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2 years ago

Is the number 0.15893 rational or irrational?

Mathematics

1 answer:

Kazeer [188]2 years ago

8 0

Answer:

rational

Step-by-step explanation:

A rational number is any integer, decimal, terminating decimal, or repeating decimal.

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ΔABC and ΔXYZ are similar triangles. If BC = x + 7, AC = x + 6, YZ = 4 − x, and XZ = 3 − x, find the value of x.

Montano1993 [528]

I believe the answer is B) -3/2 or -1.5.

Please give a heart and rating if this is right!

3 0

2 years ago

Read 2 more answers

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:

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

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

<em>f(x) and g(x) and not inverse functions</em>

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

<em>Hence, f(x) and g(x) and not inverse functions</em>

4 0

2 years ago

a total of 17100 seats are still available for the next hockey game.if 62% of the tickets are sold how many seats are in the are

BartSMP [9]

If 62% of the seats are sold;

100-62= 38% seats still available.

17100=38% seats available

17100/38= seats in 1%
450 seats

In 100%,
450×100=450000 seats total.

Hope I helped :)

3 0

2 years ago

Erica earned a total of $50,450 last year from her two jobs. The amount she earned from her job at the store was $1,250 more tha

Mariana [72]

Erica earned a total of $50,450 last year from her two jobs. The amount she earned from her job at the store was $1,250 more than four times the amount she earned from her job at the college.

Lets x be the amount she earned from here job at college

amount she earned at the store = 4 * amount earned at college + 1250

= 4x + 1250

Amount earned at college + amount earned at store = 50450

x + 4x + 1250 = 50450

5x + 1250 = 50450

Subtract 1250 from both sides

5x = 49200 (divide by 5)

x = 9840

she earn $9840 from her job at the college

5 0

2 years ago

Tyler needs to complete the table for his consumer science class. He knows that 1 tablespoon contains 3 teaspoons and that 1 cup

olga_2 [115]

Answer:

1 cup = 48 teaspoons

C = 48t

Step-by-step explanation:

Given:

1 tablespoon = 3 teaspoons

1 cup = 16 tablespoon

Write an equation that represents the number of teaspoons, t, contained in a cup, C.

Since

1 tablespoon = 3 teaspoons

And

1 cup = 16 tablespoon

Then

1 cup = 3 teaspoons × 16

1 cup = 48 teaspoons

Let

cup = C

Teaspoons = t

Therefore,

C = 48t

3 0

2 years ago