A ball is thrown upward and outward from a height of 8 feet. The height of the ball, f(x), in feet, can be modeled by
f(x) = -0.1x² +0.6x+8
where x is the ball's horizontal distance, in feet, from where it was thrown. Use this model to solve parts (a) through (c).
WEB
a. What is the maximum height of the ball and how far from where it was thrown does this occur?
The maximum height is feet, which occurs feet from the point of release.
(Round to the nearest tenth as needed.)

Answers

Answer 1

Check the picture below.

let's change the decimal values to fractions, say 0.1 to 1/10 and 0.6 to 6/10 = 3/5, so then

[tex]\textit{vertex of a vertical parabola, using coefficients} \\\\ y=\stackrel{\stackrel{a}{\downarrow }}{-\frac{1}{10}}x^2\stackrel{\stackrel{b}{\downarrow }}{+\frac{3}{5}}x\stackrel{\stackrel{c}{\downarrow }}{+8} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right)[/tex]

[tex]\left(-\cfrac{~~ \frac{3}{5}~~}{2\frac{-1}{10}}~~,~~8-\cfrac{\left( \frac{3}{5} \right)^2}{4\left(-\frac{1}{10} \right)} \right)\implies \left(\cfrac{~~ \frac{3}{5}~~}{\frac{1}{5}}~~,~~8+\cfrac{\frac{9}{25}}{\frac{2}{5}} \right)[/tex]

[tex]\left( \cfrac{3}{5}\cdot \cfrac{5}{1}~~,~~8+\left[ \cfrac{9}{25}\cdot \cfrac{5}{2} \right] \right)\implies \left(3~~,~~8+\cfrac{9}{10} \right)\implies \stackrel{\stackrel{\textit{maximum height}}{\qquad \downarrow }}{\underset{\underset{\textit{horizontal distance}}{\uparrow \qquad \quad }}{\left( 3~~,~~8\frac{9}{10} \right)}}[/tex]

A Ball Is Thrown Upward And Outward From A Height Of 8 Feet. The Height Of The Ball, F(x), In Feet, Can

Related Questions

Work out the area of the shaded shape.

Answers

Answer:

61 m²

Step-by-step explanation:

Find the area of the whole rectangle and subtract the part that is cut off

Area =  [tex]11 *8 - 9 *(8-5)[/tex]

        = [tex]88 - 9*3[/tex]

        = [tex]88 - 27[/tex]

        = [tex]61[/tex]

Units = m * m or m²

61 m²

-Chetan K

Help me with this question thanks so much

Answers

It would be 6^8 or 1,679,616
Since it’s times 6 each time and the base is 6 it can be written as an exponent 6*6*6...
Hope that helps :)

Anna categorized her spending for this month into four categories: Rent, Food, Fun, and Other.

If Anna spent a total of $2900 this month, how much did she spend on Rent?

Answers

Answer:

.26 * 2900= 754 dollars

Step-by-step explanation:

I'm not sure if it's right.

If a rectangle has a base of 6' and a height of 4' its area would be what?
A= bxh
A= 6'x4'
A= 24 sq.ft.

Answers

24 sq.ft. Is the answer if not then I’m sorry

How do I solve this? 2(-2w-1.2+7x)

Answers

-4w-2.4+14x this is the answer for this

The town of Winchester recently built an artificial body of Vater. This reservoir will store drinking water for the
town. Which of the following could cause contamination of the water and lead to human health-related problems
and loss of native species?
development of a water quality plan
B building a fence around the reservoir
C improvements to a water treatment facility
increased use of pesticides (chemicals) by farmers within the local watershed

Answers

Answer:

This reservoir, will store drinking water for the town. Which of the following could cause contamination of the water and lead to human health-related problems and loss of native species? ... Air pollution can affect human health and the health of other living things.

Step-by-step explanation:

I am confused, can someone help me

Answers

Answer:

bc=10

Step-by-step explanation:

12/bc=18/(33-18)

12/bc=18/15

18bc=12*15

18bc=180

bc=180/18

bc=10

If △CFE≅△PTR, complete each of the following statements:

CE¯¯¯¯¯¯¯¯ ≅

TR¯¯¯¯¯¯¯ ≅


∠P ≅∠

∠F ≅∠


△FEC ≅△

△RPT ≅△

Answers

Based on the definition of congruent triangles, the statements will be completed as follows:

CE ≅ PRTR ≅ FE∠P ≅ ∠C∠F ≅ ∠T△FEC ≅ △TRP△RPT ≅ △ECF

Recall the following about Congruent Triangles:

The three angles of one triangle is congruent to the three corresponding angles in another triangle if both triangles are congruent triangles.The three sides of one triangle is congruent to the three corresponding sides in another triangle if both triangles are congruent triangles.

