3. Patrick kicks a soccer ball from the ground into the air. When the ball is a horizontal distance of 12 feet from
him, it is 14 feet above the ground. When the ball is 32 feet from him, it is 7 feet above the ground.
Use quadratic regression on a graphing calculator to write a function for the height of the ball in terms of
its horizontal distance Round to the nearest thousandth (

Answers

Answer 1

Answer:

The function for the height of the ball in terms of its horizontal distance is

[tex]y = -\frac{91}{1920}\cdot x^{2}+\frac{833}{480}\cdot x[/tex]

Step-by-step explanation:

From Physics, we know that ball describes a parabolic motion, in which trajectory is described by the following second-order polynomial (quadratic function):

[tex]y = a\cdot x^{2}+b\cdot x + c[/tex] (Eq. 1)

Where:

[tex]x[/tex] - Horizontal distance, measured in feet.

[tex]y[/tex] - Vertical distance above the ground, measured in feet.

[tex]a[/tex] - Second order coefficient, measured in [tex]\frac{1}{ft}[/tex].

[tex]b[/tex] - First order coefficient, dimensionless.

[tex]c[/tex] - Zero order coefficient, measured in feet.

We can obtain the second-order polynomial associated with the soccer ball by knowing three distinct points and solving the resulting system of linear equations. If we know that [tex](x_{1},y_{1}) =(0\,ft, 0\,ft)[/tex], [tex](x_{2},y_{2})=(12\,ft, 14\,ft)[/tex] and [tex](x_{3},y_{3})=(32\,ft, 7\,ft)[/tex], then the system of linear equations is:

[tex]c = 0[/tex]

[tex]144\cdot a+12\cdot b +c = 14[/tex]

[tex]1024\cdot a +32\cdot b + c = 7[/tex]

The solution of this linear system is:

[tex]a = -\frac{91}{1920}[/tex], [tex]b = \frac{833}{480}[/tex], [tex]c = 0[/tex]

Therefore, the function for the height of the ball in terms of its horizontal distance is

[tex]y = -\frac{91}{1920}\cdot x^{2}+\frac{833}{480}\cdot x[/tex]

In addition, we present a graphic of the given function as attachment.

3. Patrick Kicks A Soccer Ball From The Ground Into The Air. When The Ball Is A Horizontal Distance Of

Related Questions

Josey has 15 quarters, 20 dimes and 10 pennies. Express as a ratio the number of quarters to total coins.

Answers

Answer:

15 : 45, 15/45, 15 to 45

Step-by-step explanation:

15 + 20 + 10 = 45 total coins.

Ratio being quarters (15) to total coins (45)

Answer:

The ratio is 15:45

Step-by-step explanation:

First, we want to know how many total quarters Josey has, which says he has 15. Then, we need to know how many total coins he has. So, 15 + 20 + 10 = 45. So, there are 45 total coins. So the ratio is 15:45. Hope this helps!

If the income tax rate is 16%, determine the amount of income tax paid on an income
of $12,400

Answers

Answer:

1900

Step-by-step explanation:

100-16=84

12400×16/100=1984

1984-84=1900

=1900

30 points for brianliest

Answers

Answer:

E Hope this helps!

Step-by-step explanation:

Happy Halloween!

Answer:

#1. yellow

#2. black

#3. blue

Hope that helps!!! Please give me the brainliest!! ;( )

56767874988558745647457546758467654858765475647567864578547834894543987843579453478974398459737956479547954 -5743785347864357843576453764753764357654376543765467578587438743589438932587534794978789487943578943587943578435879 =?

Answers

Hfkfkhhrkwydosjgycjfkgjdbaugukfyvg dhghflaijdo
Mhm 21 I think !!!!!!!

Write an equation in function notation for the relation
shown at the right.
F f(x)=-2x H f(x)=x-2
G f(x)=2x+2 J f(x)=-x+2

Answers

It’s H. Slope is rise over run so it’s 1 up and 1 to the right. Meaning that your slope is 1. You have to write the form of the linear equation y=mx+b so your slope is m. So m is 1. So you have y=x+b. To find b plug in the point (0,-2) x=0 and y=-2 so you get -2=(0)+b so you get b=-2 so the linear equation is y=x-2 so your answer is H

The correct function is  H, f(x) = x-2

What is a function?

