The table represents a proportional relationship. Give the constant of proportionality, and write an equation that represents the relationship.

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The equation of an object in free fall is the equation of a parabola

The reason the above values are correct are as follows:

The known parameters are;

The direction of the baseball is up in the air

The values of the height of the baseball after x seconds is given as follows;

[tex]\begin{array}{ccc}\mathbf{Time, \ x}&&\mathbf{Baseball \ height, \ y}\\0.5&&18\\1&&24\\1.5&&22\\2&&12\end{array}\right][/tex]

To write the equation for the path of the baseball

Solution:

The general equation of the motion of free fall is the equation of a parabola, which can be written as follows;

y = a·x² + b·x + c

From the given table, we have;

18 = a·0.5² + b·0.5 + c = 0.25·a + 0.5·b + c

18 =  0.25·a + 0.5·b + c...(1)

24 = a + b + c...(2)

22 = 2.25·a + 1.5·b + c...(3)

12 = 4·a + 2·b + c...(4)

Subtracting equation (1), from (2), to get equation (5) and subtracting equation (3) from (4) to get equation (6) gives;

6 = 0.75·a + 0.5·b...(5)

-10 = 1.75·a + 0.5·b...(6)

Subtracting equation (5) from equation (6) gives;

-10 - 6 = 1.75·a - 0.75·a = a

a = -16

From equation (5), we get;

6 = 0.75 × (-16) + 0.5·b

b = (6 - 0.75 ×  (-16))/0.5 = 36

b = 36

From equation (2), we get;

24 = (-16) + 36 + c

c = 24 - ((-16) + 36) = 4

The equation for the path of the ball is y = -16·x² + 36·x + 4

The height of the baseball after 1.7 seconds

Solution:

The height, y, of baseball after 1.7 seconds is given by substituting for the time x = 1.7 in the equation of the baseball as follows;

After 1.7 seconds, y = -16 × 1.7² + 36 × 1.7 + 4 = 18.89

The height of the baseball y, after 1.7 seconds is 18.89 feet.

Learn more about motion of an object in free fall here:

https://brainly.com/question/14113699

Answer: A shirt costs $8 and the pants cost $ 12.

Step-by-step explanation:

Let x = Cost of each shirt, y = Cost of each pant.

As per given, we have

[tex]y-x=4 \ \ \ (i)\\\\ 10x-5y = 20\ \ \ (ii)[/tex]

Multiply 5 on both sides of (i), we get

[tex]5y-5x=20 \ \ \ (iii)[/tex]

Add (ii) and (iii), we get

[tex]5x=40\\\\\Rightarrow\ x=8[/tex]

From (i), y=4+8=12

Hence, a shirt costs $8 and the pants cost $ 12.

Answer:

-12

Step-by-step explanation:

the opposite of 12 is -12

Answer:

(look in the the Step by step)

Step-by-step explanation:

When the diagonals of a quadrilateral are perpendicular, the area of that quadrilateral is half the product of their lengths.

.. A = (1/2)*d₁*d₂

Substituting the given information, this becomes

.. 58 in² = (1/2)*(14.5 in)*d₂

.. 2*58/14.5 in = d₂ = 8 in

The length of diagonal BD is 8 in.

Answer:

BD = 8 in.

Step-by-step explanation:

Answer:

it could be the 5th one !!

Answer:

4x-2

Step-by-step explanation:

(5x-10)+(-x+8)

5x-10-x+8

5x-x-10+8

4x-10+8

4x-2

Therefore, the sum is 4x-2

Answer:

4x - 2

Step-by-step explanation:

(5x - 10) + (-x + 8)

To solve this problem, one must simplify, combine like terms. One can only combine a variable unit with another variable unit, likewise, one can only combine a constant (numerical term) with another constant.

(5x - 10) + (-x + 8)

= 5x - 10 - x + 8

= 4x - 2

Answer:

Step-by-step explanation:

Answer:

485297

Step-by-step explanation:

Answer: the circumference of the entire circle is 28.26

The sector is 1/3 of the circle

The arc length is 9.42 in

ON EDGE

Answer:

The circumference of the entire circle is

28.26

π in.

The sector is

1/3

of the circle.

The arc length is

9.42

π in.

Step-by-step explanation:

Answer:

C is the correct answer

Step-by-step explanation:

Answer:

Hello there! I would say the answer is C,

Step-by-step explanation:

I hope this helps!!!

