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AleksAgata [21]

3 years ago

8

the area of a projected picture on a movie screen varies directly as the square of the distance from the projector to the screen

. if the distance of 20 feet produces a picture with an area of 64 square feet, what distance produces a picture with an area of 100 square feet?

1 answer:

Aleksandr [31]3 years ago

5 0

The answer is 1220 square feet

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If f(x) =4x2 - 8x - 20 and g(x) = 2x + a, find the value of a so that the y-intercept of the graph of the composite function (fo

amm1812

Answer:

The possible values are a = -2.5 or a = 4.5.

Step-by-step explanation:

Composite function:

The composite function of f(x) and g(x) is given by:

$(f \circ g)(x) = f(g(x))$

In this case:

$f(x) = 4x^2 - 8x - 20$

$g(x) = 2x + a$

So

$(f \circ g)(x) = f(g(x)) = f(2x + a) = 4(2x + a)^2 - 8(2x + a) - 20 = 4(4x^2 + 4ax + a^2) - 16x - 8a - 20 = 16x^2 + 16ax + 4a^2 - 16x - 8a - 20 = 16x^2 +(16a-16)x + 4a^2 - 8a - 20$

Value of a so that the y-intercept of the graph of the composite function (fog)(x) is (0, 25).

This means that when $x = 0, f(g(x)) = 25$ . So

$4a^2 - 8a - 20 = 25$

$4a^2 - 8a - 45 = 0$

Solving a quadratic equation, by Bhaskara:

$\Delta = (-8)^2 - 4(4)(-45) = 784$

$x_{1} = \frac{-(-8) + \sqrt{784}}{2*(4)} = \frac{36}{8} = 4.5$

$x_{2} = \frac{-(-8) - \sqrt{784}}{2*(4)} = -\frac{20}{8} = -2.5$

The possible values are a = -2.5 or a = 4.5.

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Answer:

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Step-by-step explanation:

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2 years ago

Which sutuation could be represented by -11

xz_007 [3.2K]

Answer:

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Step-by-step explanation:

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2 years ago

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lyudmila [28]

Answer:

29.3

Step-by-step explanation:

4x+12+5x+3x-4=360

Add the X's up & move the numbers w/out factors (X's) to the 360 side. This will look like 12x=352

Then, you divide each by 12, leaving you with x=29.3

Might be wrong, let me know and I will rework it.

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2 years ago