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3 years ago

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If f(x) =x/2 -3 and g(x) = 4x^2+ x-4, find( f + g )(x)

1 answer:

Andrei [34K]3 years ago

8 0

$f(x)=\dfrac{x}{2}-3=\dfrac{1}{2}x-3\\\\g(x)=4x^2+x-4\\\\(f+g)(x)=f(x)+g(x)\\\\(f+g)(x)=\left(\dfrac{1}{2}x-3\right)+(4x^2+x-4)=4x^2+1\dfrac{1}{2}x-7$

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A decorative floor pattern has 1 red square tile surrounded by 12 blue tiles. Write an expression to show how many total red and

Nonamiya [84]

The general equation is that for every red tile, there must be 12 blue ones.

Algebraically this is expressed as b = 12r where r is red and b is blue. Your teacher might like you to express it as y = 12x where y is blue and x is red. The meaning is the same.

For beginners it might be easier to say b = 12r. So if you have 15 reds then r = 15

b = 12 * r

b = 12 * 15

b = 180 blue tiles.

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3 years ago

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A triangle has two constant sides of length 5 feet and 7 feet. The angle between these two sides is increasing at a rate of 0.9

o-na [289]

Answer: $12.74 ft^2/s$

Step-by-step explanation:

Given

Two sides of triangle of sides 5 ft and 7 ft

and angle between them is increasing at a rate of 0.9 radians per second

let $\theta$ is the angle between them thus

Area of triangle when two sides and angle between them is given

$A=\frac{ab\sin C}{2}$

$A=\frac{5\times 7\times \sin \theta }{2}$

Differentiate w.r.t time

$\frac{\mathrm{d} A}{\mathrm{d} t}=\frac{35\cos theta }{2}\times \frac{\mathrm{d} \theta }{\mathrm{d} t}$

at $\theta =\frac{\pi }{5}$

$\frac{\mathrm{d} A}{\mathrm{d} t}=\frac{35\times cos(\frac{\pi }{5})}{2}\times 0.9$

$\frac{\mathrm{d} A}{\mathrm{d} t}=12.74 ft^2/s$

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3 years ago

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Svetllana [295]

Download the app photomath it shows you step by step :)

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3 years ago

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zloy xaker [14]

Step-by-step explanation:

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{2,3,5,7}---set of prime numbers from 0 tp 9

there are 10 numbers in the first set and 4 numbers in the second set.

4/9 is the probability that the digit he selects is a prime number

Hope that helps :)

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3 years ago