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2 years ago

8

SOMEONE PLEASE HELP ME!!!!! Element X decays radioactively with a half life of 5 minutes. If there are 890 grams of Element X, h

ow long, to the nearest tenth of a minute, would it take the element to decay to 48 grams?

1 answer:

meriva2 years ago

6 0

Answer:

32.0 min

Step-by-step explanation:

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SOMEONE PLEASE PLEASE HELP !! i need this done by 6:30 and i don’t want my grade to drop .

Blizzard [7]

Which one do you need help with

4 0

3 years ago

a trapezoid has an area of 20cm squared and a height of 5 cm. what is the sum of its top and bottom sides

bonufazy [111]

$A=\frac{a+b}{2} h$
A - area
h - height
a+b - sum of its top and bottom sides

$20=\frac{a+b}{2} \cdot 5 \\
4 = \frac{a+b}{2} \\
a+b=8$

The sum of its top and bottom sides is 8 cm.

6 0

3 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:

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

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

<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

3 years ago

Solve –x + 2y = 12 x + 6y = 20 using the elimination method. (4, 4) (0, 6) (-12, 0) (-4, 4)

coldgirl [10]

<span>–x + 2y = 12
x + 6y = 20
------------------add
8y = 32
y = 32/8
y = 4

</span>–x + 2y = 12
–x + 2(4) = 12
-x = 12 -8
x = -4

answer: <span>(-4, 4)</span>

7 0

4 years ago

A times a to the 7 power

ivolga24 [154]

Answer:

${a}^{8}$

Step-by-step explanation:

a is a¹ and you have a^7 in multiplication you add the exponents. If you were to have a numerical value, you would replace a and calculate. If a = -5 then: a^8 =

$( - 5)^{8}$

which is = 390 625

4 0

3 years ago