Given that △CFE≅△PTR, thus:

CE corresponds to PR, therefore CE ≅ PRFE corresponds to TR, therefore FE ≅ TRCF corresponds to PT, therefore CF ≅ PT∠P corresponds to ∠C, therefore ∠P ≅ ∠C∠T corresponds to ∠F, therefore ∠T ≅ ∠F∠R corresponds to ∠E, therefore ∠R ≅ ∠E

Thus, based on the definition of congruent triangles, the statements will be completed as follows:

CE ≅ PRTR ≅ FE∠P ≅ ∠C∠F ≅ ∠T△FEC ≅ △TRP△RPT ≅ △ECF

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What is the volume of a cylinder with a height of 13 and radius 6?

Answers

1470.27

v = pi r^2 (H)

v = 3.14 (6^2) (13)

v = 3.14 (36) (13)

v = 1470.27 (about)

Answer:

V = 1470

Step-by-step explanation:

V = πr²h

V = (3.14)(6²)(13)

V = (3.14)(36)(13)

V = 1469.52

2^x+2=4. yall i got this problem and i dont rlly understand how to do it. Hope yall can help me:)))))))))))))))

Answers

Answer:

[tex]x=1[/tex]

Step-by-step explanation:

Ok, so we start off with [tex]2^x+2=4[/tex]

Then, we subtract 2 from both sides so that becomes: [tex]2^x+2-2=4-2[/tex]

After that, we simplify to get: [tex]2^x=2[/tex]

Finally, the solution becomes: [tex]x=1[/tex]

Answer:

x=1

Step-by-step explanation:

2^x=4-2

2^x=2

2^x=2^1

x=1

if I set off for the market,a distance of 11km at 10am. And walk at an average speed of 3km per hour,At what time will I reach the market?​

Answers

Answer:

At 1:40 pm you will reach the market.

Step-by-step explanation:

Distance (d) = 11 km

Average speed (v) = 3 km/h

Formula:

[tex] \rm Average \: speed = \dfrac{Distance}{Time} \\ \\ \rm 3 = \dfrac{11}{t} \\ \\ \rm t = \dfrac{11}{3} \\ \\ \rm t = 3 \frac{2}{3} \\ \\ \rm t = 3 hr \: 40min[/tex]

It will take 3 hours 40 minutes to reach the market.

So, if you set off for the market at 10 am you will reach market by 1:40 pm (10 am + 3hr 40min).

3(x+9)-4x=11x-13x+23

Answers

Answer:

[tex]\huge\boxed{x=-4}[/tex]

Step-by-step explanation:

[tex]3(x+9)-4x=11x-13x+23\\\\(3)(x)+(3)(9)-4x=(11x-13x)+23\\\\3x+27-4x=-2x+23\\\\(3x-4x)+27=-2x+23\\\\-x+27=-2x+23\qquad|\text{subtrsact 27 from both sides}\\\\-x=-2x-4\qquad|\text{add}\ 2x\ \text{to both sides}\\\\x=-4[/tex]

3. Tom's entered a snowman building contest in which the person who builds the tallest
snowman wins. Currently, the record is 13.4 feet high. If Tom's snowman is currently 9 feet
high, how many more feet does he need to build on, in order to win the competition

Answers

tom's snowman has to increase by anything greater than 4.4 ft

Answer:

4.5 feet

Step-by-step explanation:

9+4.5=13.5

13.5>13.4

Name.
Solve using
Substitution
L
y = 3x + 2
6x - 2y = 8

Answers

Answer:

No solution

Step-by-step explanation:

There is no solution to the system of equations y=3x+2 and 6x-2y=8, meaning that they are parallel to each other on a graph, with no points ever intersecting on each other's lines.

Which expression is equivalent to (6x + 12)?

Answers

Answer:

2(3x + 6)

Step-by-step explanation:

a tube has a radius of 4 inches and a height of 4 inches. what's its approximate volume?