Answer:

x=29

∠C=93°

Step-by-step explanation:

180°-52°-35°=3(x+2)°

180°-87°=(3x)°+6°

93°=(3x)°+6°

(3x)°=87°

x=[tex]\frac{87}{3}[/tex]

x=29

∠C=3(x+2)°

=3(29+2)°

=3(31)°

=93°

Answer:

3x4

Step-by-step explanation:

If you draw a rectangle with a length of 4 and a width of 3, it will have 12 sq units as the area.

This is because A=lw. If the area is 12, the length and width must multiply to get 12. 3x4=12.

Answer:

there is what i would do to answer it

Answer:

circles are measur by 360°.

circles are similar triangle.

circles are two radis.

circles are one diameter.

Answer:

1,3,4

Step-by-step explanation:

Answer:

Step-by-step explanation:

the easiest thing to do is to make the half squares which you have 4 into 2 whole  squares then base times height

4x3=12

Answer:

26cm²

Step-by-step explanation:

Alrighty, let's go count squares:

On the top row, there's 4 (adding the halves together), on the second row there's 5, and on the bottom row there's also 4, so we add that all together to get:

4 + 5 + 4 = 13

But, because each square is 2 cm, we have to multiply:

13 x 2 = 26

So, the area of the shaded section is 26cm²

hope this helps:)

Answer:

6

Step-by-step explanation:

expand

x-7= 1/4x-10/4

3/4x=18/4

multiply 4 on both sides to get rid of the denominator

3x=18

x=6

check work by substituting

6-7= 1/4(6-10)

-1= 1/4(-4)

-1=-1

they are equal, so it's correct

Answer: $19,610

Step-by-step explanation:

53000(.37)=19610

Answer:

261

Step-by-step explanation:

Answer:

the answer is

13 cm:y

5 cm:x

2 cm:z

Answer:

6

Step-by-step explanation:

f(s) = x^2 - 3

f(-3) = 6

f(0) = -3

f(1) = -2

f(2) = 1

Answer:

0.5

Step-by-step explanation:

Complete question :

Between 12:00 PM and 1:00 PM, cars arrive at Citibank’s drive-thru at the rate of 6 cars per hour (0.1 car per minute). The following formula from statistics can be used to determine the probability that a car will arrive within t minutes of 12:00 PM. F(t)=1−e^−0.1t

Determine how many minutes are needed for the probability to reach 80%.

Answer:

16.09 minutes

Step-by-step explanation:

Given the function :

F(t)=1−e^−0.1t

To attain 80% probability ; 80% = 0.8

0.8 = 1 - e^-0.1t

0.8 - 1 = - e^-0.1t

-0.2 = - e^-0.1t

Take the In of both sides

In(0.2) = In( e^-0.1t)

−1.609437 = - 0.1t

Divide both sides by - 0.1

−1.609437 / -0.1 = - 0.1t / 0.1

16.09 = t

Hence, the time it'll take will be 16.09 minutes

Answer:

80/100=0.80

.8=1-e^-0.3t

.8+1=-e^-0.3t

1.8=-e^-.3t

t=5.36

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

[tex] {x}^{2} + 18x + 81[/tex]

Step-by-step explanation:

[tex](x + 9) {}^{2} [/tex]

Apply foil method.

[tex](x + 9) {}^{2} = (x + 9)(x + 9)[/tex]

Multiply the first terms, X

[tex]x \times x = {x}^{2} [/tex]

Multiply outer terms, 9 and x.

[tex]x \times 9 = 9x[/tex]

Multiply inner terms,

[tex]9 \times x = 9x[/tex]

Multiply outer terms.

[tex]9 \times 9 = 81[/tex]

Add the inner and outer terms

[tex]9x + 9x = 18x[/tex]

Write in standard form

[tex] {x}^{2} + 18x + 81[/tex]

It should be 4/7 ! If I'm wrong I apologize- but I hope this helps :)

Answer:

4/7 :)

Step-by-step explanation:

Answer:

A. p + (3p – 5) + (4p + 6)

D. 8p + 1

Step-by-step explanation:

A. p + (3p – 5) + (4p + 6)

B. p + (5 – 3p) + (6 + 4p)

C. p + 11

D. 8p + 1

E. 7p – 1

Lauryn = p tomatoes

Padma = (3p - 5) tomatoes

Kent = (4p + 6) tomatoes

Total number of tomato plants that Lauryn, Padma, and Kent grew = Lauryn + Padma + Kent

= p + (3p - 5) + (4p + 6)

= p + 3p - 5 + 4p + 6

= p + 3p + 4p - 5 + 6

= 8p + 1

Total number of tomato plants that Lauryn, Padma, and Kent grew = 8p + 1

A. p + (3p – 5) + (4p + 6)

D. 8p + 1

Answer:

Well like what? It could be anything, but what do you mean "like these"

Step-by-step explanation: