Tommy and Arnold are playing with water balloons. Arnold is standing by a bush that is 20 feet from where Tommy is standing. Tommy released a water balloon at 5 feet above the ground and hits Arnold’s chest- which is also 5 feet above the ground. The balloon reached a maximum height of 15 feet off the ground. using Tommy’s location as the starting point, help Tommy write an equation that describes the path of the water from the point of release to Arnold's chest. Using the equation y=a(x-h)^2+k
Answer:
The equation that describes the path of the water balloon is:
[tex]y =-\frac{1}{10}\cdot (x-10)^{2}+15[/tex]
Step-by-step explanation:
The motion of the water balloon is represented by quadratic functions. Tommy launches a water balloon from [tex]A(x,y) = (0\,ft, 5\,ft)[/tex] and hits Arnold at [tex]B(x,y) = (20\,ft, 5\,ft)[/tex]. Given the property of symmetry of quadratic function, water ballon reaches its maximum at [tex]C(x,y) = (10\,ft,15\,ft)[/tex], which corresponds to the vertex of the standard equation of the parabola, whose form is:
[tex]y = a\cdot (x-h)^{2}+k[/tex] (Eq. 1)
Where:
[tex]a[/tex] - Vertex parameter, measured in [tex]\frac{1}{ft}[/tex].
[tex]h[/tex], [tex]k[/tex] - Horizontal and vertical components of the vertex, measured in feet.
[tex]x[/tex], [tex]y[/tex] - Horizontal and vertical location of the ball, measured in feet.
If we know that [tex]x = 0\,ft[/tex], [tex]y = 5\,ft[/tex], [tex]h = 10\,ft[/tex] and [tex]k = 15\,ft[/tex], the vertex parameter is:
[tex]5\,ft = a\cdot (0\,ft-10\,ft)^{2}+15\,ft[/tex]
[tex]a = \frac{5\,ft-15\,ft}{(0\,ft-10\,ft)^{2}}[/tex]
[tex]a = - \frac{1}{10}\,\frac{1}{ft}[/tex]
The equation that describes the path of the water balloon is:
[tex]y =-\frac{1}{10}\cdot (x-10)^{2}+15[/tex]
Is the statement true or false? If false, give a counterexample.
For all real numbers a, b and c, a(b + c) = ab + bc.
A. true
B. false; a(b + c) = ab − ac
C. false; if a = b = c = 1, then 1(1 + 1) ≠ 1(1) + 1(1)
D. false; if a = 1, b = 2, and c = 3, then 1(2 + 3) ≠ 1(2) + 2(3)
Answer:
D. false; if a = 1, b = 2, and c = 3, then 1(2 + 3) ≠ 1(2) + 2(3)
Step-by-step explanation:
A is false, because the a is being distributed/ being multiplied to all terms inside the parenthesis, and not the term b.
B is also false. There is no indicated negative signs.
C is also false because 1(1 + 1) is EQUAL to 1(1) + 1(1)
D is true.
Write 2.08 x 10^2 in standard form.
Answer:
208
Step-by-step explanation:
If you multiply 2.08 by ten to the second power (100) Then you get 208
Scientific notations are the way through which a very small or a very large number can be written in shorthand. The given expression can be written in the standard form as 208.
What are Scientific notations?Scientific notations are the way through which a very small or a very large number can be written in shorthand. In scientific notations when a number between 1 and 10s is multiplied by a power of 10.
For example, 6,500,000,000,000 can be written as 6.5e+12.
The given expression can be written in the form of an expression as shown below.
2.08 x 10²
= 2.08 × 100
= 208
Hence, the given expression can be written in the standard form as 208.
Learn more about Scientific notation here:
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write the sentence as an equation 253 is the product of 69 and g
Answer:
253=69g or 253=69(g)
Step-by-step explanation:
A can run 3 miles in 30 minutes. How long will it take
the runner to run 2.5 miles? Use the diagram to explain.
Answer:
It will take her about 25 minutes.
Step-by-step explanation:
30 divided by 3 is ten.
It takes ten minutes to run each miles.
I don't have a diagram, but try drawing a graph with the information.
2 5. 8 11 X 2 -4 8 у 14 What is the equation of the given table?
Answer:
8-6+-2
Step-by-step explanation:
what is the answer for −3x−6+(−1)
Answer:
-3x-7
Step-by-step explanation:
Combine like terms
-6+-1 = -6-1 = -7
Hence, it's -3x-7
people wont solve my question i need it ASAP
Answer:
A pig has 10,000 kg mass more than a mass
Step-by-step explanation:
[tex]\frac{2*10^{2}}{2*10^{10}}=\frac{10^{2}}{10^{-2}}\\\\=10^{2}*10^{2}\\\\=10^{2+2}\\\\=10^{4}\\\\=10000[/tex]
Giving Brainliest
Jabari and his friend both started a part-time job at the Swimming Hole earning $13 per hour. Jabari worked 14 ½ hours his first week. Jabari agreed to pay his friend 1/10 of his salary for reimbursement of gas. How much money did Jabari pay his friend for gas?
