A man drops a ball from the top of a 300 foot cliff. The height of the falling ball is modeled
by h(t)=-16t2+300 where h is in feet and t is in seconds. How long does it take for the ball to be 44 feet above the ground?
Answer:
The ball reaches 44 ft above the ground after 4 sec.
Step-by-step explanation:
Set h(t)=-16t^2+300 equal to 44 feet and solve for time, t. Indicate exponentiation with " ^ "
-16t^2 + 300 = 44 becomes
-16t^2 + 256 = 0, or 16t^2 = 256. Then, taking the square root of both sides, we get:
4t = 16, or t = 4 sec. The ball reaches 44 ft above the ground after 4 sec.
The ball will take 4 seconds.
What are quadratic equations?A quadratic equation, or simply "quadratics," is a polynomial equation with a degree of two as its highest. This is how it is expressed:
a x² + b x + c = 0 where x is the unknown variable and the constant terms are a, b, and c.
Given equation of height h(t) = -16t² + 300...…..(1)
where h is height in feet and t is time in seconds,
and height at t = 0 is 300 feet
when ball is 44 feet above ground then time is,
put h = 44 in equation 1
44 = -16t² + 300
16t² = 300 - 44
t² = 256/16
t = √16
t = 4
Hence time taken by ball is 4 seconds.
Learn more about quadratic equations;
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X A padlock's combination is five digits long using the digits o through 9. 0/4 Numbers can repeat within the combination. What is the probability that my combination has all even numbers in it (for example 22222 or 86840)? 0.01 w 0.03 0.05 Х O 0.1 Correct answer 0.03 OFC mooton Monday or Tuesday at 3PM 4PM
Answer:
Before we discuss permutations we are going to have a look at what the words combination means and permutation. A Waldorf salad is a mix of among other things celeriac, walnuts and lettuce. It doesn't matter in what order we add our ingredients but if we have a combination to our padlock that is 4-5-6 then the order is extremely important.
If the order doesn't matter then we have a combination, if the order does matter then we have a permutation. One could say that a permutation is an ordered combination.
The number of permutations of n objects taken r at a time is determined by the following formula:
P(n,r)=n!(n−r)!
Example
A code have 4 digits in a specific order, the digits are between 0-9. How many different permutations are there if one digit may only be used once?
A four digit code could be anything between 0000 to 9999, hence there are 10,000 combinations if every digit could be used more than one time but since we are told in the question that one digit only may be used once it limits our number of combinations. In order to determine the correct number of permutations we simply plug in our values into our formula:
P(n,r)=10!(10−4)!=10⋅9⋅8⋅7⋅6⋅5⋅4⋅3⋅2⋅16⋅5⋅4⋅3⋅2⋅1=5040
In our example the order of the digits were important, if the order didn't matter we would have what is the definition of a combination. The number of combinations of n objects taken r at a time is determined by the following formula:
C(n,r)=n!(n−r)!r!
Four friends are going to sit around a table with 6 chairs. In how many ways could the friends sit?
Step-by-step explanation:
Which equation represents a line which is parallel to the line 2x+y=-82x+y=−8?
y= 2x-1
y= -2x+1
y= 1/2x -6
y= -1/2x -5
Answer:
x=7 is the line parallel to the given line x=8 . Parallel lines are the lines which are always same distance apart and never intersect. The given line is x=8 with intersects the x axis at x=8 and it is parallel to y axis with slope infinite or not defined.
Step-by-step explanation:
The Tennis Club decided to buy T-shirts for its members. Action Sports Apparel quoted the following prices for the T-shirts.
Number of T-Shirts Total Cost (dollar)
11 153
16 213
21 273
Which equation best describes the relationship between the total cost, c(t), and the number of T-shirts, t?
A.
c(t) = 12 + 12t
B.
c(t) = 21t
C.
c(t) = 21 + 12t
D.
c(t) = 132t
Answer:
C. c(t) = 21 + 12t
Step-by-step explanation:
The table shows the admission fees to one conservatory at Gardens by the Bay. Mr Tan and his friends planned a group visit for three adults and nine children. Find the amount of money they had to pay for their tickets.
per adult $2.
