Help me out. Solving equations!!!

Help please!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Dafna11 [192]

If f(x)= 3x+2 and g(x)= 4x, then

f(x)+g(x) = 3x+2+4x

= 7x+2

For f(g(x)), you work from the inside and work your way out. Another way of thinking is to go from right to left. (Inside/out and right/left are the same simply using different wording).

So what is g(x)? 4x.

Now, you take 4x and plug it into the f(x).

** Math--> English translation:

Look at the f(x) equation. Wherever you see an x in the f(x), replace the x with 4x [because 4x is the g(x)]. Basically, plug the g(x) into f(x).

So:

f(g(x)) becomes

f(4x) becomes

3 (4x)+2 = 12x+2

** Disclaimer: Notation may be inaccurate.

That's your answer. (Usually you leave it as so, but if your instructor wants it factored, then proceed).

As for the third part, I am unsure of a clear answer, so I am unable to provide an answer at the time.

**********************

Hope that helped.

DISCLAIMER:

Always double check with a reliable source, as mistakes are a possibility. Never use this, or any, platform to cheat.

6 0

3 years ago

I'm blanking on how to do this, I learned it so long ago, any help would be greatly appreciated. More interested on how to do it

anyanavicka [17]

Answer:

$\dfrac{16 y^{22}}{x^{10}z^{10}}$

Step-by-step explanation:

Given expression is ,

$\sf\longrightarrow \bigg(\dfrac{2x^3y^{-5}z^8}{8x^{-2}y^6z^3}\bigg)^{-2}$

This would be simplified using the law of exponents , some of which I will use here are ,

$(an)^m = a^m n^m$
$\dfrac{a^m}{a^n}=a^{m-n}$

$a^m a^n = a^{m+n}$
$a^{-n} = \dfrac{1}{a^n}$

Using the above laws ,

$\sf \longrightarrow \bigg[ \dfrac{2}{8} \bigg(\dfrac{x^3}{x^{-2}}\bigg)\bigg(\dfrac{y^{-5}}{y^6}\bigg)\bigg(\dfrac{z^8}{z^3}\bigg) \bigg]^{-2}$

Using the second law mentioned above , we have,

$\sf \longrightarrow \bigg[ \dfrac{1}{4}(x^{3+2})(y^{-5-6})(z^{8-3})\bigg]^{-2}$

Simplify ,

$\sf \longrightarrow \bigg[\dfrac{1}{4} x^5y^{-11}z^5\bigg]^{-2}$

Using the first law mentioned above , we have,

$\sf \longrightarrow \bigg[ \dfrac{1}{4^{-2}} x^{5(-2)} y^{-11(-2)} z^{5(-2)}\bigg]$

Simplify,

$\sf \longrightarrow 4^2x^{-10}y^{22} z^{-10}$

Finally using the fourth law mentioned above , we have ,

$\sf \longrightarrow \boxed{\bf \dfrac{16 y^{22}}{x^{10}z^{10}}}$

<h3>Option K is the correct answer.</h3>

4 0

2 years ago

What is 1/8 divided by 3

deff fn [24]

1 : 3
8

Make the whole number a fraction, by putting it over 1.

1 : 3
8 1

Turn the second fraction upside down and multiply:

1 . 1 = 1 
8 3 24

S = 1/24

5 0

3 years ago

Please help me ASAP!Please this is due soon and i don't have all day.

Helga [31]

Answer:

Section 1: 5.59%

Section 2: -2.16%

Section 3: -10.82%

Section 4: -6.54%

Section 5: -2.16%

Section 6: 7.86%

Explanation:

The formula to calculate the percent change in mass is given as:

$PercentChange = \frac{ChangeInMass}{StartingMass}*100=\frac{NewMass - OldMass}{OldMass}*100$

1- Section 1:

Old mass = 7.83 g and New mass = 8.268 g

$PercentChange = \frac{8.268-7.83}{7.83}*100 =$ 5.59%

2- Section 2:

Old mass = 7.4 g and New mass = 7.24 g

$PercentChange = \frac{7.24-7.4}{7.4}*100 =$ -2.16%

3- Section 3:

Old mass = 7.3 g and New mass = 6.51 g

$PercentChange = \frac{6.51-7.3}{7.3}*100 =$ -10.82%

4- Section 4:

Old mass = 7.49 g and New mass = 7.0 g

$PercentChange = \frac{7.0-7.49}{7.49}*100 =$ -6.54%

5- Section 5:

Old mass = 7.4 g and New mass = 7.24 g

$PercentChange = \frac{7.24-7.4}{7.7.4}*100 =$ -2.16%

6- Section 6:

Old mass = 7.89 g and New mass = 8.51 g

$PercentChange = \frac{8.51-7.89}{7.89}*100 =$ 7.86%

Hope this helps :)

6 0

3 years ago

I need help ASAP!! A, B, C, D

Scrat [10]

Answer:

C. Both f(x) and its inverse function intersect at point (2, 2).

Step-by-step explanation:

First of all, let's begin defining f(x) = y.

Since the linear function f(x) intersects at

• 6 on the y-axis; and

• 3 on the x-axis;

we can deduce the following equation:

6x + 3y = 6(3)

6x + 3y = 18

3y = -6x + 18

y = -6x/3 + 18/3

y = -2x + 6

f(x) = -2x + 6

Then, we'd want to find the inverse of f(x), which is f`¹(x).

f(x) = -2x + 6

y = -2x + 6

Interchange the variable y to x and vice versa.

x = -2y + 6

2y = -x + 6

y = (-1/2)x + 3

f`¹(x) = (-1/2)x + 3

Since both f(x) and its inverse function are equal to y, set them both as equal.

f(x) = f`¹(x)

-2x + 6 = (-1/2)x + 3

-2x + (1/2)x = 3 - 6

(-3/2)x = -3

x = 2

Substitute x = 2 into y = -2x + 6.

y = -2(2) + 6

y = -4 + 6

y = 2

Now that we know x = 2 and y = 2, then the intersection point of (x, y) must be (2, 2).

I hope this helps! Sorry if my English didn't really help with giving a clearer explanation.

3 0

4 years ago