Answer: the answer would be 18.85
Step-by-step explanation:
multiply 13 by 14.5 then divide by 1/10
Answer:
18.85
Step-by-step explanation:
Find the volume of this object. Use 3 for pi. (CAN ANYONE HeLP:))
Step-by-step explanation:
sorry for the rough handwriting but that's that
The price of dinner was $24.80. The sales tax was 8%. The server was given a 15% tip (calculated after tax was added). What was the total cost of the meal?
A
$5.70
B
$25.03
C
$30.50
D
$30.80
Answer:
D. $30.80
Step-by-step explanation:
8/100=0.08
0.08*24.80=1.984
1.984+24.80=26.78
15/100=0.15
0.15*26.78=4.017
4.017+26.78=30.80
Steven sells bags of different kinds of cookies. He made $27 selling bags of Oreos, $18 selling chocolate chips cookies, and $45 selling chunky sugar cookies. Each bag of cookies costs the same amount. What is the most that Steven could charge for each bag of cookies?
Answer:
9 dollars
Step-by-step explanation:
It would be 9 dollars because that is the only common factor that could go into 27, 28, or 45.
A car and a motorcycle, starting 35 miles apart, travel directly away from each other. The car averages 60 miles per hour and the motorcycle averages m miles per hour. The distance (d) between them after h hours can be determined using the equation below. Which equation could be used to find the distance between the car and the motorcycle after 2.5 hours?
Answer:
d = 60h + 35
Step-by-step explanation:
60 = Slope
35 = Y-intercept
You would just input whatever amount of time you need to the variable h in order to find the value of d.
When Arjun makes hot cocoa, he adds 20\text{ mL}20 mL20, start text, space, m, L, end text of chocolate syrup for every 333 ounces of hot water. Arjun's brother, Eli, adds 45\text{ mL}45 mL45, start text, space, m, L, end text of chocolate syrup for every 666 ounces of hot water. Which hot cocoa is more chocolatey? Choose 1 answer: Choose 1 answer:
Answer:
45mL hot cocoa is more chocolateyStep-by-step explanation:
When Arjun makes hot cocoa, if he add 20mL of chocolate syrup to 3ounces of water, let us know the equivalent chocolate in one ounces of water.
20mL = 3 ounces
x = 1 ounce
cross multiply
3x = 20
x = 20/3
x = 6.67 mL
This means he must have add 6.67mL of chocolate to 1 ounce of water.
Similarly, if 45mL is added to every 6 ounces
45mL = 6ounces
x = 1 ounce
cross multiply
6x = 45
x = 45/6
x = 7.5mL
This means he must have add 7.5mL of chocolate to 1 ounce of water.
The hot cocoa that is more chocolatey is the one with the highest amount of chocolate in 1 ounce. That is 45mL hot cocoa
Answer:
eli's cocoa is more chocolately. i would show proof (on khan academy), but I just skipped the q. :|
Step-by-step explanation:
Buddy downloaded 16 apps in 24 seconds. At this rate, how many apps could he download in one minute? (24 seconds = 2/5 of a minute) (1-1 Unit Rate)
Help with these math questions grade 12
Answer:
1. 15.1%
2. 8.3%
3. 12%
4. 25%
Step-by-step explanation:
1.
percent change = (new number - old number)/(old number) * 100%
percent change = (21300 - 18500)/(18500) * 100%
percent change = 15.1%
A positive percent change is a percent increase.
Answer: The percent increase is 15.1%.
2.
percent change = (new number - old number)/(old number) * 100%
percent change = (298000 - 325000)/(325000) * 100%
percent change = -8.3%
A negative percent change is a percent decrease.
Answer: The percent decrease is 8.3%.
3.
percent change = (new number - old number)/(old number) * 100%
percent change = (110 - 125)/(125) * 100%
percent change = -12%
A negative percent change is a percent decrease.
Answer: The percent decrease is 12%.
4.
percent change = (new number - old number)/(old number) * 100%
percent change = (1500 - 2000)/(2000) * 100%
percent change = -25%
A negative percent change is a percent decrease.
Answer: The percent decrease is 25%.
Gavin likes biking. This week his goal is to bike about 65 total miles over four days. Each day he wants to ride 1.5 times as far as he rode the day before. How far should he ride on each of the four days. Write the expressions for the distance Gavin needs to bike each day. Then relate these expressions to create an equation that represents Gavin's situation.