Per child $8.
Answer:
78$
Step-by-step explanation:
3 adults, 2 dollars per adult. Multiply. 3(2) = 6
9 children, 8 dollars per child. Multiply. 9(8) = 72
Add to get total sum of money they needed to pay. 72+6 = 78
Please I need help!!!!
Answer:
y=1/4x-1
Step-by-step explanation:
So lets start off by going over what slope intecerp form is.
Slope intercept form looks like this:
y=mx+b
Lets go over the different values in this formula:
y is always going to just be what mx+b equals, and you can plug in values for x to solve for it.
m is always teh slope. The slope is y/x, basically just the change in y over the change in x.
x is going to be the number you plug in a value for to solve for y.When writing slope intercept form, this will always just be x.
Lastly we have b. This is what y equals when x is 0.
Lets use this to make our slope intercept.
So we have:
y=mx+b
y and x are not going to have a written value, so we only need to determine m and b.
So lets find b.
B will be the slope. When we look at the points on the graph, we see (-4, -2) and (0, -1)
The difference in y is -1.(-2--1=-1). The difference in the x is -4.(-4-0=-4).
So b will be: -1/-4, or just 1/4:
y=1/4x+b
Now lets find b.
Lets specificly lookat what y equals when x is 0 on the graph.
We can see the point is (0, -1)
So the y intercept is -1. This means b is equal to -1:
y=1/4x-1
This is your slope intercept!
Hope this helps! :D
Sorry for bad grammar, I am writting on a strange keyboard.
How many proportional relationships are shown in the coordinate plane below?
Answer:
The answer is A) There are no proportional relationship
Step-by-step explanation:
The green line does not go through the origin and it is curved. This is not a proportional relationship.
Problems: It does not go through 0,0 and it is curved.
----------------------------------------------------------------------------------------------------------------
The blue line may go through the origin but it is curved. This is not a proportional relationship.
Problem: It is curved.
----------------------------------------------------------------------------------------------------------------
The purple line does not go through the origin. This is not a proportional relationship.
Problem: It does not go through 0,0
----------------------------------------------------------------------------------------------------------------
Conclusion: Since the green, blue, and purple line are not proportional, this means zero lines are proportional.
Note:
I know my answer is very late but I wanted to help anyone who needs it for future reference.
The graph has 0 proportional relationships.
What shows proportional relation?
The graph of a proportional relationship is a straight line through the origin or a ray whose endpoint is the origin.
How many proportional relation in graph?
In the given graph, only one purple color curve is a straight line but it is not starting through the origin.
Therefore, the graph does not have any proportional relationships.
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expanding triple brackets, i will give brainliest
Answer:
Step-by-step explanation:
Easy
(x^2+10x+24)(x+3)
(x^3+10x^2+24x + 3x^2+30x + 72)
x^3 + 13x^2+54x+72
[tex]x {3}^ + 13x + 54x + 72[/tex]
I chose the first answer, was I correct?
Explain!
Answer: Yes, by SAS
Step-by-step explanation:
This is because, two sides are equal and one angle is equal.
And also there is one angle between 2 sides, so it’s SAS
I just got done with state testing. there were two problems I didn't know how to do so I sorta guessed. But when I got home I had to figure out how to do it. Like I don't know why, but it bothers me when there is a problem I don't know how to solve. Am I the only one who is like this or nah?
Answer:
na u aint
Step-by-step explanation:
i get that feeling all the time it sucks
I NEED HELP I FORGOT HOW TO DO THIS AND I NEED HELP
-3x + 2<8
Answer:
x > -2
Step-by-step explanation:
-3x + 2 < 8
our goal is to isolate the x
subtract two from both sides
-3x < 8 - 2
- 3x < 6
divide both sides by -3
flip the sign because we divided by a negative number
x > -2
A 6 kg rock is dropped off a 10 m cliff and hits the ground with a velocity of 12.5 m/s. How much work is done by air resistance on the rock
a:119j
b:588j
c:100j
d:196j
Show all work. 5. Find the surface area of the composite figure.
