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


Related Questions

Kim sold a house for $230,000 and made a 3% commission. How much money did Kim make in commission for selling the house?

Answers

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

Step-by-step explanation:i took the test

Find the slope of:
(-4,5) and (-4, 2)

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;

brainly.com/question/3605446

#SPJ6

Solve for x: 5(x + 3) = 4(x - 3)
-18
-27
-3
-6
please help me im actually having a mental breakdown over this stuff​

Answers

Answer:

x=27

Step-by-step explanation:

It's gonna be okay! Just breathe!

You got this I believe in you!!

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.​

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.

name 2 negative integer

Answers

Answer:

A number that is less than zero

Step-by-step explanation:

-13, -56

The area of a rectangle is 6 + 3x square feet. Which of the following expressions could represent the lengths
of the sides of the rectangle?
A. 6 and 3x
B. 3 and 2 + x
C. 6 and 6 + x
D. 3 and 2 + 3x

Answers

Answer:

B

Step-by-step explanation:

3(2+x)

distribute

=6+3x

B is the correct answer !!!

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

Answers

Answer:

B

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

edge

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 me and make sure to round the answers to the nearest hundred. I’ll give you brainiest!


Thanks!!!!:)))))

Answers

Answer:

24.4

Step-by-step explanation:

Now please give me  Brainiest.

Find the slope of the line passing through the points (-8,-8) and (6,-8)

Answers

Answer:

Slope = 0

So, the line is parallel to x-axis

Step-by-step explanation:

(x₁ , y₁) = (-8, -8)      & (x₂ ,y₂) = (6 , -8)

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

Help me I don’t not understand

Answers

Sorry I couldn’t answer S,T, &F. But I hope with the other problems that I solved makes sense, in order for you to solve the other 3.

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. How many books will Holly and Ethan need to sell to make a profit of exactly $30?

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,

1.5x = 30

x = 30 / 1.5

x = 20

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

To know more about an expression follow

https://brainly.com/question/25968875

#SPJ2

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

Answers

Answer:

False

Step-by-step explanation:

40c - 300 = 40c + 200

-300 = 200

false

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

Answers

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:

The first box on the left goes to the middle box on the right! THe second box on the left goes to the first box on the right! And the last box on the left goes to the third box on the right!

Hope this helps and u understand it

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?
StartFraction 6 over 4 EndFraction = StartFraction 20 over 30 EndFraction
StartFraction 4 over 6 EndFraction = StartFraction 20 over 30 EndFraction
StartFraction 4 over 6 EndFraction = StartFraction 30 over 20 EndFraction
StartFraction 4 over 30 EndFraction = StartFraction 6 over 20 EndFraction

Answers

Answer:

20 inches wide and 30 inches tall

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:

Start Fraction 4/6

End Fraction  20/30

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

This is because 15 times 4 equals 60 and that is equal to 1 hour, well when your multiplying fractions what you do to the bottom you have to do to the top so multiply 3 times 4 thats 12 and now you have 12/4 and that is equal to 3.

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

What is the equation of this line?

Answers

Answer:

y= -5/4x + 6

Step-by-step explanation:

y= mx + b

m= -5/4 (rise over run/slope)

b= 6 (y-intercept)

-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

m = (y2-y1)/(x2-x1)

m = (-4-6)/(8-0)

m = -10/8

m = -5/4

b is the y intercept which is at 6

So the equation of the line is y = -5/4(x)+6

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

Answers

Answer:

10

Step-by-step explanation:

I’ll give brainliest!! Just zoom in to see better!!:)

Answers

Answer:

Well done

Step-by-step explanation:

Zoomed in

Find the slope of the line

Y=1/4x + 2

Answers

Answer: 14

Step-by-step explanation:

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

Answers

Answer:

make it so that its flat or turn it left

Step-by-step explanation:

PLS HELP ASAP NO ONE HELPS ME PLSSSSSSSSS.
What is the equation for the line in slope-intercept form?

Enter your answer in the box.

Answers

Answer:

y = -2x - 4

Step-by-step explanation:

-2 is our slope

-4 is our y intercept (the point which the line crosses the y axis)

y=-2/1-4

-4 is the y intercept

the slope is -4/2, but it simplifies to -2/1

(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)

18x+−10+−4x=2x+−10+−4

(18x+−4x)+(−10)=(2x)+(−10+−4)(Combine Like Terms)

14x+−10=2x+−14

14x−10=2x−14

Step 2: Subtract 2x from both sides.

14x−10−2x=2x−14−2x

12x−10=−14

Step 3: Add 10 to both sides.

12x−10+10=−14+10

12x=−4

Step 4: Divide both sides by 12.

12x

12

=

−4

12

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!

SOMEONE PLZ HELP JSJSJSNSJNSNSNSNSNNS I HAVE 30 MINS LEFT PLZ

Answers

Answer:

the answer is d. x >=4

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

please someone help me solve this

Answers

Answer:

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

Step-by-step explanation:

A(1 , 3)  & B  (4 , 7)

[tex]Slope = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}\\\\= \frac{7-3}{4-1}\\\\= \frac{4}{3}[/tex]

please help its due today!

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]

387/4300 as a percent

Answers

Answer:

9%

Step-by-step explanation:

Convert the fraction to a decimal, then multiply by  

100. Hope this helps!

This would equal nine percent.
Other Questions
A country imports goods and services worth $700 million and exports goodsand services worth about $500 million. This means that the country has an)a. trade surplus b. trade deficit c. comparative advantage d. absolute advantage State one reason why it is important to be loyal in your life. The cost of a banquet can be calculated using the function b=75+15n where brepresents the total cost and n represents the number of people attending. If the totalcost of the banquet is 130, how many people attended the banquet? (Round to thenearest whole number) hi uhm help im bad at math Find the missing length indicated.?1249285012. 6. Which of the following element pairs would most likely form an ionic compound? (5pts) a. Ca and Ni b. Cu and Ar c. F and S d. Zn and K e. Na and Cl f. V and O g. He and Xe h. Sn and Na i. C and Br j. Sr and P k. Cr and I l. Ag and NO 3 What is one way plants and animals are similar? question 1................ please help me quickly MATCHA)AbioticD)MigrationB)AcclimationE)AnthropogenicC)Biotic 24. caused or produced by humans 25. environmental factor that is nonliving 26. an organisms change in response to a change in the environment 27. environmental factor that is living or was living 28. movement from one location to another by an organism or population The relationship between catabolism and anabolism is most similar to the relationship between which of the following pairs of terms? free energy, entropy exergonic; endergonic exergonic; spontaneous work, free energy Is 0.07 equal to 0.007 1) The entire nation seemed to be drowning in debt.What rhetorical device is used in this sentence?A) anaphoraB) hyperbolemetaphorD)metonymyE)simile What is the area of the triangle with vertices(-1,-4), (-3, -2), andd (-4,-2)? 9x-7i > 3(3x-7u)Can you simplify I GIVE BRAINLIEST !! Please help with this question! Tell how you know, Question worth 20 points! Find the slope of the line passing through the points (-8, 3) and (7,3) A wheat plant that is light green in color is found growing in a field. Biochemical analysis reveals that chloroplasts in this plant produce only 50% of the chlorophyll normally found in wheat chloroplasts. Propose a set of crosses to determine whether the light-green phenotype is caused by a mutation in a nuclear gene or in a chloroplast gene. What are the different ways in which students can create positive digital footprints 14. Why doesn't the inner core have convection?