On a game show, contestants shoot a foam ball toward a target. The table includes points along one path the ball can take to hit the target where x is the time that has passed since the ball was launched and y is the height at this time. Time (x) Height (y) 0 10 2 24 16 10 How high was the ball after 8 seconds? 20 feet 42 feet 96 feet 106 feet.

Answers

Answer 1

After 8 seconds the ball height was 42 units.

It is given that on a game show, contestants shoot a foam ball toward a target. The table includes points along one path the ball can take to hit the target where x is the time that has passed since the ball was launched and y is the height at this time.

It is required to find how high was the ball after 8 seconds.

What is a parabola?

It is defined as the graph of a quadratic function that has something bowl-shaped.

The orbit of the ball will be a parabola.

We know the standard form of a quadratic function:

[tex]\rm y=ax^2+bx+c[/tex]      where [tex]\rm \\a\neq 0[/tex]

At x = 0 and y = 10, we get:

[tex]\rm 10 =a(0)^2+b(0)+c\\\rm 10= c\\\rm c=10[/tex]

At x = 2 and y=24, we get:

[tex]\rm 24= a(2)^2+b(2)+c\\\rm 24=4a+2b+10\\\rm 4a+2b=14[/tex]....(1)

At x = 16 and y = 10, we get:

[tex]\rm 10= a(16)^2+b(16)+c\\\rm 10=256a+16b+10\\\rm 256a+16b=0 \\[/tex]....(2)

By solving equations (1) and (2), we get;

a = - 1/2, b = 8 and c = 10

Putting these values in the standard form of a quadratic function, we get:

[tex]\rm y = - \frac{1}{2} x^2+8x+10\\[/tex]

Now, after 8 seconds means when x = 8, we get:

[tex]\rm y=-\frac{1}{2}\times 8^2 +8\times8+10\\\rm y = -32+64+10\\\rm y= 42[/tex]

Thus, after 8 seconds the ball height was 42 units.

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Answer 2

Answer:

b

Step-by-step explanation:


Related Questions

HELP PLEASE! 40 POINTS AND WILL MARK BRAINLIEST.

Describe how to find the 12th term from the sequence below.
f(1)=4
f(n)=f(n-1)+5

Answers

The first term, f(1) = 4, to find the second term,

which is f(2-1) = f(1) = 4, so second term, f(2) = 4+5

hence 9, to find the terd term,

which is f(3-1) = f(2) = 9, so terd term, f(3) = 9+5

hence 14, so common difference is 5.

12 term is 59.

Please help me out :)

Determine the intercepts of the line

Answers

Answer:

x-intercept: (15/7 , 0)

y-intercept: (0, 5/2)

*just plug in y=0 to find the X-intercept and x=0 for the y-intercept

A rectangular driveway is 40 feet long
and 14 feet wide. What is the
perimeter of the driveway?

Answers

Answer:

p=108

Step-by-step explanation:

Answer:

108 ft^2

Step-by-step explanation:

_____________

|                           |

|                           |

|                           |   40ft

|                           |

|                           |

_____________

           14ft

40+40+14+14 = 108 ft squared

What is 44.8 multipled by 44.8

Answers

Answer:

2007.04

Step-by-step explanation:

Answer?
What is it?

7m-7-6m-16=1+4m

Answers

7m-7-6m-16=1+4m

7m - 6m - 7 - 16 = 1 + 4m

    m       -   23  = 1 + 4m

m - 23 + 23 = 1 + 23 + 4m

m = 4m + 24

m - 4m = 4m - 4m + 24

-3m = 24

m = 24: (-3)

m = - 8

hi again,

7m-7-6m-16=1+4m

7m-6m-4m=1+7+16

-3m=24

m=24/-3

m=-8

Hope this helps

Starting at noon, the temperature dropped steadily at a rate of 0.8 degrees Celsius every hour. For each of these situations, write and solve an equation and describe what your variable represents. a. How many hours did it take for the temperature to decrease by 4.4 degrees Celsius?

Answers

Answer:

5.5 hours

Step-by-step explanation:

For every 1 hour, there is a 0.8 degrees Celsius drop in temperature.

Let "t" represent the total amount of temperature dropped.

Let "h" represent the number of hours

The given scenario can be represented with the equation below:

[tex] t = 0.8h [/tex]

To find the number of hours (h), it takes for the temperature to decrease by 4.4 degrees Celsius, plug in the value of t in the equation, and solve for h.

[tex] t = 0.8h [/tex]

[tex] 4.4 = 0.8h [/tex]

Divide both sides by 0.8

[tex] 5.5 = h [/tex]

It would take 5.5 hours for the temperature to decrease by 4.4 degrees Celsius.


ASAP!!! FOR BRAINlIEST!!

Answers

Answer:

No

Step-by-step explanation:

the value x is used twice, meaning when graphed it is going to meet to points at the same time, which makes it not a functions.

