Answer:
[tex]3^{x-1}[/tex]
Explanation:
Given
[tex]\frac{(3^{x+1})(3^{x-1})^2}{9^x}[/tex]
Required
Find its equivalent
[tex]\frac{(3^{x+1})(3^{x-1})^2}{9^x}[/tex]
Expand the numerator
[tex]\frac{(3^{x+1})(3^{x-1})(3^{x-1})}{9^x}[/tex]
Apply law of indices: [tex]a^m * a^n = a^{m+n}[/tex]
This gives
[tex]\frac{3^{x+1+x-1+x-1}}{9^x}[/tex]
Collect like terms
[tex]\frac{3^{x+x+x+1-1-1}}{9^x}[/tex]
[tex]\frac{3^{3x-1}}{9^x}[/tex]
Express [tex]9^x[/tex] as a factor of 3
[tex]\frac{3^{3x-1}}{3^2^x}[/tex]
Apply law of indices: [tex]\frac{a^m}{a^n} = a^{m-n}[/tex]
This gives
[tex]3^{3x-1-2x}[/tex]
[tex]3^{3x-2x-1}[/tex]
[tex]3^{x-1}[/tex]
Hence,
[tex]\frac{(3^{x+1})(3^{x-1})^2}{9^x}[/tex] is equivalent to [tex]3^{x-1}[/tex]
What are some tests for assessing each of the health-related components of fitness
Answer:
The fitness gram and pacer test
Explanation:
If (4^a^-2)(4^3) = 64^2 , what is the value of a? a. 0 b. 4 c. 5 d. 7 e. 8
Answer:
[tex]\boxed{a=4}[/tex]
Explanation:
Part 1. Finding product of [tex](4a^2)(4^3)[/tex]
Step 1. [tex]4^3=64[/tex]
Step 2. [tex](4a^2) * (64) = (64 * 4)(a^2)[/tex]
Step 3. [tex](64 * 4)(a^2) = 256a^2[/tex]
[tex]\boxed{(4a^{2})(4^3) = 256a^{2}}[/tex]
Part 2. Simplifying the equation & solving for a
Step 1. [tex]\sqrt{256a^{2}} = \sqrt{64^{2}}[/tex] ⇒ [tex]16a = 64[/tex]
Step 2. [tex]\frac{16a}{16} = \frac{64}{16}[/tex] (divide both sides by coefficient of variable)
[tex]\boxed{a = 4}[/tex]
if p(x) = x+ 7/ x-1 and q (x) = x^2 + x - 2, what is the product of p(3) and q(2)? a. 50 b. 45 c. 40 d. 20 e. 6
Answer:
d. 20
Explanation:
p(x)= x+7 / x-1p(3)= 3+7 / 3-1 = 10/2 = 5 (where x=3)
again,
q(x)= x^2+x-2q(2)= 2^2+2-2 = 4+2-2 = 4 (where x=2)
so, p(3) x q(2) = 5x4 = 20Answer:
d. 20
Explanation:
P(3) = 3 + 7 / ( 3-1) = 10/2 =5
q(2) = 2^2 +2-2 = 4 + 2 -2 =4
P(3) * q(2) = 5 * 4 = 20
Morgan opens a savings account that earns simple interest at the rate of 4.5\%4.5%4, point, 5, percent annually. If she initially deposits \$50$50dollar sign, 50 in the account, what is the minimum number of years it will take for her savings to be at least \$68$68dollar sign, 68, assuming she makes no other deposits or withdrawals?
Answer:
8
Explanation:
Who is 11 on this app
how is DIO alive after he was stuck in Jonathons arms and how did he get into the secret compartment without erina knowing
Right after he recognized Jonathan existed dead, Dio tore off his head with his hair/neck tendrils and moved to put his head onto Jonathan’s body.
How is DIO alive after he was stuck in Jonathons arms?Right after he recognized Jonathan existed dead, Dio tore off his head with his hair/neck tendrils and moved to put his head onto Jonathan’s body. He then dragged himself into a secret chamber inside the same bomb-proof coffin that Erina utilized to escape.
After Erina was rescued, the coffin existed cast back into the sea, with Dio still inside. He presumably went into a condition of hibernation. He waited there for nearly 100 years until a pack of a fisherman off the coast of Africa happened to reel the casket in. Thinking they had found treasure, they opened the casket and awoke the vampire, who then christened himself as absolutely DIO.
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Half the difference of 18 and a number n is equal to the sum of n and three. what is the value of n?
Answer:
n=12
Explanation:
First you have to write out the equation for the problem.
(18+n)/2=n+3
To get rid of the fraction, multiply both sides by 2.
18+n=2n+6
Now subtract n and subtract 6 from both sides and you will have your answer.
12=n
Answer:
n=4
Explanation:
(18-n)/2=n+3
2*((18-n)/2)=(n+3)*2
18-n=2n+6
+n +n
18 = 3n+6
-6 -6
12 =3n
÷3 ÷3
4=n
n=4