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

Answers

Answer 1

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]


Related Questions

Jeans are on sale for $16 per pair. How much will 4 pairs of jeans cost?

Answers

Answer:

4 pairs cost $64

Step-by-step explanation:

16*4=64$

find the area of the equilateral triangle.if its perimeter is 24cm​

Answers

Answer:

16√3 cm²

Step-by-step explanation:

The perimeter of a triangle is the sum of its all three sides. Since this is an equilateral triangle, all sides are equal.

Let's consider one side of the triangle to be 'x'

Givent that, the perimeter is 24cm,

The equation should be x + x + x = 24

⇒3x = 24

∴ x = 8 cm

To find the area of the triangle, we need to find the height, and for that, we can use trigonometry.

Since it is an equilateral triangle, all angles are exact 60°.

let's draw a line and mark it as 'h'.

we can use sine formula to find out the opposite i.e. h

sin∅ = opposite ÷ hypotaneous

sin 60° = h ÷ 8

h = 8 sin 60°

h= 4√3

Now, let's find the area

Area = 1/2 × base × height

Area = 1/2 × 8 × 4√3

area= 16√3 cm²

A 24ft flagpole has a shadow of 9ft. A soldier standing next to the flagpole has a shadow of 2.25 feet. How tall is the soldier?

Answers

Answer:

6 feet

Step-by-step explanation:

Let's form a proportion;

24                    x

____    =      _____ ,

 9                   2.25

24(2.25) = 9x,

54 = 9x,

x = height of soldier = 6 feet

Answer:

6 feet

Step-by-step explanation:

[tex]\frac{height of object}{length of shadow}[/tex]

Let the hight of the soldier be x

[tex]\frac{24}{9}[/tex] = [tex]\frac{x}{2.25}[/tex]

x = (24×2.25)/9 = 6ft

GEOMETRY/EASY PROBABILITY, urgent!

Answers

Answer:

2/7, 3/7

Step-by-step explanation:

Total outcomes=7

No. 6 outcomes=2

P(E)= Favourable outcomes/total outcomes

    =2/7

Total even no.= 3

∴ P(E)= 3/7

Mark me as brainliest

I need help plz!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Answers

Answer:

Bruh.

Step-by-step explanation:

A,C and D are points on a circle of radius 4 cm, centre o. BA and BC are tangents to the circle. OB=10cm work out the length of arc ADC. give your answer correct to 3 significant figures

Answers

Answer:

Step-by-step explanation:

OB = 10 cm

OA = OC = Radius = 4 cm

COS <AB = OA/OB = 4/10 = 2/5 =

COS< COB = OC/OB = 4/10 = 2/5

=> <AOC = <AOB + <COB

=> <AOC = Cos-¹(2/5) + Cos-¹(2/5)

=> <AOC = 2 Cos-¹(2/5)

=> <AOC = 2 * 66.42

=> <AOC = 132.84°

if D is in minor arc then length of arc ADC. = ( 132.84°/360°) 2π = 9.274 cm

if D is in major arc then length of arc ADC. = ((360° -132.84°)/360°) 2π = 15.859 cm

Please answer quickly!

Find the equation of the line.

Y=__x + __

Answers

Answer:

y = 3x + 3

Step-by-step explanation:

Using slope intercept form: y = mx + b

where m is the slope(rise over run/change in y over change in x), and b is the y intercept(point where x is 0). We can derive the equation by simply using our mathmatical principles of slope and y intercept. Because our y intercept is where x is 0. Our y intercept is 3 since x is 0 when y is 3 because it touches the axis. Since y is 6 when x is one.

y = mx + b

6 = m(1) + 3

-3 -3

_________

3 = m

_________

m = 3

_________

An m of 3 means that you rise 3 every 1 run or 3y every 1x.

Therefore, our equation in slope intercept is:

y = 3x + 3

Sales tax is calculated as a percentage of the sales price. If sales tax is 7%, what is the sales tax on clothing that costs $150?

Answers

Answer:

$160.50

Step-by-step explanation:

You multiply $150 by .15 to find out what 15% of it  (10.50)

You add the values to get $160.50

10.5 is  the sales tax on clothing that costs $150

What is Percentage?

percentage, a relative value indicating hundredth parts of any quantity.

Given that Sales tax is calculated as a percentage of the sales price.

sales tax is 7%

We need to find the the sales tax on clothing that costs $150

Convert 7% to the decimal value by dividing with 100.

7/100=0.07

Now multiply 0.07 with 150

0.07×150

Zero point zero seven times of one hundred and fifty.

10.5

Hence, 10.5 is  the sales tax on clothing that costs $150

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show work .-12.4+9.2

Answers

Answer: -12.4 + 9.2 = -3.2

4-2=2

9-12=3

Step-by-step explanation: An easy way that I've found is to just subtract the smaller digits (9.2) from the larger digits (12.4) and make the answer a negative.

Answer:

-3.2

Step-by-step explanation:

This is the longer explanation.

-12.4+9.2 let's start with the tenth values.

