How many times does 9 go into 204

What is the rate of change and initial value for the linear relation that includes the points shown in the table? x; 1,3,5,7

BARSIC [14]

Answer:

The rate of change is -5

The initial value is 25

Step-by-step explanation:

Since, this is a linear relation

so, we can select any two points and find equation of line

points are (1,20) and (3,10)

so,

$x_1=1,y_1=20$

$x_2=3,y_2=10$

now, we can find slope

$m=\frac{y_2-y_1}{x_2-x_1}$

now, we can plug values

$m=\frac{10-20}{3-1}$

$m=-5$

now, we can use point slope form of line

$y-y_1=m(x-x_1)$

now, we can plug values

$y-20=-5(x-1)$

now, we can solve for y

$y=-5x+25$

we know that

slope is the rate of change

So, the rate of change is -5

For finding initial value , we can plug x=0 and find y

$y=-5\times 0+25$

$y=25$

So, initial value is 25

3 0

2 years ago

A ball dropped from the top of a building can be modeled by the function f(t)=-16^2+36, where t represents time in seconds

Viefleur [7K]

Answer:

The ball is dropped from a height of 36 feet

The bee and the ball will collide after approximately 1.3 seconds

The bee and the ball will collide at approximately 8 feet above the ground

The ball hits the ground after 1.5 seconds

Step-by-step explanation:

The complete question is

A ball dropped from the top of the building can be modeled by the function f(t)=-16t^2 + 36 , where t represents time in seconds after the ball was dropped. A bee's flight can be modeled by the function, g(t)=3t+4, where t represents time in seconds after the bee starts the flight.

The graph represents the situation.

select all that apply

1) The bee launches into flight from the ground.

2) The ball is dropped from a height of 36 feet.

3) The bee and the ball will collide after approximately 1.3 seconds.

4) The bee and the ball will collide after approximately 8 seconds.

5) The bee and the ball will collide at approximately 8 feet above the ground.

6) The bee and the ball will not collide.

7) The ball hits the ground after 1.5 seconds

see the attached figure to better understand the problem

Verify all the options

case 1) The bee launches into flight from the ground.

The statement is false

Because

we have

$g(t)=3t+4$

For t=0

$g(t)=3(0)+4=4\ ft$

That means ----> The bee launches into flight from a height 4 feet above the ground

case 2) The ball is dropped from a height of 36 feet

The statement is true

Because

For t=0

$f(t)=-16(0)^2+36=36\ ft$

case 3) The bee and the ball will collide after approximately 1.3 seconds

The statement is true

Because

Equate f(t) and g(t)

$-16t^2+36=3t+4$

$-16t^2-3t+32=0$

solve the quadratic equation by graphing

The solution is t=1.324 sec

see the attached figure N 2

case 4) The bee and the ball will collide after approximately 8 seconds

The statement is false

Because, the bee and the ball will collide after approximately 1.3 seconds (see case 3)

case 5) The bee and the ball will collide at approximately 8 feet above the ground

The statement is true

Because

For t=1.324 sec

substitute the value of t in f(t) or g(t)

$g(t)=3(1.324)+4=7.97\ ft$

case 6) The bee and the ball will not collide

The statement is false

see case 3) and case 5)

case 7) The ball hits the ground after 1.5 seconds

The statement is true

Because

we know that

The ball hit the ground when the value of f(t) is equal to zero

so

For f(t)=0

$-16t^2+36=0$

$t^2=\frac{36}{16}$

$t=\frac{6}{4}=1.5\ sec$

4 0

2 years ago

Read 2 more answers

In a bag there are 3 red marbles, 2 yellow marbles, and 1 blue marble. what is the probability in simplest form of a yellow marb

dangina [55]

Answer:

The probability is 1/3, or in percent form, 33.3%.

Step-by-step explanation:

First, add up all the marbles. 3 plus 2 plus 1 equals 6 total marbles.

There are 2 yellow marbles out of 6 total marbles. Make it a fraction: 2/6.

Simplify the fraction by dividing by 2, to get 1/3, which is 33.3%.

Hope this helps! Feel free to give me Brainliest if you feel this helped. Have a good day, and good luck on your assignment. :)

5 0

2 years ago

How long will it take for the balance of an account to double if the savings account earns 0.75% annual interest compounded mont

spin [16.1K]

Let the amount deposited (principal) be x, then the amount after the required time = 2x.
A = P(1 + r/n)^nt: where A is the future value = 2x, P is the principal = x, r is the rate = 0.75%, n is the number of accumulation in a year = 12, t is the number of years.

2x = x(1 + 0.0075/12)^12t
2 = (1 + 0.000625)^12t
log 2 = 12t log (1.000625)
log 2 / log (1.000625) = 12t
1109.38 = 12t
t = 92 years

4 0

3 years ago

Emily, Jean, and Amanda live in apartments on the 5th, 6th and 7th floors. One girl likes basketball, one likes football, and th

ss7ja [257]

Answer:

Assuming you mean baseball in stead of basketball, if must be the 5th floor.

Step-by-step explanation:

"The girl on the fifth floor thinks soccer is boring" implies that on the 5th floor lives the football or baseball fan. However, it cannot be the football fan since it is already known that she lives on 6th.

So the baseball fan, which is Jean, lives on 5th.

3 0

3 years ago

How many times does 9 go into 204​

How many times does 9 go into 204