A function is defined as a relation between a set of inputs having one output each, a function is a relationship between inputs where each input is related to exactly one output.

Given is a graph,

Slope is rise over run, so it’s 1 up and 1 to the right.

It means that the slope is 1.

We know that, the general form of the linear equation y = mx+b where slope is m.

Here, So m is 1.

So we have y=x+b.

To find b plug in the point (0,-2) x=0 and y=-2

Thus, we get, b=-2

Therefore, the linear equation is y=x-2

Hence, the correct function is  H, f(x) = x-2

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Hurry I don’t understand any of this!

Answers

Answer:

it's the second one! 11√3 - 7√6

Answer:

B.

Step-by-step explanation: You have to simplify the radical expressions [tex]\sqrt{48}[/tex] simplified is [tex]4\sqrt{3}[/tex] and [tex]\sqrt{58}[/tex] simplified is [tex]3\sqrt{6}[/tex].

Next, collect the like terms [tex]7\sqrt{3} + 4\sqrt{3} = 11\sqrt{3}[/tex] then [tex]4\sqrt{6}- 7\sqrt{6} = 7\sqrt{6}[/tex]

Then you'll put it all together which will give you an answer of  [tex]11\sqrt{3} - 7\sqrt{6}[/tex]

An empty shipping box weighs 300 grams the box is then filled with t shirts each t shirt weighs 100 grams the equation 100t + 300 = w represents the relationship between the quantities in this situation where is the weight im grams of the filled box and number if shirts in the box. Select all possible solutions for (t,w) to the equation 100t + 300 =w

Answers

Answer:

Step-by-step explanation:

Given the equation of the weight of an empty shipping box expressed as:

100t + 300 = w

We are to select all possible solutions for (t,w) to the equation 100t + 300 =w. From the equation the input variable is t which serves as the DOMAIN while the output variable is w which serves as the RANGE. To get the possible of t, we will need to find the values of t that will make the function to exist. Since the number of t shirts are always positive, this means that the value of t exists on all positive real numbers. Hence the Domain is expressed as:

Domain: [0, ∞)

Since the weight w must also be positive, the lowest value of w we can get it at when t = 0. Substitute into the equation:

100t + 300 =w

100(0) + 300 = w

300 = w

w = 300

Hence the minimum output (weight) that we can have is 300, the Range of the expression will be expressed as:

Range: [300, ∞)

please help!!!
-8×f(0)+4×g(-8)​

Answers

Answer:

Simplified Expression - 32gx

Step-by-step explanation:

-8×f(0)+4×g(-8)​

0+4xg×(-8)

0-4xg×8

0-32gx

-32gx

SUM

5 out of 7 people wear contacs.what fraction of the students wear contacs

Answers

Answer:

5/7

Step-by-step explanation:

hope this helps

An airline states that an airplane flight between two cities takes 2.5 hours. The airline also says that the actual flying time can change by up to 15% of that amount.

What are the shortest and longest times for the airplane flight? Round your answer to the nearest tenth of an hour.

Enter the correct answers in the boxes.

Answers

Answer:

The shortest time is 2.1 hours and the longest time is 2.9 hours

Step-by-step explanation:

First, find the amount of time if it increases by 15%:

2.5(1.15)

= 2.875

= 2.9

Next, find the amount of time if it decreases by 15%:

2.5(0.85)

= 2.125

= 2.1

So, the shortest time is 2.1 hours and the longest time is 2.9 hours

The shortest time for the airplane flight will be; 2.125 hours and the longest time will be; 2.9 hours.

What is the percentage?

A percentage is a minimum number or ratio that is measured by a fraction of 100.

Given that the flight take the time is 2.5 hours But the time can fluctuate by 15 %

We need to first calculate 15 % of 2.5 hours.

For this, we will use percentage;

15 % of 2.5 hours

= 15 / 100 × 2.5 hours

= 0.15 × 2.5 hours

= 0.375 hours.

Now, the shortest time is;

= 2.5 h - 0.375 h

= 2.125 h

Then, the longest time will be;

= 2.5 h + 0.375 h

= 2.875 h

Therefore, the shortest time for the airplane flight will be; 2.125 hours and the longest time will be; 2.9 hours.

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Please ASAP , Help find the original slope and the parallel slope

Answers

Answer:

The slope for both is ½ because every unit to the right (x axis) is increasing by 1.