Step-by-step explanation:
let the first-day ride be x
Then the second-day ride will be =1.5 x
The third-day ride will be=1.5(1.5x)
The Fourth-day ride will be=1.5*1.5(1.5x)
hence for the four days the distance covered is
65=x+1.5x+1.5*1.5x+1.5*1.5*1.5x
65=x+1.5x+2.25x+3.375x
65=8.125x
divide both sides by 8.125 we have
x=65/8.125
x=8mile
the first-day ride be x=8miles
the second-day ride will be =1.5 x =1.5*8= 12miles
The third-day ride will be=1.5(1.5x) = 18miles
The Fourth-day ride will be=1.5*1.5(1.5x) = 27miles
· Evaluate f(2a + b), where f(x) = 4x2 – 3x.
Answer:
2af+bf = 2af+bf
Step-by-step explanation
f(x) = 4x2 – 3x. = x(4x−3)
Which one?
A. B. C. or D?
Answer:
Its B
Step-by-step explanation:
Its B prob
Answer for brainliest!
Answer:
-5, -6, -7, -8, -9, -10, -11
Step-by-step explanation:
Answer:
-12<x<-9/2Step-by-step explanation:
2x+9<o
x>-12
-12<x<-9/2Joe and Carmen are partners in a business. Joe makes $2.00 profit for every $5.00 profit that Carmen makes. If Carmen makes $20 on the first item they sell, how much profit will Joe make?
Gianna earned $466.90 at her job when she worked for 23 hours. How much money did she earn each hour?
Answer:
About $20.30
Step-by-step explanation:
$466.90 divided by 23.
Jen bought 5 CD's for $57.50. What was the unit price?
Answer:
$11.50 per CD
Step-by-step explanation: u have to make 5 into 1, thats divinding. Then u divide $57.50 by 5, there's your unit price :)
Would you rather discover alien life or an animal that was thought to be extinct?
[tex]\boxed{I\; would\; say\; an\; animal\; that\; was\; thought\; to\; be\; extinct.}[/tex]
≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈
The reason i say this is because i don't really want to run into something that i don't know much about. I do know quite a bit about extinct animals more than i do aliens. So, that's my reasoning.
≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈≈
[tex]\boxed{Hope\;i\;helped!}\\\\\boxed{Thanks,\;AnimeBrainly}[/tex]
what is the equation of a line parallel to y=3x-2 and goes through the point (-1,1)
Answer:
y = 3 x − 29
Step-by-step explanation:
First, let's find the slope of the line
y = 3 x + 2
As the equation is already in slope-intercept form
y = m x + c
Slope = 3
Let a point ( x , y ) be on the new line.
By finding the slope again,
y − 1 x − 10 = 3
y − 1 = 3 ( x − 10 )
y − 1 = 3 x − 30
Which can then be converted to different forms:
Standard form:
3 x − y = 29
Equation form:
3 x − y−29 = 0
Slope-intercept form:
y = 3 x − 29
graph{3x-y=29 [-32.3, 47.7, -34.1, 5.9]}
Your answer should be a polynomial in standard form. ( d^2 +3) (d^2 +2d +1)
Answer:d^4+2d^3+4d^2+6d+3
Step-by-step explanation:
Triangle A has side lengths 3,4 and 6. Triangle B had side lengths 6,8 and 12 triangle A and B are?
Answer:
Similar
Step-by-step explanation:
Both triangles have corresponding sides, so they are similar.
The two triangles A and B are similar to each other.
What is the similarity?If two objects are having the same shape then they will be termed as similar. So in mathematics, if two figures have the same shapes, lines or angles then they are called similar.
Given that triangle, A has side lengths 3,4, and 6. Triangle B had side lengths 6,8 and 12.
The second triangle is dilated by factor 2. This means in triangle B the sides are two times the side of triangle A.
Therefore, the two triangles A and B are similar to each other.
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help TWT ;-;-;-;-;-;-;
Answer:1
Step-by-step explanation:
Answer:
the answer is 1
Step-by-step explanation:
for how many tickets is the cost the same for club members and non-members?
Answer:
The cost will be the same for 2 club members as for 1 non-member.
Step-by-step explanation:
There will never be a number of tickets where the price for a given number of club members is the same for the same number of non-members.
However, if two club members purchase tickets, their cost is 2($3) = $6.
If one non-member purchases a ticket, the cost is 1($6) = $6.
help me..i’m not sure what to do
Answer:
$41,500
Step-by-step explanation:
In order to find net worth you must subtract the persons liabilities from the persons assets. Therefore, $113,000 - $71,500 = $41,500.
Hope this helps! Have an excellent day mate!