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2 years ago

Mike and Jasmine have a combined age of 30. Mike is 3 years younger than twice Jasmines age. How old is Mike?

1 answer:

6 0

Mike is 19.

If you turn the question into an equation it turns to:
J x 2 - 3 = M

So since you don’t know Jasmine’s age you would use guess and check. 8,9, and 10 didn’t work but when you put in 11:
11 x 2 - 3 = M
22 - 3 = M
19 = M

And to check your work
J + M has to equal 30 so,
11 + 19 = 30
30 = 30

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. Simplify (−34.67)0

maksim [4K]

If it's -34*0 then it is equal to 0 because anything times 0 is 0.

If it were -34.67 to the power of 0, then It would have been equal to -1. This is because anything to the power of 0 is 1. In this case though the base is negative so it would be -1.

But the answer is 0.

5 0

2 years ago

F(x)=3x 2 +9f, left parenthesis, x, right parenthesis, equals, 3, x, squared, plus, 9 and g(x)=\dfrac{1}{3}x^2-9g(x)= 3 1 x 2

34kurt

Answer:

$f(g(x)) = \frac{1}{3}x^4 - 18x^2 + 252$

$g(f(x)) = 3x^4 + 18x^2 + 18$

f(x) and g(x) and not inverse functions

Step-by-step explanation:

Given

$f(x) = 3x^2 + 9$

$g(x) = \dfrac{1}{3}x^2 - 9$

Required

Determine f(g(x))

Determine g(f(x))

Determine if both functions are inverse:

Calculating f(g(x))

$f(x) = 3x^2 + 9$

$f(g(x)) = 3(\frac{1}{3}x^2 - 9)^2 + 9$

$f(g(x)) = 3(\frac{1}{3}x^2 - 9)(\frac{1}{3}x^2 - 9) + 9$

Expand Brackets

$f(g(x)) = (x^2 - 27)(\frac{1}{3}x^2 - 9) + 9$

$f(g(x)) = x^2(\frac{1}{3}x^2 - 9) - 27(\frac{1}{3}x^2 - 9) + 9$

$f(g(x)) = \frac{1}{3}x^4 - 9x^2 - 9x^2 + 243 + 9$

$f(g(x)) = \frac{1}{3}x^4 - 18x^2 + 252$

Calculating g(f(x))

$g(x) = \dfrac{1}{3}x^2 - 9$

$g(f(x)) = \frac{1}{3}(3x^2 + 9)^2 - 9$

$g(f(x)) = \frac{1}{3}(3x^2 + 9)(3x^2 + 9) - 9$

$g(f(x)) = (x^2 + 3)(3x^2 + 9) - 9$

Expand Brackets

$g(f(x)) = x^2(3x^2 + 9) + 3(3x^2 + 9) - 9$

$g(f(x)) = 3x^4 + 9x^2 + 9x^2 + 27 - 9$

$g(f(x)) = 3x^4 + 18x^2 + 18$

Checking for inverse functions

$f(x) = 3x^2 + 9$

Represent f(x) with y

$y = 3x^2 + 9$

Swap positions of x and y

$x = 3y^2 + 9$

Subtract 9 from both sides

$x - 9 = 3y^2 + 9 - 9$

$x - 9 = 3y^2$

$3y^2 = x - 9$

Divide through by 3

$\frac{3y^2}{3} = \frac{x}{3} - \frac{9}{3}$

$y^2 = \frac{x}{3} - 3$

Take square root of both sides

$\sqrt{y^2} = \sqrt{\frac{x}{3} - 3}$

$y = \sqrt{\frac{x}{3} - 3}$

Represent y with g(x)

$g(x) = \sqrt{\frac{x}{3} - 3}$

Note that the resulting value of g(x) is not the same as $g(x) = \dfrac{1}{3}x^2 - 9$

Hence, f(x) and g(x) and not inverse functions

4 0

2 years ago

What are the solution(s) to the quadratic equation 40 – x2 = 0?

Anna35 [415]

Answer:

$x=-2\sqrt{10}, \\x= 2\sqrt{10}$

Step-by-step explanation:

6 0

2 years ago

A backpack costs $18 and has a 7 percent tax. How much will Sheila have to pay for the BBC avkpack after tax

gayaneshka [121]

Price before tax = $18

Tax = 7% x $18 = 0.07 x 18 = $1.26

Price after tax = $18 + $1.26 = $19.26

Answer: $19.26

3 0

2 years ago

Colleen plans to start a small business by making and selling skirts. A sewing machine costs $250, and she estimates that she wi

Dmitrij [34]

Let C(x) be the function which calculates the total cost of making x skirts.

There is going to be a fixed constant, 250, to which we will add 15$ per x skirts.

So C(x)=250+15x

Answer: 250+15x

7 0

2 years ago

Read 2 more answers