Answers

Step-by-step explanation:

that is the same as the volume of a cylinder :

pi×r²×height = pi×4²×4 = pi×64 = 201.0619298... in³

≈ 201 in³

Volume is a three-dimensional scalar quantity. The volume of the tube is 201.0619 inches³.

What is volume?

A volume is a scalar number that expresses the amount of three-dimensional space enclosed by a closed surface.

The volume of a cylinder is given by the formula as shown below,

Volume of a cylinder = πr²h

where r is the radius of the cylinder while h is the height of the cylinder.

Given that a tube has a radius of 4 inches and a height of 4 inches. Therefore, the volume of the tube will be,

The volume of the tube = π × R² × h

                                       = π × (4 inches)² × (4 inches)

                                       = 64π inches³

                                       = 201.0619 inches³

Hence, the volume of the tube is 201.0619 inches³.

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You have been asked to analyze the popcorn recipes of three different local theatres in order to figure out which theatre has the best popcorn. In this case, the "best" popcorn is the most buttery! In your quest to find the best, you meet with each theatre manager individually and ask for the ratio of oil to popcorn kernels that they use in their recipes. Here are their responses.

The manager of Theatre A says that they usually go through about 15 cups of popcorn kernels and about 5 cups of oil each weeknight.
The manager of Theatre B says that they order 18 cups of oil and 72 cups of popcorn kernels each week.
The manager of Theatre C says that their concessions use 6 cups of oil and 32 cups of popcorn kernels on a busy Saturday.
You also ask about the amount of salt each theatre uses in their recipe. Their responses are below.

Theatre A uses 2 cups of salt for every 10 cups of oil.
Theatre B uses cup salt for every cup of oil.
Theatre C uses 1 cup of salt for every 6 cups of oil.
For each of the following ratio problems, use a double number line or an equation to solve. Type your answers as numbers.

If Theatre A uses 27 cups of popcorn kernels, how many cups of oil will they use?

_____cups

Answers

Answer:    The ratio value of oil to popcorn kernels for theatre C is 6 / 32 = 3 / 16.

Step-by-step explanation: Given that the manager of Theatre A says that they usually go through about 15 cups of popcorn kernels and about 5 cups of oil each weeknight.

Then, the ratio value of oil to popcorn kernels for theatre A is 5 / 15 = 1 / 5.

Given that the manager of Theatre B says that they order 18 cups of oil and 72 cups of popcorn kernels each week.

Then, the ratio value of oil to popcorn kernels for theatre B is 18 / 72 = 1 / 4.

Given that the manager of Theatre C says that their concessions use 6 cups of oil and 32 cups of popcorn kernels on a busy Saturday.

Then, the ratio value of oil to popcorn kernels for theatre C is 6 / 32 = 3 / 16.

is ( -5, 6) ( -2, 0) ( 0, 6) ( 0, 2) ( 1, -3) a function

Answers

Answer:

No

Step-by-step explanation:

No, ( -5, 6) ( -2, 0) ( 0, 6) ( 0, 2) ( 1, -3) do not make up a function. It does not pass the vertical line test when graphed, as there are 2 points, (-5, 6), and (0, 6), that lines up on the same y-value.

WHAT PERCENT OF 200 IS 28???? HELP MEEEEEE!!!!!!!!!

Answers

Answer:

14%

Step-by-step explanation:

Find the quotient of 29 and 200.

[tex]\frac{28}{200}=0.14[/tex]

Therefore, 28 is 14% of 200.

The number 28 is 14% of the number 200.


What is the percentage?

The percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.

Given that the number is 200 and 28 is what percent of 200 will be calculated as:-

The percentage will be calculated as:-

200 x (X)% = 28

X% = ( 28 x 100) / 200

X% = 14%

Therefore, the number 28 is 14% of the number 200.

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3
Evaluate the function f(x) = (x + 2)2 for the given inputs.
a. f(5)=
b. f(-3) =
c. f (x+3) =

Answers

Answer:

a. 49

b. 1

c. x^2+10x+25

Step-by-step explanation:

Symply substitute the values (5, -3, x+3) in the equation (x+2)^2

2. Harry puts $5 in his piggy bank every
week. What type of slope does this
scenario describe? Explain.

Answers

Answer:

linear

Step-by-step explanation:

Answer:

Linear slope of 5/1

Step-by-step explanation:

The rate is constant.

Hope that helps

What is the end behavior of the function f(x)=−3/4x^2?

Answers

Answer:

[tex]f(x)\longrightarrow-\infty[/tex], as [tex]x\longrightarrow+\infty[/tex]

Step-by-step explanation:

We can see that the larger the input, the smaller the output

Which equation represents this statement?

The product of 1/5 and a number is equal to 1/1 2.


1/5n=1/1 2

1/5÷n=1/1 2

1/5−n=1/1 2

1/5+n=1/1 2

Answers

Answer:

answer is B

Step-by-step explanation:

Nick drives 7 miles in ten minutes how many miles would nick drive if he drove at the same rate for 2 hours?

Answers

Answer 84 miles

Step-by-step explanation:

2hrs= 120min

7 miles/ 10 min = x miles/ 120 min

x = 84 miles

Answer:
84 miles
Explanation:
2 hours = 120 minutes
120 / 10 = 12
12 x 7 = 84

Does 28/4 have a remainder

Answers

No but it equals to 7 :)

Remainder=0

Quotient=7

Thanks!!

Which ordered pair (a, b) is the solution to the given system?
2a-5b=1
3a+5b=14
(1, 3)
(3, 1)
(29/5,15)
15,29/5

Answers

Answer:

2a - 5b = 1

3a + 5b = 14

Let's solve this system using elimination. Add the equations together to cancel the b-terms, then solve for a.

   2a - 5b = 1

  3a + 5b = 14

+___________

   5a - 0 = 15

        5a = 15

          a = 3

Next, plug 3 for a into either of the equations and solve for b.

 2a - 5b = 1

2(3) - 5b = 1

   6 - 5b = 1

      - 5b = -5

          b = 1

Lastly, check all work by plugging both values for their respective variables.

    2a - 5b = 1

2(3) - 5(1) = 1

        6 - 5 = 1  --  This is true

    3a + 5b = 14

3(3) + 5(1) = 14

        9 + 5 = 14  --  This is true

The solution to the system of equations is (3, 1).

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

Find the midpoint of Segment AB if A (-5, 6) and B(1.-3).
Midpoint Formula: (X: + X2, Y + y2)
2 2

Answers

Answer:

(-2, 1.5)

Step-by-step explanation:

x-coordinate = ½(1 - 5) = -2

y-coordinate = ½(-3 + 6) = 1.5

Only 19 and 21!!!!!
Thank You!!!!

Answers

Step-by-step explanation:

19. 4x² - 13x + 3

4x² - 1x - 12x + 3

x(4x - 1) -3(4x - 1)

x-3 4x-1

Ok done. Thank to me:>

Sammy's rabbit can eat 70 pounds of food in 80 days. Part A: At that same rate, how much food will Sammy need to feed his rabbit in 24 days? Part B: How long will it take his rabbit to eat 87.5 pounds of food? Part C: Suppose Sammy buys his rabbit a companion. Together, the rabbits need can eat 95 pounds of food in 65 days. Approximately how much food will Sammy need to buy in order to feed both rabbits inl year ( 365 daya)? Round to the nearest tenth.​

Answers

Part A

The rabbit can eat 70 pounds of food in 80 days. The unit rate is 70/80 = 0.875 pounds of food per day. Multiply this with the 24 days to get the total amount eaten over that timespan.

24*0.875 = 21

Answer:  21 pounds of food

=========================================================

Part B

x = number of days

The rabbit eats at a unit rate of 0.875 pounds per day. After x number of days pass by, the rabbit has eaten a total of 0.875x pounds of food. Set this equal to 87.5 and solve for x.

0.875x = 87.5

x = (87.5)/(0.875)

x = 100

Answer: 100 days

=========================================================

Part C

This is is similar to part A, just with different numbers. We could follow those steps to get the answer, but I'll go another route.

Instead, I'll use a proportion to solve.

(95 pounds)/(65 days) = (x pounds)/(365 days)

95/65 = x/365

95*365 = 65*x

34675 = 65x

65x = 34675

x = 34675/65

x = 533.461538

x = 533.5

Answer: 533.5 pounds of food

A middle school had a school spirit day. In one class the ratio of students who wore school colors to the number of students who didn’t was 8 to 5. Ten students didn’t wear school colors

Answers

Answer:

Step-by-step explanation:

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