5 \\\\x = 45[/tex]
Which term is a perfect square of the root 3x^4
The product of two consecutive even integers is 36 less than 18 times their sum. Find the two integers
Answer:
34 and 36
Step-by-step explanation: 7 1 17 15
product of two consecutive even integer x(x+2) x is even
product of two consecutive even integer x(x + 2) plus 36 equal 18(x +x + 2)
x(x+2) + 36 = 18(x +x +2)
x² + 2x + 36 = 18x + 18x + 36 36's cancel, 2x - 36x = -34x
x² - 34x = 0 solve for x
x( x - 34) = 0 x = 0 and 34 only 34 is an even number!
x = 34 and 36
