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PolarNik [594]
3 years ago
6

Let ƒ(x) = x^2 + 2x and g(x) = 2x. Evaluate the composition (ƒ ∘ g)(2).

Mathematics
1 answer:
FinnZ [79.3K]3 years ago
7 0

Answer:

The answer is option D.

Step-by-step explanation:

f(x) = x² + 2x

g(x) = 2x

To find (ƒ ∘ g)(2) first find (ƒ ∘ g)

To find (ƒ ∘ g) wherever you see x in f(x) replace it with g(x)

That's

(ƒ ∘ g) = (2x)² + 2(2x)

= 4x² + 4x

Substitute 2 into the expression

That's

(ƒ ∘ g)(2) = 4(2)² + 4(2)

= 4(4) + 8

= 16 + 8

= 24

Hope this helps you.

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Svetach [21]

Answer: <em>320ft², ~326.73cm², ~628.32mm², 186yd², ~615.75m², 96in²,</em>

<em>2376ft³</em>

Step-by-step explanation:

8) For a cube we will find the area of the three pairs of squares

First pair: 8ft * 6ft = 48ft²    Second pair: 8ft * 8ft = 64ft²

Third pair: 8ft * 6ft = 48ft²    (I think that says 6? Could say 5)

Multiply each pair by two and add them up:

48ft² * 2 = 96ft²      64ft² * 2 = 128ft²      48ft² * 2 = 96ft²

96ft² + 128ft² + 96ft² = <em>320ft²</em>

<em></em>

9) For a cylinder we will add the area of the lateral area and the two circles

Lateral Area: 8πcm *  9cm = 72πcm² or  ~226.19cm²

Area of <em>one</em> circle: π*4² = 16π  or  ~50.27cm²

Multiply that by 2 and we get   ~100.54cm²

Then we add up 100.54cm² and 226.19cm² to get the answer: <em>~326.73cm²</em>

<em></em>

10) For the cone we will use: A = πr(r + √(h² + r²))

A = 8πmm(8mm + √(15²mm + 8²mm))

A = 8πmm(8mm + 17mm)

A = 8πmm*25mm = <em>~628.32mm²</em>

<em></em>

11) I will start with the two triangles

One triangle: 1/2 * 6yd * 8yd = 24yd²

Two triangles = 48yd²

Next, the two rectangles in the back

Base rectangle: 8yd * 5yd = 40yd²

Back Triangle: 6yd * 8yd = 48yd²

Lastly, the top triangle

Top Triangle: 10yd * 5yd = 50yd²

Add them up to get: <em>186yd²</em>

<em></em>

12) For a sphere I will use: A = 4πr²

A = 4π(7m)²

A = 4π * 49m²

A = 196πm²  OR   <em>~615.75m²</em>

<em></em>

13) For a pyramid I will use: A = a² + 2a√((a²/4)+h²)

A =(6in)² + 2*(6in)*√((6²/4)+4²)

A = 36in² + 12in*√(9²+16in²)

A = 36in² + 12in * 5in

A = 36in² + 60in² = <em>96in²</em>

<em></em>

Extra Credit!

14) What is the volume of a pool with dimensions: 22ft long, 18ft wide, and 6 ft deep?

Strangely, the Extra Credit is much easier than the original problems but I'm not complaining!

Simply multiply each dimension and you get the volume of the pool, so:

22ft * 18ft * 6ft = <em>2376ft³</em>

<em></em>

I hope this helped!

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The slope is -2 because y = mx + b

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