Rise is 1, run is 2

Answer:

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

Step-by-step explanation:

Calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 8, 1) and (x₂, y₂ ) = (8, 9) ← 2 points on the green line

m = [tex]\frac{9-1}{8+8}[/tex] = [tex]\frac{8}{16}[/tex] = [tex]\frac{1}{2}[/tex]

Repeat with (x₁, y₁ ) = 0, 6) and (x₂, y₂ ) = (2, 7) ← 2 points on the blue line

m = [tex]\frac{7-6}{2-0}[/tex] = [tex]\frac{1}{2}[/tex]

Since the slopes of both lines are equal, then the lines are parallel

(3, 2), у = х +5
Write the slope intercept from

Answers

Answer:

Y= x^2 + 5x - 22

Step-by-step explanation:

Slope intercept form= y=Mx+b

Translate please.... Two times the sum of a number and 5 equals 3

Answers

Answer:

2(c+5)=3

Step-by-step explanation:

It is 2 times the quantity c+5, and it all equals 3

The equation of Two times the sum of a number and 5 equals 3 will be; 2(c+5)=3

What does it mean to solve an equation?

An equation represents equality of two or more mathematical expression.

When someone asks you to solve an equation, then they usually mean to find the values of the unknowns for which that equation would be true (the equality between expressions should hold true for those values).

WE have been given the statement as;  Two times the sum of a number and 5 equals 3.

We are asked to find the equation of the given statement.

Here 2 times the quantity c+5, and it all equals 3

Therefore, the equation will be;

2(c+5) = 3

Learn more about solving equations here:

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a rectangle has a length of 12 cm and a height of 5 cm. how long is the diagonal

Answers

Answer:

13cm

Step-by-step explanation:

The formula for diagonal is [ d = √h²+l² ] where h = height and l = length.

Solve with what we are given.

d = √5²+12²

d = √25+144

d = √169

d = 13

Best of Luck!

What is 3/8 divided by 1/3? I need help asap

Answers

in decimal form it is 1.125
0.125 is the answer

What is the value of X in the equation 7× + 2y =48, when y = 3​

Answers

The answer has to be 1 I did it step by step !

Answer:

[tex]x=6[/tex]

Step-by-step explanation:

[tex]7x+2\left(3\right)=48[/tex]

[tex]7x+2\cdot \:3=48[/tex]

[tex]7x+6-6=48-6[/tex]

[tex]7x=42[/tex]

[tex]\frac{7x}{7}=\frac{42}{7}[/tex]

[tex]x=6[/tex]

The area of a rectangle is 365.2 square meters and its length is 22 m. Find the width of the rectangle.

Answers

Answer: 16.6m

Step-by-step explanation:

Area - Length x Width

365.2/22

16.6m

The ratio of the numbers of gold to silver to bronze is 2:3:2. What is definitely true about the medals Italy got

(A) Italy got a total of 7 medals
(B) 2/7 of the medals are bronze
(C) 40% of the total medals are gold
(D) more than half of the medals are silver

Answers

Answer:

pls help me as well

Step-by-step explanation:

btw which school do u study in?

the only statement that is definitely true based on the given ratio is (B) 2/7 of the medals are bronze.

Based on the given ratio of gold to silver to bronze medals being 2:3:2, we can deduce the following:

(A) Italy got a total of 7 medals: This statement cannot be determined based solely on the given ratio. The total number of medals received by Italy is not explicitly provided.

(B) 2/7 of the medals are bronze: This statement is true. Since the ratio of bronze medals to the total medals is 2/(2+3+2) = 2/7, it means that 2/7 of the medals are bronze.

(C) 40% of the total medals are gold: This statement is false. The ratio given does not indicate that 40% of the medals are gold. Without knowing the total number of medals, we cannot determine the percentage.

(D) More than half of the medals are silver: This statement is false. The given ratio indicates that the number of silver medals is less than the combined number of gold and bronze medals, which means that less than half of the medals are silver.

In summary, the only statement that is definitely true based on the given ratio is (B) 2/7 of the medals are bronze.

Learn more about ratio here

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One angle of a triangle measured 95
the other two angles are in a ratio of 5:12what are the measures of those two angles

Answers

Answer:

Both angles: one = 25 degrees, the other equals 60 degrees

Step-by-step explanation:

Do 95 + 5x + 12x = 180.

x = the angle.