On a number line, when you're adding a positive number to a negative number you go up. -.4+.2 would be -.2, but if that's too difficult imagine if it was tens place meaning -4+2 which would equal 2 but the difference is you have to add the decimal in this problem. So the answer is -.2.

Now, we are adding 9 to -12. On a number line, think of it as being positioned at -12 and having to go up 9 times because remember when you're adding a positive number to a negative number you go up. When you go up the number line 9 times you stop at -3. When you go back down subtracting 9, you'll be placed at -12. So our answer is -3.

-3.0+-.2= -3.2. When you add -.2 to -3 you end up with -3.2. Line it up as a typical addition problem if you need to.

2. The area A of a rectangle is represented by the formula A = lw where l is the length
and w is the width. The length of the rectangle is 5.

Write an equation that makes it easy to find the width of the rectangle if we know the
area and the length.

Answers

Answer:

rearrange the formula A=lw and make the width the subject of the formula

therefore to find width, the formula is w=A/l

Width = Area/Length

What is the Area of Rectangle?

Area of rectangle is the region occupied by a rectangle within its four sides or boundaries.

The area of a rectangle depends on its sides. Basically, the formula for area is equal to the product of length and breadth of the rectangle. Whereas when we speak about the perimeter of a rectangle, it is equal to the sum of all its four sides. Hence, we can say, the region enclosed by the perimeter of the rectangle is its area.

Area of rectangle = Length x Breadth(or width)

A = L*W

Given,

Length = L = 5

Width = W

Let Area = A

according to the formula of rectangle,

A = L*W

If Area and length is given,

W = A/L

Width = Area/Length = Area/5

Therefore, the equation is Width = Area/Length

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which fraction is less 2/10 or 5/8 or neither they are equal

Answers

2/10 is less, because with a common denominator they are 8/40 and 25/40.  Since 5/8 = 25/40, and 8/40 is smaller than that, 2/10 is smaller.

Answer:

2/10 is less than 5/8

Step-by-step explanation:

2/10 =0.20

5/8= 0.625

0.20<0.625

What is the name of the lake located at letter B on the map above? Answer is C :)

Answers

Answer:

the answer is C. lake Texoma

hope this helps

a) What is y=mx+b?
b) What does the m stand for?
c) What does the b stand for?
d) Where do I find the x & y?
e) If I get two coordinate points how do I find the slope? What is the formula?
f) If I get a graph, how do I find the slope?

Answers

a) y=mx+b is slope intercept form.

b) the m is the slope of the line.

c) the b is the y-intercept

d) the x-axis is horizontal, the y-axis is vertical.

e) m = rise/run = y2-y1/x2-x1

f) pick 2 points on the graph & determine their coordinates. find the difference in the y-coordinates (the rise) & the difference in the x-coordinates (the run) & divide them.

What is the solution of the equation x2=64

Answers

The answer for the equation is x=32

show how the point at (4,5) on the graph of f(x) translates for f(x-2)+7​

Answers

Answer:

The point at (4,5) on the graph of f(x) translates for f(x-2)+7​ is (6,12)

Step-by-step explanation:

Function of graph : f(x)

Rule : f(x)→f(x-c)

When the graph shifts to right by c units

Coordinates (x,y)→(x+c,y)

Rule : f(x)→f(x)+c

When the graph shifts up by c units

Coordinates (x,y)→(x,y+c)

So, Graph f(x-2)+7

Now given graph f(x)

Shift this right by 2 units and then shift up by 7 units

So, f(x)→ f(x-2)+7

Now , Translation of point(4,5)

Using rule :

When shift by 2 units right

(4,5) →(4+2,5)=(6,5)

Now  shift up by 7 units

(6,5) →(6,5+7)=(6,12)

So, the point at (4,5) on the graph of f(x) translates for f(x-2)+7​ is (6,12)

Help? Find angle psw

Answers

The angle is about 80°

Plz help :( I don’t understand

Answers

PLEASE MARK AS BRAINLIST

Answer:

1. 2x-20+2x-15=13

4x-35=13

4x=13+35

4x=48

x=12

2. x-4+9=2x-4

2x-x= -4+9+4

x=9

3. IJK=41+130=171

4. KJD=88-50=38

In a sequence of numbers, a3=0, a4=4, a5=8, a6=12, and a7=16. Based on this information, which equation can be used to find the nth term in the sequence, an?

an=4n−12
A sub n is equal to 4 n minus 12

an=−12n+4
A sub n is equal to negative 12 n plus 4

an=−4n+12
A sub n is equal to negative 4 n plus 12,

an=12n−4

Answers

Answer:

an=−4n+12

A sub n is equal to negative 4 n plus 12,

Step-by-step explanation:

a) name the transversal connecting 1 and 5
b) name the transversal connecting 7 and 14
c) name the transversal connecting 8 and 11
d) name the transversal connecting 7 and 15
e) name the transversal connecting 3 and 9

Answers

Answer:

a) Name the transversal connecting 1 and 5. Line r b) Name the transversal connecting 7 and 14. Line q c) Name the transversal connecting 8 and 11. Line s d) Name the transversal connecting 6 and 15. Line q e) Name the transversal connecting 3 and 9. Line p

Step-by-step explanation:

The angles pairs and the transversal connecting them are:

a. <1 and <5: transversal r.

b. <7 and <14: transversal q

c. <8 and <11: transversal s

<6 and <15: transversal q.