Answer:
4130 m²Step-by-step explanation:
[tex]2\cdot35\cdot20+2\cdot35\cdot15+2\cdot20\cdot15+2\cdot9\cdot18+2\cdot9\cdot21+18\cdot21=\\\\=1400+1050+600+324+378+378=4130\,m^2[/tex]
can an ace help me now plss
Answer:
Graph B
Step-by-step explanation:
[tex]y = x^2[/tex] is a quadradic function. It graphs as a parabola. It has a vertex point of (0,0) and it opens upwards.
See the graph attached.
Hope this helps.
Stephanie borrowed $4,500 at a simple interest rate of 3.5% to buy a motorcycle. How much interest did she have to pay if the loan was taken out for 3 years?
C
Step-by-step explanation:
hope this helps
Please Help me with this question!! I have a time limit
The Garcia family drives 3/4 of the distance to their grandparent's house
in 3/4 hour.
How many hours will it take
to drive to their grandparent's house at the same rate?
a= 1
b=9/16
c=1 and 7/9
Answer:
a=1
Step-by-step explanation:
because 3/4 hour is 45 minute and it takes 4/4 distance to their grandparents hous ein 4/4 hour so 45÷3=15, 15×4=60 which is 1hour
The Answer is A: 1 hour
Step-by-step explanation:
since they can drive 3/4 the distance in 3/4 hours, they can also drive 1/2 the distance in 1/2 hours and so on. If they want to visit the grandparent's house, they need to drive 4/4 the distance which is equivalent to 1 so it will take 1 hour for them to go to the house at the same rate.
A Tip From Me To You:
sometimes the question tries to trick you to make you overthink it so don't overthink it, try to just solve it simply.
Have a great day! <3
Which inequality is equivalent to −<7 - y < 7 ?
Answer: you didn't provide anything for us to answer
Step-by-step explanation:
A file is 261 megabytes is being downloaded. If the download is 14.1% complete, how many megabytes have been downloaded? Round your answer to the nearest tenth.
Answer:
36.80
Step-by-step explanation:
261 x .141 = 36.801
How do you do this?
Find M
Answer:
Step-by-step explanation:
Let angle ABZ be angle 1 and angle ZBC be angle 2.
Angle 1 = 85 degree
Angle 2 = 6x + 9
measure of angle ABC = 24x+4
Angle 2 = ABC - 85
6x + 9 = 24x + 4 - 85
6x - 24x = 4 - 85 - 9
-18x = -90
x = -90/-18 = 90/18 =
x = 5
Therefore the measure of angle 2 = 6*5 + 9 = 30+9 = 39 degree
Therefore the measure of angle ZBC = 39 degree
Hope you understand
Please mark as brainliest
Thank You
Math
HELPP PLEASEEE
It is 1.32 pm, Sem will go to the store in 12 minutes. What time will Sam go
to the store?
Answer: 1:44
Step-by-step explanation: 1:32. take the 32 and add 12. 1:44
Answer:
1:32
Now add 12 minutes to 32.
1:44
Step-by-step explanation:
The number on the left of the colum is the hour and the number on the right of the colum is the minutes.
Solve the problem please
Answer:
3x + 2x + 4x =180
9x = 180
x = 20
4x 2x 3x
= 4 ×20 = 2× 20 = 3× 20
=80 = 40 = 60
f(n) = 2n− 5; Find f(−8)
Answer:
Step-by-step explanation:
Putting value of n = - 8 in the equation
F(n) = 2n− 5
F(-8) = 2(-8) - 5
= - 16 - 5 = - 21
Answer plzz
2. What fraction of the students spent 7 hours doing homework that
week ? Express in simplest form.*
Hours Spent Doing Homework
A combined total of $53,000 is invested in two bonds that pay 2% and 8.5% simple interest. The annual interest is $3,335.00. How much is invested in each bond? The amount invested at 2% is $ The amount invested at 8.5% is $
Answer:
8.5 = $35,000
2% = $18,000
Step-by-step explanation:
two equations can be derived from the question
x + y = $53,000 equation 1
0.02x + 0.085y = $3,335.00. equation 2
x = amount invested in 2% bond
y = amount invested in 8.5% bond
multiply equation 1 by 0.02
0.02x + 0.02y = 1060 equation 3
subtract equation 2 from 3
0.065y = 2275
y = 35,000
substitute for y in equation 1
53,000 - 35,000 = 18,000
A group of students stood in a circle to play a
game. The circle had a diameter of 22 meters.
