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

Answers

Answer 1

Answer:

26.4 m

Step-by-step explanation:

The path the ball follows is given by the function

[tex]y=-\dfrac{1}{4}x^2+\dfrac{33}{5}x[/tex]

Before it hits the ground means y will be zero.

[tex]0=-\dfrac{1}{4}x^2+\dfrac{33}{5}x\\\Rightarrow x(-\dfrac{1}{4}x+\dfrac{33}{5})=0\\\Rightarrow x=0, -\dfrac{1}{4}x+\dfrac{33}{5}=0\\\Rightarrow x=0, x=\dfrac{33}{5}\times4\\\Rightarrow x=0, 26.4[/tex]

There are two points where the vertical displacement is zero the point at which Nate tosses the ball and the point where it lands.

So, the ball travels 26.4 m horizontally before it hits the ground.

Answer 2

Solving the quadratic equation, it is found that the ball travels 26.4 feet horizontally before it hits the ground.

The height of the ball, after an horizontal distance of x feet, is given by:

[tex]y(x) = -\frac{1}{4}x^2 + \frac{33}{5}x[/tex]

Converting the fractions to decimal:

[tex]y(x) = -0.25x^2 + 6.6x[/tex]

It hits the ground when:

[tex]y(x) = 0[/tex]

Then:

[tex]-0.25x^2 + 6.6x = 0[/tex]

[tex]0.25x^2 - 6.6x = 0[/tex]

[tex]x(0.25x - 6.6) = 0[/tex]

[tex]x = 0[/tex], or:

[tex]0.25x - 6.6 = 0[/tex]

[tex]0.25x = 6.6[/tex]

[tex]x = \frac{6.6}{0.25}[/tex]

[tex]x = 26.4[/tex]

The ball travels 26.4 feet horizontally before it hits the ground.

A similar problem is given at https://brainly.com/question/10489198


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The equation - 2 (x + 1) = (y – 5)^2 is represented by which graph?

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Step-by-step explanation:

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Answer:

9%

Step-by-step explanation:

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This would equal nine percent.

(WILL GIVE BRAINLIEST) Solve for x.
-2(-9x+5)-4x=2(x-5)-4

Simplify your answer as much as possible

Answers

Answer:

−2(−9x+5)−4x=2(x−5)−4

Step 1: Simplify both sides of the equation.

−2(−9x+5)−4x=2(x−5)−4

(−2)(−9x)+(−2)(5)+−4x=(2)(x)+(2)(−5)+−4(Distribute)

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14x+−10=2x+−14

14x−10=2x−14

Step 2: Subtract 2x from both sides.

14x−10−2x=2x−14−2x

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Step 3: Add 10 to both sides.

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Step 4: Divide both sides by 12.

12x

12

=

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x= -1/3

Step-by-step explanation:

Good luck! Hope this helps! <3

Answer :

[tex]x = - \frac{1}{3} [/tex]

or you can just write x = -0.3

hope this helps!

Luis rides his bicycle 3/4 mile in 15 minutes, or 1/4 hour, along the bike trail. Assuming he rides at a constant rate, what is his speed, in miles per hour?​

Answers

Answer: 3

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Julio is running in a 13.1-mile race. There are water stops every 2.75 miles along the route from the beginning of the race.
What is the distance between the last water stop and the end of the race? Enter your answer in the box.

Answers

Answer:

The distance between the last water shop and the end of the race is 2.1 miles

Step-by-step explanation:

Keep on adding 2.75 until you get the number 11 or you can just multiply 2.75 by 4 and get 11. Subtract 11 from 13.1 and you will get 2.1 miles.

I hope this helps

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Answers

Answer: 14

Step-by-step explanation:

What is the equation of this line?

Answers

Answer:

y= -5/4x + 6

Step-by-step explanation:

y= mx + b

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-I hope this helps have a great day!

Answer:

y = -5/4(x)+6

Step-by-step explanation:

to find the equation of this line, we must first find the slope

We can write the equation of this line y = mx + b where m is the slope and b is the y-intercept

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Answers

Answer:

Slope = 0

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Step-by-step explanation:

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[tex]Slope = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}\\\\\=\frac{-8-[-8]}{6-[-8]}\\\\=\frac{-8+8}{6+8}\\\\= 0[/tex]

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Answer:

24.4

Step-by-step explanation:

Now please give me  Brainiest.

If the average grade of an English class rose from 70 to 80 what is the approximate percent increase

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Answer:

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ASAP HELP BRAINLIEST 100 POINTS PLZ PLZ PLZ HELP



Michelle is having a poster printed from a picture that is 4 inches wide by 6 inches tall. The enlarged poster is 20 inches wide and 30 inches tall. Which proportion can be used to represent the picture sizes?
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StartFraction 4 over 6 EndFraction = StartFraction 30 over 20 EndFraction
StartFraction 4 over 30 EndFraction = StartFraction 6 over 20 EndFraction

Answers

Answer:

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Step-by-step explanation:

if the height went from 6 to 30 that means it grew by 5 so the poster would be

20 inches wide and 30 inches tall

Answer:

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PLEASE HELP FAST!!!!Match each description to the expression that can be used to represent it.

