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tatyana61 [14]
2 years ago
9

5(3 - x) < -2x + 6 what inequality

Mathematics
1 answer:
blagie [28]2 years ago
8 0
The answer is x < 11/5
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A rocket is launched from a tower what time will the rocket reach its max
Lena [83]

Answer:

Step-by-step explanation:

A science class designed a ball launcher and tested it by shooting a tennis ball up and off the top of a 15-story building. They determined that the motion of the ball could be described by the function: h(t) = -16t2 + 144t + 160, where ‘t’ represents the time the ball is in the air in seconds and h(t) represents the height, in feet, of the ball above the ground at time t.

a) Graph the function h(t) = -16t2 + 144t + 160 (see below)

      b) What is the height of the building?

The height of the building is also the height of the tennis ball before it is launched into the air. This occurs when t=0 so substitute 0 for t and you get:

H(0) = -16(0)2 + 144(0) + 160

The height of the building is 160 feet.

 c) At what time did the ball hit the ground?

The ball hits the ground when the height is 0. Therefore, we are looking for a solution to: -16t2 + 144t + 160 = 0

Use the quadratic formula or put this into a calculator. The solution is t=10 and -1, but only 10 makes sense. Therefore, the ball hits the ground at 10 seconds.

  d) At what time did the ball reach its maximum height?

You can put this into the calculator or you can realize that the maximum height is also

− the vertex. The x-value (‘t’ in this case) is 2

−144

which is (2)(−16) = 4.5.

Therefore, the ball reached its maximum height at 4.5 seconds.

   e) What is the maximum height of the ball?

We calculated the time of the maximum height (4.5 seconds). Therefore, substitute 4.5 into the function to find the maximum height.

-16(4.5)2 + 144(4.5) + 160

The maximum height is 484 feet.

5 0
2 years ago
if you know that 7 x 8=56, how can you use the commutative property of multiplication to find the product of 8 x 7 ?
Fofino [41]
Its the same thing because your just switching the order which doesn't matter when your adding or multiplying
5 0
3 years ago
Find the slope from the following table: x 2 3 4 y 4 5 6
Sindrei [870]

Answer:

the slope is 1

Step-by-step explanation:

The linear equation is y=x+2

7 0
3 years ago
Distance between (-7,-6) and (-2,-16)
Archy [21]

Exact form:

2\sqrt\ 13

Decimal form:

7.21110255 or 7.21

5 0
2 years ago
Read 2 more answers
A) Find a recurrence relation for the number of bit strings of length n that contain a pair of consecutive 0s.
Fed [463]

Answer:

A) a_{n} = a_{n-1} + a_{n-2} + 2^{n-2}

B) a_{0} = a_{1} = 0

C)   for n = 2

  a_{2} = 1

for n = 3

 a_{3} = 3

for n = 4

a_{4} = 8

for n = 5

a_{5} = 19

Step-by-step explanation:

A) A recurrence relation for the number of bit strings of length n that contain a  pair of consecutive Os can be represented below

if a string (n ) ends with 00 for n-2 positions there are a pair of  consecutive Os therefore there will be : 2^{n-2} strings

therefore for n ≥ 2

The recurrence relation for the number of bit strings of length 'n' that contains consecutive Os

a_{n} = a_{n-1} + a_{n-2} + 2^{n-2}

b ) The initial conditions

The initial conditions are : a_{0} = a_{1} = 0

C) The number of bit strings of length seven containing two consecutive 0s

here we apply the re occurrence relation and the initial conditions

a_{n} = a_{n-1} + a_{n-2} + 2^{n-2}

for n = 2

  a_{2} = 1

for n = 3

 a_{3} = 3

for n = 4

a_{4} = 8

for n = 5

a_{5} = 19

7 0
3 years ago
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