- i hope this makes sense

A right cylinder is sliced perpendicular to its base.
What is the shape of the resulting two-dimensional cross section?

A. Triangle
B. Trapezoid
C. Circle
D. Rectangle

Answers

When a right cylinder is sliced perpendicular to its base, the cross section that we will have is

D. Rectangle

Mensuration of Solids

Description of Rectangle

A rectangle is a solid shape with six faces and four vertices, it has two of it sides equal.

Description of Cylinder

We have the square based cylinder, the triangular base cylinder etc.

Unlike the Rectangle, the cylinder has no vertice.

Please see attached the image of cylinders

Learn more about cylinders here:

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Answer:

The players club is playing with the players

Step-by-step explanation:

give me a good Answer to my Question

What is the scale factor of this dilation? a:1/2 b:2/3 c:3/4 d:3/2

Use a calculator to find decimal estimates to two decimal places (hundredths) for the following irrational number: √19​

Answers

Answer:

The answer is 4.35, rounded two decimals to hundredths place.

some text here to make the answer slightly longer for some good reasons. yep.

Which relationships have the same constant of proportionality between yyy and xxx as the equation y=\dfrac{5}{2}xy= 2 5 ​ xy, equals, start fraction, 5, divided by, 2, end fraction, x? Choose 3 answers: Choose 3 answers: (Choice A) A 5y=2x5y=2x5, y, equals, 2, x (Choice B) B 8y=20x8y=20x8, y, equals, 20, x (Choice C) C (Choice D) D (Choice E) E xxx yyy 111 2\dfrac{1}{2}2 2 1 ​ 2, start fraction, 1, divided by, 2, end fraction 444 101010 777 17\dfrac{1}{2}17 2 1 ​ 17, start fraction, 1, divided by, 2, end fraction

Answers

Answer:

[tex]8y = 20x[/tex]

Step-by-step explanation:

Given

[tex]y=\dfrac{5}{2}x[/tex]

Required

Determine equivalent expressions

A. 5y = 2x

[tex]y=\dfrac{5}{2}x[/tex]

Multiply through by 5

[tex]5 * y=\dfrac{5}{2}x * 5[/tex]

[tex]5y=\dfrac{25}{2}x[/tex]

This is not equivalent

B.  8y = 20x

[tex]y=\dfrac{5}{2}x[/tex]

Multiply both sides by 8

[tex]8 *y=\dfrac{5}{2}x * 8[/tex]

[tex]8y=\dfrac{5 * 8}{2}x[/tex]

[tex]8y=\dfrac{40}{2}x[/tex]

[tex]8y = 20x[/tex]

The other options are not clear.

However, another possible relationship is when

[tex]y=\dfrac{5}{2}x[/tex]is cross multiplied

This gives:

[tex]2y = 5x[/tex]

Answer:

d=          y =x

Step-by-step explanation

i clicked on all the awnser and got it write

What is the solution of: 4-2x/7 - 3x+2/3

Answers

Answer:

  (-27x -2)/21

Step-by-step explanation:

Perhaps you want to combine the two fractions. This is done using a common denominator.

  [tex]\dfrac{4-2x}{7}-\dfrac{3x+2}{3}=\dfrac{3(4-2x)}{7\cdot3}-\dfrac{7(3x+2)}{7\cdot3}\\\\=\dfrac{3(4-2x)-7(3x+2)}{21}=\dfrac{12-6x-21x-14}{21}=\boxed{\dfrac{-27x-2}{21}}[/tex]

__

Additional comment

If you need to simplify this further, you can apply the distributive property.

  = -9/7x -2/21

Hannah has a credit card with an APR of 11. 90% and a billing cycle of 30 days. The following table shows Hannah’s transactions in the month of April. Date Amount ($) Transaction 4/1 322. 95 Beginning balance 4/10 19. 87 Purchase 4/14 50. 00 Payment 4/19 71. 21 Purchase If Hannah’s credit card company calculates finance charges using the daily balance method, what will her April finance charge be? a. $2. 71 b. $3. 20 c. $3. 30 d. $3. 61.

Answers

The finance charge of April month of Hannah's credit card which is calculated by daily balance method is $3.30.

What is finance charge?

The finance charge is the amount of the money which borrowed, including the interest amount and other fees.

The following table shows Hannah’s transactions in the month of April.

       Date       Amount ($)   Transaction  

        4/1        322.95           Beginning balance

        4/10      19.87               Purchase    

        4/14      50.00              Payment  

        4/19      71. 21                Purchase

Average balance in the account,

[tex]A=(322.95\times10)+[(342.87)\times4]+(292.82\times5)+(364.03\times11)\\A=10069.41[/tex]

Hannah has a credit card with an APR of 11. 90% and a billing cycle of 30 days. The finance charges,

[tex]\rm FC=\dfrac{10069.41\times11.9}{365\times100}\\FC\approx3.30[/tex]

Hannah’s credit card company calculates finance charges using the daily balance method,

The finance charge of April month of Hannah's credit card which is calculated by daily balance method is $3.30.

