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Soloha48 [4]
3 years ago
7

In the equation 9^2 x 27^3 = 3^x, what is the value of x? Show your work on scratchpaper

Mathematics
1 answer:
IceJOKER [234]3 years ago
7 0

Answer:

x=13

Step-by-step explanation:

9^2 * 27^3 = 3^x

We need to get each term with a base of 3

9^2 = (3^2) ^2

We know that a^b^c = a^(b*c)

(3^2) ^2 = 3^(2+2) = 3^4

27^3 = (3^3) ^3 = 3^(3*3) = 3^9

Replacing these in the original equation

3^4 * 3^9 = 3^x

We know that a^b *a^c = a^(b+c)

3^4 * 3^9  =3^(4+9) = 3^13 = 3^x

The bases are the same, so the exponents must be the same

x=13

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The measure of two supplementary angles are 12q-9 and 8q+14 find the measures of the angles
Gwar [14]
First choose 1 equation and set it equal to 180 because supplementary angles equal up to 180 degrees. 

12q - 9 =180                                                              

Now solve for q.

12q - 9 +9 = 180 + 9

12q = 189

12q/12 = 18912

q = 15.75

now subtract 15.75 from 180

180.00 - 15.75 = 164.25

Your angles equal to 164.25 and 15.75 degrees.

4 0
3 years ago
Witch is longer 2 feet or 30 inches
lesya [120]
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3 years ago
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What is the solution?( no solution or all real numbers) -3(x-1) > -3x - 2.
Step2247 [10]

Answer:

No solution

Step-by-step explanation:

So first we have to Distribute;

-3x + 3 > -3x - 2

This is an solution which means that they can never intersect on a graph.

We can solve further if you want;

Add 3x to both sides;

The x cancel themselves out.

3 > -2

6 0
3 years ago
Find all solutions in the interval [0, 2π). 7 tan3x - 21 tan x = 0
mihalych1998 [28]
To solve the trigonometric expression we proceed as follows;
7(tan x)^3-21tanx=0
this can be written as:
7(tan x)^3=21tanx
dividing through by 7 we get:
(tan x)^3=tan x
dividing through by tan x we get:
(tanx)^1=1
hence;
tan x=+\-1
when tan x=1
x=45
when tan x=-1
x=-45
Given that our answer should be at the interval [0,2π] the answer:
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3 0
3 years ago
Find the generating function for the sequence 1,-2,4,-8, 16, ...
kirill [66]

Answer:

  a(x)=\dfrac{1}{1+2x}

Step-by-step explanation:

The generating function a(x) produces a power series ...

  a(x)=a_0+a_1x+a_2x^2+a_3x^3+\dots

where the coefficients are the elements of the given sequence.

We observe that the given sequence has the recurrence relation ...

  a_0=1;a_n=-2a_{n-1} \quad\text{for n $>$ 0}

This can be rearranged to ...

  a_n+2a_{n-1}=0

We can formulate this in terms of a(x) as follows, then solve for a(x).

\sum\limits^{\infty}_{n=1} {a_{n}x^n} =a(x)-a_0 \quad\text{and}\\\\\sum\limits^{\infty}_{n=1} {2a_{n-1}x^n} =(2x)a(x) \quad\text{so}\\\\\sum\limits^{\infty}_{n=1} {(a_n+2a_{n-1})x^n}=0=a(x)-a_0+2xa(x)\\\\a(x)=\dfrac{a_0}{1+2x}=\dfrac{1}{1+2x}

The generating function is ...

  a(x) = 1/(1+2x)

3 0
3 years ago
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