Write the new points after the translation and write the rule in coordinate notation.

You roll a red die, a yellow die, a blue die, and a green die. What is the size of the sample space of all possible outcomes of

VARVARA [1.3K]

Answer:

216 outcomes for the sample space. (c)

Step-by-step explanation:

4 0

4 years ago

Which quadratic rule represents the data in the table?

NeX [460]

Since there are already choices in the question, I suggest you just substitute in the values of x to each choice and check whether the corresponding value for y appears. This is also called the trial and error method in multiple choice.

The answer that represents the data in the table is C. <span>y = x^2 – 5.</span>

3 0

3 years ago

The longest side of an acute triangle measures 30 inches. The two remaining sides are congruent, but their length is unknown.

lakkis [162]

The smallest perimeter is 72.44 inches. The longest side of an acute triangle measures 30 inches. The two remaining sides are congruent, but their length is unknown. As much as possible, the sum of the length of the two remaining side must be greater than the other side. Given the side is 30, then the sum of the two remaining sides should be greater than 30 inches.

7 0

3 years ago

Which linear equations have one solution? Check all that apply.

Nina [5.8K]

Its the third and the fourth one

7 0

3 years ago

Kesha threw her baton up in the air from the marching band platform during practice. The equation h(t) = −16t² + 54t + 40 gives

lapo4ka [179]

Answer:

a) 40 feet

b) 54 ft/min

c) 4 mins

Step-by-step explanation:

Solution:-

- Kesha models the height ( h ) of the baton from the ground level but thrown from a platform of height hi.

- The function h ( t ) is modeled to follow a quadratic - parabolic path mathematically expressed as:

h ( t ) = −16t² + 54t + 40

Which gives the height of the baton from ground at time t mins.

- The initial point is of the height of the platform which is at a height of ( hi ) from the ground level.

- So the initial condition is expressed by time = 0 mins, the height of the baton h ( t ) would be:

h ( 0 ) = hi = -16*(0)^2 + 54*0 + 40

h ( 0 ) = hi = 0 + 0 + 40 = 40 feet

Answer: The height of the platform hi is 40 feet.

- The speed ( v ) during the parabolic path of the baton also varies with time t.

- The function of speed ( v ) with respect to time ( t ) can be determined by taking the derivative of displacement of baton from ground with respect to time t mins.

v ( t ) = dh / dt

v ( t )= d ( −16t² + 54t + 40 ) / dt

v ( t )= -2*(16)*t + 54

v ( t )= -32t + 54

- The velocity with which Kesha threw the baton is represented by tim t = 0 mins.

Hence,

v ( 0 ) = vi = -32*( 0 ) + 54

v ( 0 ) = vi = 54 ft / min

Answer: Kesha threw te baton with an initial speed of vo = 54 ft/min

- The baton reaches is maximum height h_max and comes down when all the kinetic energy is converted to potential energy. The baton starts to come down and cross the platform height hi = 40 feet and hits the ground.

- The height of the ball at ground is zero. Hence,

h ( t ) = 0

0 = −16t² + 54t + 40

0 = -8t^2 + 27t + 20

- Use the quadratic formula to solve the quadratic equation:

$t = \frac{27+/-\sqrt{27^2 - 4*8*(-20)} }{2*8}\\\\t = \frac{27+/-\sqrt{1369} }{16}\\\\t = \frac{27+/-37 }{16}\\\\t = \frac{27 + 37}{16} \\\\t = 4$

Answer: The time taken for the baton to hit the ground is t = 4 mins

3 0

3 years ago