Learn more about finance charges here;

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Which graphs show a proportional relationship? Select all that apply.

Answers

Answer:

A, D

Step-by-step explanation:

The graph of a proportional relation is a straight line that passes through the origin.

Answer: A, D

Joogh bought reaps for $3 each and biscuits for $6 each. The total cost was 108. Write an equation in standard form showing the relationship reaps (x) and biscuits (y)

Answers

Answer:

3x + 6y = 108

Step-by-step explanation:

We are given the cost of x ($3) and y ($6) and the total cost (which will be on the right side of the = sign)We know that x + y = total. This means that we will add $3 and $6 to get the total.You would multiply $3 by x in case there is more than one reap purchased. This applies to biscuits as well.In conclusion, you would use this information to get...3x + 6y = 108 (or $3y + $6y = $108)

If I am incorrect in my reasoning, please let me know so that I can plan better for my future answers. Have an amazing day.

What is the solution to the system of equations below?

x + 3 y = 15 and 4 x + 2 y = 30
(7 , 2)
(2, 7)
(4, 3)
(3, 4

Answers

Answer:

Step-by-step explanation:

x + 3y = 15   ×4

4x + 2y = 30   ×1

4x + 12y = 60

 -       -       -

4x + 2y = 30

      10y = 30

y = 30/10

y = 3

To solve for x, substitute y = 3 into any of the equations

x + 3(3) = 15

x + 9 = 15

x =  15 - 9

x = 6

(6,3)

This should be the answer but I don't see that in the options u listed, so I don't know what else it should be.

The required solution to the system of equations is (x, y) = (6, 3).  

Given the system of equations:

x + 3y = 15

4x + 2y = 30

Multiply Equation 1 by 2 to make the coefficients of y in both equations equal:

2(x + 3y) = 2(15)

2x + 6y = 30

Subtract Equation 2 from the modified Equation 1 to eliminate the variable x:

(2x + 6y) - (4x + 2y) = 30 - 30

-2x + 4y = 0

Divide the resulting equation by 2 to simplify it further:

-x + 2y = 0

Now, we have a new equation:

3) -x + 2y = 0

Add the new Equation 3 to the original Equation 1 to eliminate the variable x again:

(x + 3y) + (-x + 2y) = 15 + 0

5y = 15

Solve for y:

y = 15 / 5

y = 3

Now, substitute the value of y back into Equation 1 to find x:

x + 3(3) = 15

x + 9 = 15

x = 15 - 9

x = 6

Learn more about equations here:

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#SPJ4

pls answer , please brainlist

Answers

Option 4. Hope this helps :)

Answer: Option 4 - 1440

Step-by-step explanation:

2 Square Sides : Take 12 times 12 and times by two for both sides.

12 x 12 = 144     144 x 2 = 288

4 rectangular sides : The multiplication of 12 times 24

12 x 24 = 288    288 x 4 = 1152

Added All Together : 288 + 1152 = 1440

A regulation basketball has a diameter of about 9 in. What is the best approximation for the volume of this ball? 3050 in³ 382 in³ 215 in³ 84. 8 in³.

Answers

The best apporximation for the volume of this ball is 382 cubic inches.

What is the volume of the ball?

The volume of the ball is calculated by the formula V = 4 / 3πr³. This formula is the same in the whole world.

Given

A regulation basketball has a diameter of about 9 in.

The radius of the ball is;

[tex]\rm Radius = \dfrac{Diameter}{2}\\\\Radius=\dfrac{9}{2}\\\\Radius=4.5\ inches[/tex]

The volume of the ball is;

[tex]\rm Volume =\dfrac{4}{3}\pi r^3\\\\Volume=\dfrac{4}{3} \times 3.14 \times 4.5^3\\\\Volume =\dfrac{144.53}{3}\\\\Volume = 381.51\\\\Volume = 382 \ In^3 \ apporx[/tex]

Hence, the best apporximation for the volume of this ball is 382 cubic inches.

To know more about volume click the link given below.

https://brainly.com/question/10647788

If r= 9 units and x = 4 units, then what is the volume of the cylinder shown above?

Answers

Answer:

Volume of the cylinder is. 1017.36

Step-by-step explanation:

[tex]V=\pi r^2h[/tex] is the area of a cylinder.

Let's plug in our values.

-----

3.14 = pi

9 = radius

x = height

-----

V = (3.14)(9)^2(4)

V = (3.14)(81)(4)

V = (3.14)(324)

V = 1017.36

PLEASE HELP!!!!!!!!
also, show all work
Thank you:)

Answers

Problem 1

Answer:  104 cubic inches

----------------------

Explanation:

The prisms are similar so they have the same shape, but different sizes.

