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3 years ago

Write an expression that is equivalent to 8(2y+4)

1 answer:

8 0

An expression that is equivalent to 8 (2y+4) is 16y × 32.

8×2y=16y

8×4=32

Since you can't add a variable with a regular number its just 16y × 32.

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A ball is thrown into the air from a height of 4 feet at time t = 0. The function that models this situation is h(t) = -16t2 + 6

katrin2010 [14]

Answer:

Part a) The height of the ball after 3 seconds is $49\ ft$

Part b) The maximum height is 66 ft

Part c) The ball hit the ground for t=4 sec

Part d) The domain of the function that makes sense is the interval

[0,4]

Step-by-step explanation:

we have

$h(t)=-16t^{2} +63t+4$

Part a) What is the height of the ball after 3 seconds?

For t=3 sec

Substitute in the function and solve for h

$h(3)=-16(3)^{2} +63(3)+4=49\ ft$

Part b) What is the maximum height of the ball? Round to the nearest foot.

we know that

The maximum height of the ball is the vertex of the quadratic equation

Convert the function into a vertex form

$h(t)=-16t^{2} +63t+4$

Group terms that contain the same variable, and move the constant to the opposite side of the equation

$h(t)-4=-16t^{2} +63t$

Factor the leading coefficient

$h(t)-4=-16(t^{2} -(63/16)t)$

Complete the square. Remember to balance the equation by adding the same constants to each side

$h(t)-4-16(63/32)^{2}=-16(t^{2} -(63/16)t+(63/32)^{2})$

$h(t)-(67,600/1,024)=-16(t^{2} -(63/16)t+(63/32)^{2})$

Rewrite as perfect squares

$h(t)-(67,600/1,024)=-16(t-(63/32))^{2}$

$h(t)=-16(t-(63/32))^{2}+(67,600/1,024)$

the vertex is the point (1.97,66.02)

therefore

The maximum height is 66 ft

Part c) When will the ball hit the ground?

we know that

The ball hit the ground when h(t)=0 (the x-intercepts of the function)

$h(t)=-16t^{2} +63t+4$

For h(t)=0

$0=-16t^{2} +63t+4$

using a graphing tool

The solution is t=4 sec

see the attached figure

Part d) What domain makes sense for the function?

The domain of the function that makes sense is the interval

[0,4]

All real numbers greater than or equal to 0 seconds and less than or equal to 4 seconds

Remember that the time can not be a negative number

6 0

3 years ago

When I evaluate m=2 , h=1 then what would mh+3 would be?

Andrei [34K]

Answer:5

Step-by-step explanation: since you know that m=2, and h=1, mh is the same as m × h, or 2×1. Which is equal to 2, you then add 3 to get your answer

7 0

3 years ago

Question 1 (1 point) Solve for x. 44° (4x+8) 60 Solve for x°

Sladkaya [172]

Answer:

bbrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrreeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee

Step-by-step explanation:

8 0

3 years ago

The table shows some ordered pairs that belong to the quadratic function h.

erastova [34]

Answer:

C. Are all real numbers greater than or equal to -8.

Step-by-step explanation:

Real numbers can be said to be all continuous values of quantity, which can be negative or positive values.

The range of h, h(x), in the table given are all real numbers.

The least of the range of h on the table is -8. All the other range values, namely, -7, 1, 17, and 41 are all greater than -8. None is less than -8.

Therefore, we can conclude that the range values of h "are all real numbers greater than or equal to -8".

6 0

3 years ago

Help me please, I need help

Natalija [7]

Answer:

+ 5.90

Because -5.90 in rational value is positive 5.90

5 0

4 years ago