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Gala2k [10]
3 years ago
6

Double the sum of a double the number and quotient of five and two

Mathematics
1 answer:
Vika [28.1K]3 years ago
4 0

Answer:

The required expression is 2(2x+\frac{5}{2})

Step-by-step explanation:

Let the number be x

We are supposed to write the algebraic expression of given statement

Double the number = 2x

Quotient of five and two =\frac{5}{2}

Now we are given that Double the sum of a double the number and quotient of five and two

So, Sum of a double the number and quotient of five and two =2x+\frac{5}{2}

So, Double the sum of a double the number and quotient of five and two =2(2x+\frac{5}{2})

Hence The required expression is 2(2x+\frac{5}{2})

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A toy rocket is launched from a platform that is 48 ft high. The rocket height above the ground is modeled by h=-16t^2+32t+48. a
Komok [63]

Answer:

a) 64 feet

b)  3 seconds

Step-by-step explanation:

a)

The maximum height of h=h(t) can be bound by finding the y-coordinate of the vertex of y=-16x^2+32x+48.

Compare this equation to y=ax^2+bx+c to find the values of a,b,\text{ and } c.

a=-16

b=32

c=48.

The x-coordinate of the vertex can be found by evaluating:

\frac{-b}{2a}=\frac{-32}{2(-16)

\frac{-b}{2a}=\frac{-32}{-32}

\frac{-b}{2a}=1

So the x-coordinate of the vertex is 1.

The y-coordinate can be found be evaluating y=-16x^2+32x+48 at x=1:

y=-16(1)^2+32(1)+48

y=-16+32+48

y=16+48

y=64

So the maximum height of the rocket is 64 ft high.

b)

When the rocket hit's the ground the height that the rocket will be from the ground is 0 ft.

So we are trying to find the second t such that:

0=-16t^2+32t+48

I'm going to divide both sides by -16:

0=t^2-2t-3

Now we need to find two numbers that multiply to be -3 and add to be -2.

Those numbers are -3 and 1 since (-3)(1)=-3 and (-3)+(1)=-2.

0=(t-3)(t+1)

This implies we have either t-3=0 or t+1=0

The first equation can be solved by adding 3 on both sides: t=3.

The second equation can be solved by subtracting 1 on both sides: t=-1.

So when t=3 seconds, is when the rocket has hit the ground.

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Bas_tet [7]

Answer:

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Step-by-step explanation:

8 0
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