The linear scale factor from small to large is:

large/small = 10/4 = 2.5

Meaning that we multiply each dimension of the smaller prism by 2.5 to get the corresponding side length of the larger prism

4*2.5 = 10

This linear scale factor is then cubed to get the volume scale factor

(2.5)^3 = 15.625

Which tells us:

larger volume = 15.625*(smaller volume)

smaller volume = (larger volume)/15.625

smaller volume = (1625)/15.625

smaller volume = 104 cubic inches

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

Problem 2

Answer:  650 square inches

----------------------

Explanation:

We will go back to the linear scale factor of 2.5

This time, we square it to get (2.5)^2 = 6.25

This is the surface area scale factor.

larger surface area = 6.25*(smaller surface area)

larger surface area = 6.25*(104)

larger surface area = 650 square inches

3x^3 - 8y2 if x =2 and y =-3

Answers

I don’t kno I’m trynna find out

Someone help me please!

Answers

Answer:

Your answer is no.

Step-by-step explanation:

It is only proportional up till 3/84, the next one is 4/112, not 4/100

What is y=-1/4x+4 written in standard form?

Answers

Answer:

x + 4y = 16

Step-by-step explanation:

have a good day

Answer:

x + 4y = 16

Step-by-step explanation:

If Chad drove 168 miles in 2 hours, how many hours will it take Chad to drive 840 miles traveling at the same rate?

Answers

Answer:

10 hours

Step-by-step explanation:

First we need to find the rate Chad is driving. The rate is equal to distance/time, so we do 168/2, which is 84 mph. Then we have to find the time, which is distance/rate, so that would be 840/84, which is 10 hours.

Answer:

10 hours

Step-by-step explanation:

If Chad drove 168 miles in 2 hours than he drove 84 miles in one hour. If he drove 840 miles than you divide 840 by 84 and you get 10 hours. To check your work you can do 84*10= 840 miles 84=representing the miles per hour and 10=representing the amount of hours he drove.

URGENT

A mailman (M) is located 450 feet from a Post Office (P). The mailman notices a bird (B) flying at a 42° angle of elevation from his line of sight. How high (h) is the bird flying over the Post Office? Round to the nearest whole number. (Show all work)​

Answers

Answer:

We can use the sine law to find h. First, we determine the angle between the line of sight and h:

180 - 90 - 39 = 51 degrees

The sine law states that the ratio of one triangle's angle to the opposite side's length is the same as another angle to its opposite side's length, so we can solve for h as follows:

h/sin(39) = 500/sin(51)

h = 500*sin(39)/sin(51)

When we round to the nearest whole number, we get h = 405 ft.

how to do this question plz ​

Answers

Step-by-step explanation:

Hey there!

Here;

The equation is; y = 3x + 2

X = -2 -1 1 2

y = -4 -1 5 8

Now; the coordinates are ; (-2,-4), (-1,-1), (1,5), (2,8).

After this plot them on graph.

Hope it helps..

Fill in the blank. Using the number line below, the plotted number is
when rounded to the nearest hundred.
150
200
250
300
350

Answers

I think it’s 400 hope it helps

Cual es la ecuación de la recta que pasa por el punto (1, 2) y tiene una inclinación de 71.56505118

Answers

Answer:

La inclinación de una recta esta definida como el ángulo entre el eje x positivo y la recta.

Primero, podemos escribir genéricamente una recta como:

y = p*x + s

donde p es la pendiente de la recta, y s es la ordenada al origen.

Sabemos que para una recta que pasa por los puntos (a, b) y (c, d) podemos escribir la pendiente como:

p = (d - b)/(c - a)

Y también sabemos que si θ es el ángulo de inclinación, entonces:

p = tan(θ)

Entonces en este caso sabemos que:

p = tan(71.56505118°) = -0.828

Entonces esta recta es:

y = -0.828*x + s

y sabemos que pasa por el punto (1, 2), entonces podemos remplazar esos valores en la ecuación para encontrar el valor de s.

2 = -0.828*1 + s

s = 2 + 0.828 = 2.828

La ecuación es:

y = -0.828*x + 2.828

Is it important to know the steps in solving your own problems? why or why not

Answers

Answer:

yes

Step-by-step explanation:

because when you include the steps, you can find out where you made a mistake (in case) and correct it easily.

solve for the variable​

Answers

For this problem your going to want to do the equation backwards 100-4=96 then you want to divide 96 by -12 we already know that the variable is going to be a negative because two negatives equal a positive so if it’s easier for you to divide by taking off the negative sign you can go ahead and do so but 96/-12=-8 (please mark brainliest)

What is the difference between 7/10 and 14/15

Answers

Answer:

11

Step-by-step explanation:

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