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Mayra is the middle child of the family is a, Sakshi is 1 year older than maya is 1+a, and Amul is 2 years younger than Maya is a-2.

Answer:

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Enter your answer in the box.

Answers

Answer:

y = -2x - 4

Step-by-step explanation:

-2 is our slope

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y=-2/1-4

-4 is the y intercept

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please someone help me solve this

Answers

Answer:

[tex]\frac{4}{3}[/tex]

Step-by-step explanation:

A(1 , 3)  & B  (4 , 7)

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Answers

A hierarchy of quadrilaterals is shown. Name the figures that complete the hierarchy. Number the figures in your response to indicate where in the diagram they belong.

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Answer:

x=27

Step-by-step explanation:

It's gonna be okay! Just breathe!

You got this I believe in you!!

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Answers

Answer: kim made $6,900 in commission for selling the house

Step-by-step explanation:i took the test

Find the slope of:
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Answers

The slope is undefined.

What is a slope?

In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction

Given points (-4 ,5) and (-4 ,2).

If a line passes through two points (x₁ ,y₁) and (x₂, y₂) ,

then the equation of line is

y - y₁ = (y₂- y₁) / (x₂ - x₁) x (x - x₁)

To find the slope;

m =  (y₂- y₁) / (x₂ - x₁)

m = (2-5) / (-4+ 4)

here,  (x₂ - x₁)  =0

That means the slope is undefined.

Therefore, the slope is undefined.

To learn more about the slope;

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The area of a rectangle is 6 + 3x square feet. Which of the following expressions could represent the lengths
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Answers

Answer:

B

Step-by-step explanation:

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distribute

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Answer:

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Step-by-step explanation:

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Answers

Answer:The answer would be 20 books divide 15 \ 1.50 equals 10 then multiply 10 by 2

Step-by-step explanation:

The number of books sold by Holly and Ethan to get a profit of $30 will be 20.

What is an expression?

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that Holly and Ethan decide to sell some of their books at a flea market. The booth rental costs $15, and they will sell each book for $1.50.

The number of books will be calculated as,

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x = 30 / 1.5

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Answers

Answer:

B. 12.40

Step-by-step explanation:

Add all the hours

Total profit divided by the amount of hours

What is the value of the expression
-1s/20r if r= -1/4 and s= 4/5?
Simplify your answer.​

Answers

Answer:

[tex]\frac{4}{25}[/tex]

Step-by-step explanation:

Given expression:

          [tex]-\frac{1s }{20r}[/tex]  

   r  = [tex]-\frac{1}{4}[/tex] , s = [tex]\frac{4}{5}[/tex]

Now;

     [tex]-\frac{1s }{20r}[/tex]    = [tex]-\frac{s}{20r}[/tex]

              Insert the parameters:

                = [tex]-\frac{\frac{4}{5} }{20 x (-\frac{1}{4} )}[/tex]  

               = - [tex]\frac{\frac{4}{5} }{-5}[/tex]  

              -x - = +

                = [tex]\frac{4}{5}[/tex] x [tex]\frac{1}{5}[/tex]

                = [tex]\frac{4}{25}[/tex]

please help. i will give brainliest to the right answer

Answers

Answer:

use math-way it will really helps

Answer:

I believe its 15 because when substituting the number 15 means that when working the question out, both sides equal to the same number if x is equal to 1 for example

Write and equation in slope-intercept form of the line that passes through the points
(-5,-12) and (1,6)
The equation is y=

Answers

Answer:

Step 1: We need to use slope formula* to determine what m (or the slope) is.

[tex]m = \frac{6 - (-12)}{1 - (-5)}\\\\m = \frac{18}{6} = 3[/tex]

Step 2: Now we use this slope, ONE of the given points, and slope-intercept form** to determine b.

[tex]6 = 3(1) + b\\\\6 = 3 + b\\\\3 = b[/tex]

Step 3: The final answer can now be found by using the slope and y-intercept (or b) that we just found.

[tex]y = 3x + 3[/tex]

For Reference:

*Slope formula

[tex]m = \frac{y_{2} - y_1}{x_2 - x_1}[/tex]

*Slope-intercept Formula

[tex]y = mx + b[/tex]

Please help meee I really need help I’ve been struggling badly..

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Answer:

make it so that its flat or turn it left

Step-by-step explanation:

name 2 negative integer

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Answer:

A number that is less than zero

Step-by-step explanation:

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75c- 300 - 35 c =25c + 15c + 200

Answers

Answer:

False

Step-by-step explanation:

40c - 300 = 40c + 200

-300 = 200

false

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