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2 years ago

If f(x) = 5x+4 and g(x) = x-4, find (f o g)(x) and (g o f)(x)

Mathematics

1 answer:

Vikki [24]2 years ago

7 0

Step-by-step explanation:

F(g(x)) = F(x-4)

= 5(x-4) +4

= 5x-20+4

=5x-16

G(f(x)) = G(5x-4)

= (5x-4) -4

= 5x-8

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A teenager who is 5 feet tall throws an object into the air. The quadratic function LaTeX: f\left(x\right)=-16x^2+64x+5f ( x ) =

tia_tia [17]

Answer:

At approximately x = 0.08 and x = 3.92.

Step-by-step explanation:

The height of the ball is modeled by the function:

$f(x)=-16x^2+64x+5$

Where f(x) is the height after x seconds.

We want to determine the time(s) when the ball is 10 feet in the air.

Therefore, we will set the function equal to 10 and solve for x:

$10=-16x^2+64x+5$

Subtracting 10 from both sides:

$-16x^2+64x-5=0$

For simplicity, divide both sides by -1:

$16x^2-64x+5=0$

We will use the quadratic formula. In this case a = 16, b = -64, and c = 5. Therefore:

$\displaystyle x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

Substitute:

$\displaystyle x=\frac{-(-64)\pm\sqrt{(-64)^2-4(16)(5)}}{2(16)}$

Evaluate:

$\displaystyle x=\frac{64\pm\sqrt{3776}}{32}$

Simplify the square root:

$\sqrt{3776}=\sqrt{64\cdot 59}=8\sqrt{59}$

Therefore:

$\displaystyle x=\frac{64\pm8\sqrt{59}}{32}$

Simplify:

$\displaystyle x=\frac{8\pm\sqrt{59}}{4}$

Approximate:

$\displaystyle x=\frac{8+\sqrt{59}}{4}\approx 3.92\text{ and } x=\frac{8-\sqrt{59}}{4}\approx0.08$

Therefore, the ball will reach a height of 10 feet at approximately x = 0.08 and x = 3.92.

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2 years ago

What is 2x12=24 I got the answer

strojnjashka [21]

You were right 24 is the answer. :)

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3 years ago

if the farm needs to pack 12,70,224 litchis in boxes that hold 144 litchis ,how many boxes would be required .

uysha [10]

For this, we will divide 1,270,224 by 144.

1,270,224 ÷ 144 = 8,821.

For this result, we can conclude that the number of boxes required to pack 1,270,224 litchis is 8,821 boxes.

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What is the scintific notation of 4,497,000,000

Diano4ka-milaya [45]

4,497,000,000 = <span>4.497 x 10^9</span>

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2 years ago

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Which sequence of transformations will change figure PQRS to figure P′Q′R′S′?

masya89 [10]

Answer:

Counterclockwise rotation about the origin by 90 degrees followed by reflection about the y-axis .

Step-by-step explanation:

The shape is moved to the opposite quadrant of the second shape then flied directly onto the second shape.

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