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Mamont248 [21]
3 years ago
5

Adam, Brian, and Casey are all brothers. Brian is three years less than twice Casey’s age. Adam is 9 years older than Casey. The

sum of their ages is 46. How old is each of the brothers
Mathematics
1 answer:
blagie [28]3 years ago
8 0

Let Casey's age be x

Brian's age will be -3 from 2 times x ( Casey's age ) so it will be 2x-3

Adam's age will be Casey's age (x) + 9 which is x+9

NOW the sum of all these ages is 46 so..

Casey's age + Brian's age + Adam's age = 46

x + 2x-3 + x+9 = 46

2x + x + x + 9 -3 = 46

4x + (9 - 3) = 46

4x - 6 = 46

now transfer the numbers on the left one by one to the other side( right )

4x = 46 - 6        ( always remember the sign of the number becomes the                            opposite when we transfer them to other side)

4x = 40

x = 40 / 4

x = 10

so x = Casey's age = 10

2x - 3 = Brian's age = 2 * 10 - 3

                                = 20 - 3   =   17

x + 9 = Adam's age = 10 + 9 = 19

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Given functions f ( x ) = 1 √ x and m ( x ) = x 2 − 4 , state the domains of the following functions using interval notation.
babunello [35]

The domain of a function f(x)/m(x) = 1/√x(x² - 4) is (0, ∞) - {0, 2, -2} for other function is shown in the solution.

<h3>What is a function?</h3>

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

We have:

f(x) =  1/√x

m(x) = x² - 4

Domain of f(x)/m(x):

f(x)/m(x) = (1/√x)/(x² - 4)

f(x)/m(x) = 1/√x(x² - 4)

The denominator cannot be zero:

√x(x² - 4) ≠ 0

x(x - 2)(x+2) ≠ 0

x ≠ 0, 2, -2

and x > 0

Domain of f(x)/m(x) is:   (0, ∞) - {0, 2, -2} or \:\left(0,\:2\right)\cup \left(2,\:\infty \:\right)

Domain of f(m(x)):

f(m(x)) = 1/√(x² - 4)

x² - 4 > 0

Domain: \rm \left(-\infty \:,\:-2\right)\cup \left(2,\:\infty \:\right)

Domain of m(f(x)):

= ((1/√x)² - 4)

Domain: \:\left(0,\:\infty \:\right)

Thus, the domain of a function f(x)/m(x) = 1/√x(x² - 4) is (0, ∞) - {0, 2, -2} for other function is shown in the solution.

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2 years ago
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irina1246 [14]
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3 years ago
Read 2 more answers
Explain in easy terms, how the signs of the last terms of the two binomial factors of a trinomial are determined?
shutvik [7]

Explanation:

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  (x +a)(x +b)

The product is ...

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If the <em>constant</em> term (ab) is <em>negative</em>, the signs of (a) and (b) are <em>different</em>.

If the constant term (ab) is <em>positive</em>, the signs of (a) and (b) will both match the sign of the coefficient of the linear term (a+b).

___

Of course, the sum (a+b) will have the sign of the (a) or (b) value with the largest magnitude, so when the signs of (a) and (b) are different, the factor with the largest magnitude will have the sign of (a+b), the x-coefficient.

<u>Example</u>:

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