95 + 17x = 180.

minus 95

17x = 85

divide by 17.

x= 5

then do 5(5) and 5(12) to get your two angles.

Answer:

25 and 60

Step-by-step explanation:

One angle of a triangle measured 95

the other two angles are in a ratio of 5:12, what are the measures of those two angles?

So 95 + 5x + 12x = 180

(Combine like terms)

95 + 17x = 180

(Subtract 95 from both sides)

17x = 85

(Divide 17 from both sides)

x = 5

Now plug 5 into 5 and 12

5x = 25

12x = 60

60 + 25 + 95 = 180 :)

Lia Edwards

*XTRA PTS* can someone please explain how to find the domain and the range of a coordinate/set of relations

Answers

Answer:

Domain: X coordinates

Range: Y coordinates

Step-by-step explanation:

The domain is the set of all first elements of ordered pairs (x-coordinates). The range is the set of all second elements of ordered pairs (y-coordinates). Only the elements "used" by the relation or function constitute the range. Domain: all x-values that are to be used (independent values).The range is the set of all second elements of ordered pairs (y-coordinates). Only the elements "used" by the relation or function constitute the range. Domain: all x-values that are to be used (independent values). Range: all y-values that are used (dependent values).

Which one?
A. B. C. or D? ​

Answers

Answer:

the answer is C

Step-by-step explanation:

GLAD TO HELP!!

Answer:

C

Step-by-step explanation:

not 100 % sure but here you go!!

12-5h=h+6 whats the answer

Answers

Answer:

h=1

Step-by-step explanation:

hope it helps

Sun Gold paint is made by mixing 3 parts yellow to 2 parts
red. How much red is to be mixed with 4 quarts of yellow?

Answers

3 parts red I think please don’t hate me I don’t know :((

I’m stuck on this for about 20 minutes, can someone help and explain step by step to me?

Answers

Answer:

The answer is [tex]-\frac{1}{15}[/tex]

Step-by-step explanation:

I used my calculator and inputted everything.

4+63 (56x6)=

what is the answer

Answers

Answer:

Step-by-step explanation:

4 + 63 = 67

67(56x6)

if its 56x^6 then

3752x^6

Which shows the order of the angles from smallest to
largest?
O angle A, angle B, angle C
O angle B, angle A, angle C
angle B, angle C, angle A
O angle C, angle A, angle B

Answers

Answer is angle A angle B Andgle C

Answer:

O angle A, angle B, angle C

Find the degree of the monomial.

Pleas show workkk

Answers

Answer:

11

Step-by-step explanation:

9(x^1)(y^3)(z^7)

Add degrees.

1+3+7 = 11

The school orchestra sells snacks at thier concerts to raise money. At the spring concert they made 9/8 as much money as they made at their fall concert. Did they make more money at their spring or fall concert?

Answers

Answer:

More money was made at the spring concert

Step-by-step explanation:

Here, we want to know if more or less money was made during the spring or fall concert

from the question, we are told that the amount made at spring concert is 9/8 of what is made at a fall concert

Since 9/8 is greater than 1, we can confidently say that the amount made at the spring concert is greater than what she made at the fall concert

Inline skates typically have weeks with a diameter of 74mm. The wheels are typically manufactured so that the diameter is very from this value by at most .1mm. Right and solve an absolute-value equation to find the maximum and minimum diameter of the wheels

Answers

Answer:

1wesegserghfyheyeryeryeryreyeryryryyryryeryryeryeryreyeyeryerfwetetu trash

A rectangle whose area is 336 square feet has a length that is 4 meters less than
the twice the width. Find the dimensions of the rectangle.

Answers

Answer:

L = 2(16.675) - 13.2 = 20.15 ft

W = 16.675 ft

Solution

width = x

length = 2x - 4m

m = 3.3 ft

Area = W × L = 336 ft^2

(2x - 4(3.3)) × x = 336 ft^2

solve for x

2x^2 - 13.2x = 336 ft^2

quadratic equation reveals 2 X's

x = -10.075, 16.675

a distance can't be a negative so...

x = 16.675 ft

L = 2(16.675) - 13.2 = 20.15 ft

W = 16.675 ft

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