<3 and <9: transversal p.

Note the following about what a transversal is:

A transversal is a line that intercepts or cut-across two straight lines.

A transversal will connect two angles that lie in two other straight lines the transversal intercepts.

The two angles connected by a transversal can lie on opposite sides of a transversal or on same side along the transversal.

Let's determine the transversal connecting the following given angles:

<1 and <5, is connected by transversal r.

<7 and <14 is connected by transversal q

<8 and <11 is connected by transversal s

<6 and <15 is connected by transversal q

<3 and <9 is connected by transversal p

Therefore, the answers are:

a. <1 and <5: transversal r.

b. <7 and <14: transversal q

c. <8 and <11: transversal s

<6 and <15: transversal q.

<3 and <9: transversal p.

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Solve the system of equations below. 3/+4,/9-12 = 17 2v1 +3,11+52 = 18 -V5-VT-12 = -6​

Answers

Answer: -6 You answered your own question-

Kiara baked 30 oatmeal cookies and 48 chocolate chip cookies to package in plastic containers for her teacher
friends at school
She wants to divide the cookies into identical containers so that each
container has the same number of each kind of cookie.
If she wants each container to have the greatest number of cookies possible, how many plastic containers does she
need?

Answers

Answer: 16 containers?

Step-by-step explanation:

Number of oatmeal cookies with Kiara = 30

Number of chocolate chips cookies with Kiara = 48

To find the greatest number of container neded so that there are equal amount of each cookies in each , we have to find the HCF of 30 and 48 .

Factors of 32 = 1 , 2 , 4 , 6 , 8 , 16 and 32

Factors of 48 = 1 , 2 , 3 , 4 , 6 , 8 , 12 , 16 , 24 and 48

Common and highest among these factors = 16

Which means 16 is the HCF of 32 and 48 .

∴ Kiara will need 16 plastic containers .

Which theorem correctly justifies why the lines m and n
are parallel when cut by transversal k?

converse of the corresponding angles theorem

converse of the alternate interior angles theorem

converse of the same side interior angles theorem

converse of the alternate exterior angles theorem

Answers

Converse of the alternate interior angles theorem is correct
converse of the alternate interior angles theorem is correct

please help!! i need math help loll

Answers

Answer:

x=3

Step-by-step explanation:

Answer:

x = 3

Step-by-step explanation:

3 * 3 * 3 = 27

Hope this helps and pls do mark me brainliest if you can:)

Chips are $1.49 a bag. They are 27% off. What is the new price?
A. $1.09
B. $3.20
C. $87.25

Answers

Answer:

A

Step-by-step explanation:

you do 1.49 x 0.79 to find the remaining amount after the discount and it is 1.09

which of these is correct? will give brainliest C:

Answers

Answer:

$7.50/lb    answer A is correct

Step-by-step explanation:

Find the unit cost:  $ per pound:

 Calculate

      $3.00

--------------------

   (2/5) lb

It's slightly easier to calculate the equivalent

 $3.00

------------- = $7.50/lb    answer A is correct

 0.4 lb

Answer: D. $1.20 per pound

Step-by-step explanation:

Because 2/5= 0.4 in a decimal form.

If you multiply 0.4 times 3= 1.2 just that in D they are adding a zero (0).

1.20= 1.2

Graph the given inequality.
-3 > n
How do I do this?

Answers

-3 > n is the same as n < -3 after you flip both sides and flip the inequality.

To graph this, we place an open hole at -3 on the number line. Then we shade to the left to indicate all values smaller than -3. The open hole says "the endpoint is not included". This is because -3 is not smaller than itself.

We would have a filled in circle if we had "or equal to" as part of the inequality, but we don't.

The graph is shown below.

Two-Step Equations 2/5x−3=−17

Answers

Answer:

x =-35

Step-by-step explanation:

2/5x−3=−17

Add 3 to each side

2/5x−3+3=−17+3

2/5x = -14

Multiply each side by 5/2

5/2 * 2/5x = -14 * 5/2

x = -35

Answer:

x = -35

Step-by-step explanation:

Add 3 to each side, so it now looks like this: 2/5x = -14Divide each side by 2/5 to cancel out the 2/5 next to x. It should now look like this: x = -35

I hope this helps!

please please pleaseee

Answers

Answer:

a. C= 5/9(F-32)

Step-by-step explanation:

you have to subtract 32 from both sides so that leaves you with f-32=9/5c and so then you need to multipy each side my 5/9 and that leaves yoh with 5/9(f-32)=c

Find the average rate of change of g(x)=3x^2 ver the interval [-5, -3].

Answers

Answer:

ill help

Step-by-step explanation:

Which point represents (5,-3) on the graph?

Answers

Answer:

Point D

because you go 5 to the right and 3 down.

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