Sam is 5 years old. His older brother, Tom, is three times as old as Sam. When Sam is 20, how old will Tom be?

Answers

Answer 1

Answer: Sam is 5
Tom is 3 times older so 3*5=15
The difference between them is 15-5=10 years
When Sam is 20 we add the difference 20+10=30, and we have Tom's age :)

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Solve for x: 3(x + 1) = −2(x − 1) + 6.

There are 9 roses and 7 diasies. What is the ratio of roses to daisies?

Answers

$9:7$
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Let f(x)=4x-1 and g(x)=2x^2+3. Perform each function operations and then find the domain.1. (f+g)(x) 2. (f-g)(x) 3. (g-f)(x) 4. (f times g)(x) 5. f/g(x) 6. g/f(x)

Answers

The domain of a function is the set of input values, the function can take.

The values of the composite functions are:

$\mathbf{(f + g)(x) = 2x^2 + 4x +2}$

$\mathbf{(f - g)(x) = -2x^2 + 4x - 4}$

$\mathbf{(g - f)(x) = 2x^2 - 4x + 4}$

$\mathbf{(f * g)(x) = 8x^3 - 2x^2 -12x + 4}$

$\mathbf{(f / g)(x) = ((4x - 1 ))/((2x^2 - 3))}$

$\mathbf{(g / f)(x) = (2x^2 - 3)/(4x - 1 )}$

The functions are given as:

$\mathbf{f(x) = 4x - 1}$

$\mathbf{g(x) = 2x^2 + 3}$

$\mathbf{(1)\ (f + g)(x)}$

This is calculated as:

$\mathbf{(f + g)(x) = f(x)+ g(x)}$

So, we have:

$\mathbf{(f + g)(x) = 4x - 1 + 2x^2 + 3}$

Collect like terms

$\mathbf{(f + g)(x) = 2x^2 + 4x - 1 + 3}$

$\mathbf{(f + g)(x) = 2x^2 + 4x +2}$

There is no restriction on the value of x.

So, the domain is: $\mathbf{(-\infty,\infty)}$

$\mathbf{(2)\ (f - g)(x)}$

This is calculated as:

$\mathbf{(f - g)(x) = f(x) - g(x)}$

So, we have:

$\mathbf{(f - g)(x) = 4x - 1 - 2x^2 - 3}$

Collect like terms

$\mathbf{(f - g)(x) = -2x^2 + 4x - 1 - 3}$

$\mathbf{(f - g)(x) = -2x^2 + 4x - 4}$

There is no restriction on the value of x.

So, the domain is: $\mathbf{(-\infty,\infty)}$

$\mathbf{(3)\ (g - f)(x)}$

This is calculated as:

$\mathbf{(g - f)(x) = -(f - g)(x) }$

So, we have:

$\mathbf{(g - f)(x) = 2x^2 - 4x + 4}$

There is no restriction on the value of x.

So, the domain is: $\mathbf{(-\infty,\infty)}$

$\mathbf{(4)\ (f * g)(x)}$

This is calculated as:

$\mathbf{(f * g)(x) = f(x) * g(x)}$

So, we have:

$\mathbf{(f * g)(x) = (4x - 1 )* (2x^2 - 3)}$

$\mathbf{(f * g)(x) = 8x^3 - 2x^2 -12x + 4}$

There is no restriction on the value of x.

So, the domain is: $\mathbf{(-\infty,\infty)}$

$\mathbf{(5)\ (f /g)(x)}$

This is calculated as:

$\mathbf{(f /g)(x) = (f(x) )/(g(x))}$

So, we have:

$\mathbf{(f / g)(x) = ((4x - 1 ))/((2x^2 - 3))}$

There are restrictions to the value of x.

So, the domain is: $\mathbf{(-\infty,-\sqrt{(3)/(2)} ) \ u\ ( -\sqrt{(3)/(2)},\sqrt{(3)/(2)}})\ u\ (\sqrt{(3)/(2)},\ \infty)}$

$\mathbf{(6)\ (g /f)(x)}$

This is calculated as:

$\mathbf{(g /f)(x) =1 / (f(x) )/(g(x))}$

So, we have:

$\mathbf{(g / f)(x) = (2x^2 - 3)/(4x - 1 )}$

There are restrictions to the value of x.

So, the domain is: $\mathbf{(-\infty, (1)/(4))\ u\ ((1)/(4),\infty)}$

Answers

The answer is 6^3

6*6*6= 216

6^3= 216

Final answer:

The given multiplication of 6 • 6 • 6 can be represented using an exponent as 63. The exponent is 3 because the number 6 is being multiplied by itself three times.

Explanation:

In mathematics, the operation of repeated multiplication is often represented using exponents. When you multiply a number by itself repeatedly, the way to express that using exponents is to write the base number and an exponent showing how many times the base number is being multiplied. In your example, you are multiplying 6 by itself 3 times, so the expression that represents this using exponents is 63.