Nate tosses a ball up a hill for his dog to chase. The path of the ball is modeled by the function y=- 1 4 x^ 2 + 33 5 x. , where x is the ball's horizontal distance from Nate in feet and y is the ball's height in feet. The hill is modeled by the line y = 1/5 * x . How far does the ball travel horizontally before it hits the ground? (in feet, round to tenth place if necessary )

Answers

Answer 1

Answer:

The ball's horizontal distance from Nate in feet when the ball hits the ground is 25.6 feet

Step-by-step explanation:

The given equation that represents the path of the ball is y = -1/4·x² + 33/5·x

The equation of the that models the hill is y = 1/5 × x  = 1/5·x

Where, x represents the ball's horizontal distance from Nate in feet and y represents the ball's height in feet

To find the point of contact, we equate both equations to find the common solutions as follows;

-1/4·x² + 33/5·x = 1/5·x

-1/4·x² + 33/5·x - 1/5·x = -1/4·x² + 32/5·x = 0

-1/4·x² + 32/5·x = 0

0 = 1/4·x² - 32/5·x

1/4·x² - 32/5·x = 0

x·(1/4·x - 32/5) = 0

x = 0 or 1/4·x - 32/5, and x = 32/5 × 4 = 128/5 = 25.6

The ball's horizontal distance from Nate in feet = x = 25.6 feet

The ball's horizontal distance from Nate in feet when the ball hits the ground is 25.6 feet.


Related Questions

Find the inner product for (-4, 9, 8) * (3,2,-2) and state whether the vectors are perpendicular.
a.-10; no
c.10; no
b.-10; yes
d.10; yes

Answers

Answer:

a

Step-by-step explanation:

they are not perpendicular and the answer is -10

QUESTION 3 of 10: You sample a 2 square mile neighborhood and find 20 people in your target demographic. If your trade area has a radius
of 10 miles and the population across the area is similar to your sample neighborhood, how many people in your target demographic live in
your trade area?
a) 1,000
b) 1,760
Oc) 3,140
d) None of the Above

Answers

Answer:3,140

Step-by-step explanation:

Hi Please help I have no idea what the answer is

Answers

Answer: 80

Step-by-step explanation:

100+80 =180

Answer:

The answer is 80° :)

Hope it helps you

Jack's mother gave him 50 chocolates to give to his friends at his birthday party. He gave 3 chocolates to each of his friends and still had 2chocolates left. Write an equation showing how many friends were at the party.

Answers

to start off, 50 - 2 is 48, to account for the chocolates he had left. 48 divided by 3 is 16, so Jack has 16 friends at the party!!

What is the change in the y-values and x-values on the graph?The change in the y-values is 40 and the change in the x-values is 1.

Answers

Answer:

If you are asking for the slope

Step-by-step explanation:

m = 40

45% of 200
35% of 150
10% of 20
30% of 15
52.5
>
4.5
>
2
>
110
20% of 50
Reset
Next
reserved

Answers

I just gave you the answers :)

simultaneous equations
x^2+3xy=10
x=2y

Answers

9514 1404 393

Answer:

  (x, y) = (-2, -1) or (2, 1)

Step-by-step explanation:

Substitute for x in the first equation:

  (2y)^2 +3(2y)y = 10

  10y^2 = 10

  y^2 = 1

  y = ±1

  x = 2y = ±2

Solutions are (x, y) = (-2, -1) or (2, 1).

what is 64 ÷ (15 - 7) x2 - 9 using pemdas​

Answers

Answer:

7

Step-by-step explanation:

Hope this helps. Pls give brainliest.

A BODMAS rule states that inter mathematical expressions should be solved in the order of BODMAS from left to right.

Solving equation by BODMAS rule:

An abbreviation Bodmas is used to aid children in remembering the order of operations when performing mathematics. The various activities we can perform with integers in math are called "operations". "Brackets, Order, Division, Multiplication, Addition, Order of operations" is the abbreviation for "Brackets, Order, Division, Multiplication, Addition, Subtraction".

[tex]\to 64 \div (15 - 7) \times 2 - 9 \\\\\to \frac{64}{ (15 - 7)} \times 2 - 9\\\\\to \frac{64}{8} \times -7\\\\\to 8-7\\\\\to 1[/tex]

Therefore, the final answer is "1".

Find out more about the equation here:

brainly.com/question/10413253

Solve the system of equations.
2.5y + 3x = 27
5x – 2.5y = 5
What equation is the result of adding the two equations?
What is the solution to the system?

Answers

Answer:

8x = 32

x = 4

y = 6

Step-by-step explanation:

2.5y + 3x = 27

5x – 2.5y = 5

_____________

8x = 32 (equation obtained after adding the two equations)

x = 32/8

x = 4

Plug x = 4 in 2.5y + 3x = 27

2.5y + 3*4 = 27

2.5y + 12 = 27

2.5y = 27 - 12

2.y5= 15

y = 15/2.5

y = 6

Plot the image of Point Q under the translation (x,y) (x-3, y + 4)

Answers

Answer:

(0, 3)

Step-by-step explanation:

Subtract 3 units from the X-coordinate

Add 4 units from the Y-coordinate

Clare was solving an equation, but when she checked her answer she saw her solution was incorrect. She knows she made a mistake, but she can’t find it. Where is Clare's mistake?