Which measurement is closest to the area of the
circle in meters ?
Answer: Choice C) 379.94 square meters
=========================================================
Work Shown:
Diameter = 22 meters
Radius = 11 meters (half the diameter)
We'll plug r = 11 into the formula below
A = pi*r^2
A = 3.14*11^2
A = 379.94
This value is approximate since pi = 3.14 is approximate. Use more decimal digits of pi to get a more accurate area value.
Forensic computer investigators must _____.
find a way to get the evidence, no matter what it takes
develop new software to accomplish the investigation
render opinions based on demonstrable facts
bring in the computer and the criminal when they come to court
Answer:
D.) Bring in the computer and the criminal when they come to court.
It came in my test.
24 times 57 times 34 plus 50
Answer:
46,562 :) Brainliest pleaseeee
~Answer~
46,562
24*57*34=46,512
46,512+50=46,562
Could someone please show me how to factor this using the x method
Answer:
(x + 2) (8x + 3)
Step-by-step explanation:
[tex]8x^{2}[/tex] + [tex]19x + 6[/tex]
= (x + 2) (8x + 3)
L = 3/a = 3/8
R = 16/a = 16/8 = 2
\ac/
L V R
/ \
/ b \
where letters have their usual meaning. Comparing 8x² + 19x + 6 to ax² + bx + c,
ac = 8*6 = 48
b = 19
Factors of ac or 48 :-
1 * 48
2 * 24
3 * 16
As the sum of 3 and 16 is 19(or b), our required pair is 3 and 16.
On the left side:
L = 3/a = 3/8
On the right side:
R = 16/a = 16/8 = 2
Therefore, factorized form is (x + 3/8)(x + 2) which can be written as (8x + 3)(x + 2).
How this method works:
Make a X with ac and b on the top and bottom of the X, where ac and b are taken from ax² + bx + c.
On the left side we have d/a and e/a. Basically d and e are those values that we get after solving the whole question.
Step1: find the pair(s) for which sum of factors of ac = b. Here it is 3 and 16.
Step2: put these values in place of d and e.
Step3: solve left anf right of X,
Left = d/a = 3/8
Right = e/a = 16/8 = 2
Step4: whatever you get, put that in (x+?)(x+?) in place of ?.
Y is directly proportional to x write a formula in terms of x find the value of y when x is 0.6 find the value of x when y is 38.5
Answer:
a) [tex]x=\frac{y}{k}[/tex]
b) [tex]y=0.6k[/tex]
c) [tex]x=\frac{38.5}{k}[/tex]
Step-by-step explanation:
From the question we are told that:
[tex]y=38.5[/tex]
[tex]x=0.6[/tex]
Generally the equation for the directly proportional variable is mathematically given by
[tex]y \alpha x[/tex]
[tex]y=kx[/tex]
Where
[tex]K=proportionality\ constant[/tex]
a)
The Formula in terms of x
[tex]x=\frac{y}{k}[/tex]
b)
[tex]y=k(0.6)[/tex]
[tex]y=0.6k[/tex]
c)
[tex]38.5=kx[/tex]
[tex]x=\frac{38.5}{k}[/tex]
Please help
Extra hundred points and brainleist
Answer:
A
Step-by-step explanation:
It is A. The problem asks for the interval when the marlin's height is always increasing. Therefore, you want to look at the left half of the parabola, as the line is going into the peak. The right half is declining. The peak is at around 2 (on the x-axis), so you know that the ending interval number has to be 2. The marlin's height begins to go up starting at 0, so the interval is 0 <= x <= 2. Any number past two is a declining height, and the increase starts at 0.