What point is an x-intercept of the quadratic function f(x)=(x+6)(x-3)

If a sprinkler waters 1/12 of a lawn in 1/4 hour, how much time will it take to water the entire lawn?

liubo4ka [24]

Answer:

3 hours

Step-by-step explanation:

1/12 = 1/4 of an hour

1 hour = 4/12

2 hours = 8/12

3 hours = 12/12

3 0

2 years ago

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for the past 3 months, grace used her cell phone for 43 min, 62 min, and 57 min.how many minutes would she have to use her cel p

Irina18 [472]

1357 divide 55 into 4

6 0

3 years ago

A spherical hot-air balloon has a diameter of 55 feet. When the balloon is inflated, the radius increases at a rate of 1.5 feet

abruzzese [7]

Answer:

The time it would take to inflate the balloon to approximately two-thirds of its maximum volume is approximately 46.90 minutes

Step-by-step explanation:

The given parameters are;

The diameter of the balloon = 55 feet

The rate of increase of the radius of the balloon when inflated = 1.5 feet per minute

We have;

dr/dt = 1.5 feet per minute = 1.5 ft/min

V = 4/3·π·r³

The maximum volume of the balloon = 4/3 × 3.14 × 55³ = 696556.67 ft³

When the volume is two-thirds the maximum volume, we have;

2/3 × 696556.67 ft³ = 464371.11 ft³

The value of the radius, r₂ at that point is found as follows;

4/3·π·r₂³ = 464371.11 ft³

r₂³ = 464371.11 ft³ × 3/4 = 348278.33 ft³

348278.333333

r₂ = ∛(348278.33 ft³) ≈ 70.36 ft

The time for the radius to increase to the above length = Length/(Rate of increase of length of the radius)

The time for the radius to increase to the above length ≈ 70.369 ft/(1.5 ft/min) ≈ 46.90 minutes

The time it would take to inflate the balloon to approximately two-thirds of its maximum volume ≈ 46.90 minutes.

4 0

3 years ago

Suppose the graph of a cubic polynomial function has the same zeroes and passes through the coordinate (0, -5). Write the equati

amid [387]

In this we know all three zeros and one point from which the graph pass.
So we will let specific cubic polynomial function of the form
$f(x) = a(x - x_1)(x-x_2)(x-x_3)$

As we know zeros are that point where we will get value of function equal to zero. So it is basically in form $(x_n , 0)$

SO in given question zeros are (2 , 0) , (3, 0) and (5,0)
So we can say $x_1 = 2 , x_2 = 3 , x_3 = 5$

So required equation is
$f(x) = a (x-2)(x-3)(x-5)$
              $= a[(x^2 - 2x - 3x + 6)(x-5)]$
              $= a[(x^2 - 5x+6)(x-5)]$
              $= a(x^3 - 5x^2 + 6x- 5x^2 + 25x - 30)$
              $= a(x^3 - 10x^2+31x-30)$
Now we have one point (0 , -5) from which graph passes.
So we say at x = 0 , f(x) = -5
$-5= a (0-0+0 - 30)$
$-5 = -30a$
$a = \frac{-5}{-30} = \frac{1}{6}$
So required equation of cubic polynomial is
$f(x) = \frac{1}{6}(x^3 -10x^2+31x-30)$

For finding y - intercept we simply plugin x = 0 in given equation.
As we know at x = 0 , value of function is -5.
So y - intercept is -5.

4 0

3 years ago

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PLZ HELP WILL MARK BRAINLIEST

Fantom [35]

Answer:

g(x) = (1/6)(x +7)^2 -8

Step-by-step explanation:

The transformation ...

g(x) = a·f(x -h) +k

represents vertical scaling by a factor of 'a', right shift by h units, and up shift by k units. You want the function g(x) for f(x) = x^2, a = 1/6, h = -7, and k = -8. Those transformations give you ...

g(x) = (1/6)(x +7)^2 -8

6 0

3 years ago