Answers

Answer:

The Second Step.

Step-by-step explanation:

We are given the original equation:

[tex]12(5+2y)=4y-(5-9y)[/tex]

In her first step, Clare distributed both sides:

[tex]72+24y=4y-5-9y[/tex]

There are two errors:

First, the product of 5 and 12 is 60 and not 72.

Second, on the right-hand side of the equation, the negative must be distributed to all terms. Hence, the correct result should be:

[tex]\displaystyle 60 + 24y = 4y - 5 + 9y[/tex]

Instead of what she had obtained.

Help please! Many thanks

Answers

Answer:

v = 3

Step-by-step explanation:

The Douglas family visits SeaLand and is charged $72.00 for 2 adult and 3 child tickets. The Williams family also visited SeaLand and was charged $78.00 for 1 adult and 5 child tickets. How much would it cost the Lopez family to go to SeaLand if they have 3 adults and 4 children?

Answers

Answer:

It would cost the Lopez family $102.00 to go to Sealand

Step-by-step explanation:

Assume that the cost of each adult ticket is $x and the cost of each child ticket is $y

The adult's ticket costs $x

The child's ticket costs $y

∵ The Douglas family is charged $72.00 for 2 adult and 3 child tickets

2x + 3y = 72 ⇒ (1)

∵ The Williams family was charged $78.00 for 1 adult and 5 child tickets

x + 5y = 78 ⇒ (2)

Let us solve the system of equations to find x and y

→ Multiply equation (2) by -2 to make the coefficients of x equal in

   values and different in signs

∵ -2(x) + -2(5y) = -2(78)

-2x + -10y = -156 ⇒ (3)

→ Add equations (1) and (3) to eliminate x

∵ (2x + -2x) + (3y + -10y) = (72 + -156)

∴ -7y = -84

→ Divide both sides by -7 to find y

y = 12

→ Substitute the value of y in equation (1) or (2) to find x

∵ x + 5(12) = 78

∴ x + 60 = 78

→ Subtract 60 from both sides

∴ x + 60 - 60 = 78 - 60

x = 18

The cost of each adult ticket is $18 and the cost of each child ticket

   is $12

∵ Lopez family has 3 adults and 4 children

∴ The cost of the tickets = 3(18) + 4(12) = 54 + 48

∴ The cost of the tickets = 3(18) + 4(12) = 102

It would cost the Lopez family $102.00 to go to Sealand

Select ALL 4 ways of displaying a relation.
Scatter plots
In words
Mapping Diagrams
Table
o Pie Graph
Graph
O Ordered Pairs

Answers

Answer:

Scatter plots

Pie graph

graph

in words

A 16 ounce bag of cereal cost $2.88 what is the cost per ounce

Answers

Answer:

the answer is 0.18 because you just dived the 2.88 by 16 and you get your answer

Step-by-step explanation:

NEED ASAP PLEASE!!!!

Answers

Answer:

1. they are congruent

2. 180 degrees

Which of the following does NOT have a value of -5?
Group of answer choices

F. 21 + (-26)

G. -15 - (-10)

H. -25 + 20

J. -13 - 18

Answers

Answer:

J. -13-18

Step-by-step explanation:

J will give the value -31

Please help!!!

Complete the following proof
Given: DE || BC
Angle 1 = angle 2
Prove: AB = AC

Answers

Answer:

Step-by-step explanation:

statement-reason

DE=BC     - given

Angle 1= Angle 2 - given

Angle 2= Angle 3 - corresponding angles

Angle 1= Angle 4 - corresponding angles

Triangle ADE is congruent to Triangle ABC by AAS

therefore AB= AC

Q.E.D.

How many dots are the next pattern?

. .. ... ....
. .. ...
. ..
.


that's the point, help me solve it.

Answers

i think it might be

. .. ... ....

or

. ..

Given the formula for volume of a box, V=lwh, which answer would you get if you solve for h?

Answers

Answer:

Step-by-step explanation:

h=V/lw

If m ∥ n and the slope of line m is 3, what is the slope of line n? A. 13 B. –13 C. –3 D. 3

Answers

Answer:

3

Step-by-step explanation:

When 2 lines are parallel, they have the same slope. Since m║n, the slope of m will be equal to the slope of n.

The required slope of line n which is parallel to line m is 3. Option D is correct.

Given that,
If m ∥ n and the slope of line m is 3, what is the slope of line n is to be determined.

What is the slope of the line?

The slope of the line is a tangent angle made by line with horizontal. i.e. m =tanx where x in degrees.

Here,
The property of line state that, when lines are parallel to each the than the angle of inclination or slope of all the parallel lines are equal.
So, in given condition Line m is parallel to line n implies the slope of line m and n are equal.

Thus, the required slope of line n which is parallel to line m is 3.

Learn more about slopes here:

https://brainly.com/question/3605446

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A painter needs to obtain a particular shade of green paint by mixing yellow paint with blue paint in the ratio 3:5. If he buys 45 litres of yellow paint, how many litres of blue are required?

Answers

Answer:

75 litres of Blue

Step-by-step explanation:

Divide the amount of yellow liters by 3, you'll get 15. To get the amount of blue needed, you multiply 5 by 15.

Mr. and Mrs. Galloway are planning to build a new fence around their garden. They are comparing the different measurements for their plans. Plan A · Posts are 4.25 feet in length. · Posts must be installed LaTeX: \frac{7}{8}7 8 feet below ground level. Plan B · Posts are 6 LaTeX: \frac{3}{4}3 4 feet in length. · Posts must be installed 1. 5 feet below ground level. What will be the height of the fence in Plan A?​

Answers

Answer:

5 1/8 feets

Step-by-step explanation:

Given that:

PLAN A:

Length of post = 4.25 feets

Post must be 7/8 feets below the ground

Height of fence in PLAN A :

Converting 4.25 feets to decimal :

4.25 feets = 4 feets + 0.25 feets

0.25 feets = 1/4 feets

4 + 1/4 feets = 4 1/4 feets

4 1/4 feets + 7/8 feets

17 /4 feets + 7 /8 feets = [(34 + 7) / 8] feets

[(34 + 7) / 8] feets = 41/ 8 feets

41 / 8 feets = 5 1/8 feets

Help idk what to do and I’m dumb

Answers

Answer:

.5 = 5/9, .583 = 7/12, .3 = 1/3, and .36 =4/11

Step-by-step explanation:

Just divide the numerator by the denominator (4/9 = 4 divided by 9) and you will get the repeating decimal.

Please mark brainliest:)

Answer:

0.5. 5/9

0.583. 7/12

0.3. 1/3

0.36 4/11

Maureen rolls a fair dice and flips a fair coin.
What is the probability of obtaining a 6 and a head?

Answers

1/6 times 1/2 = 1/12

The probability of obtaining a 6 and a head is 1/12 if Maureen rolls a fair dice and flips a coin.

What is a probability?

It is a likeliness of happening an event. It lies between 0 to 1 .

Probability= Number of events/number of outcomes

How to calculate probability?

When Maureen rolls a fair dice then probability of obtaining a six is 1/6

When Maureen flips a fair coin then probability of obtaining a head is 1/2

So the probability of obtaining a six and a head is 1/6*1/2

=1/12

Hence the probability of obtaining a six and a head is 1/12

Learn more about probability at https://brainly.com/question/24756209

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I WILL GIVE BRAINLIST THING IF YOU DO BOTH

Answers

Answer: b

Step-by-step explanation: I took the test

Results for kiona sells tickets to the school play. The ratio of student tickets to adult tickets sold is 4:3. Kiona sold 280 tickets altogether . How many student tickets did Kiona sell?

Answers

Answer:

160

Step-by-step explanation:

It is given that, the ratio of student tickets to adult tickets sold is 4:3. Let students tickets is 4x and adult tickets is 3x.

Total no of tickets = 280

ATQ,

4x+3x=280

7x = 280

x = 40

Students ticket = 4x

= 4(40)

= 160

So, 160 students ticket is sold by Kiona.

Write a function in any form that would match the graph shown below.

Answers

Answer:

e4rf

Step-by-step explanation:

Find the equivalent function of sin(180+x)

Answers

Answer:

The equivalent function of [tex]sin\left(180^{\circ }+x\right)[/tex] will be: [tex]-\sin \left(x\right)[/tex]

i.e.

[tex]\sin \left(180^{\circ \:}+x\right)=-\sin \left(x\right)[/tex]

Step-by-step explanation:

Considering the function

[tex]sin\left(180^{\circ }+x\right)[/tex]

Solving

[tex]sin\left(180^{\circ }+x\right)[/tex]

Using the angle sum identity:

[tex]\sin \left(s+t\right)=\sin \left(s\right)\cos \left(t\right)+\cos \left(s\right)\sin \left(t\right)[/tex]

[tex]=\sin \left(180^{\circ \:}\right)\cos \left(x\right)+\cos \left(180^{\circ \:}\right)\sin \left(x\right)[/tex]

as

[tex]\cos \left(180^{\circ \:}\right)=\left(-1\right)[/tex]

[tex]\sin \left(180^{\circ \:}\right)=0[/tex]

so

[tex]=0\cdot \:\cos \:\left(x\right)+\left(-1\right)\cdot \:\sin \:\left(x\right)[/tex]

[tex]=0\cdot \cos \left(x\right)-1\cdot \sin \left(x\right)[/tex]

[tex]=0-1\cdot \sin \left(x\right)[/tex]

[tex]=0-\sin \left(x\right)[/tex]

[tex]=-\sin \left(x\right)[/tex]

So, the equivalent function of [tex]sin\left(180^{\circ }+x\right)[/tex] will be: [tex]-\sin \left(x\right)[/tex]

Therefore:

[tex]\sin \left(180^{\circ \:}+x\right)=-\sin \left(x\right)[/tex]

PLEASE HELP! If xy=40 is that an inverse or direct variation, or neither.

Answers

Answer:

inverse variation

Step-by-step explanation:

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