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3 years ago

11

Find the common ratio for the geometric sequence for which

lt="a_1" align="absmiddle" class="latex-formula">=3 and $a_5$ =48. A. -3 B. -2 C. 3 D. 2

2 answers:

tigry1 [53]3 years ago

4 0

hsじぇいrんふぉそ具jんじょおlっっっkjか、

worty [1.4K]3 years ago

3 0

Answer:

An= A1 * r^n-1

A5= 3 * r^5-1

48= 3*r^4

48÷3=r^4

16=r^4

r=

$\sqrt[4]{16}$

r=2

The answer is D. 2

Espero que te sirva

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Tony has 2 3/4 quarts of lemonade and paper cups that each hold 1/2 of a quart. How many paper cups can Tony fill with lemonade?

Alex Ar [27]

The total number of paper cups that Tony can fill with the available lemonade is 5 $\frac{1}{2}$ quarts

Step by step explanation :

Step 1 :

Total quantity of lemonade Tony has = 2 $\frac{3}{4}$ quarts = $\frac{11}{4}$ quarts

Total quantity of lemonade that the paper cup can hold = $\frac{1}{2}$ quarts

We need to find the total number of paper cups that can be filled with the available lemonade.

Step 2 :

The number of paper cups that can be filled with the available lemonade can be obtained by dividing the total available lemonade with the quantity that each cup can hold.

Hence the total number of paper cups = $\frac{11}{4}$ × $\frac{2}{1 }$

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Step 3 :

Answer :

The total number of paper cups that Tony can fill with the available lemonade is 5 $\frac{1}{2}$ quarts

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PLEASE!!! NEED HELP ASAP!!! 50 PTS AND BRAINLIEST!!!

noname [10]

1) Inverse function: $f^{-1}(x)=g(x)=\frac{x+4}{3}$

2) $f(1) = -1, g(-1) = 1$

3) $f(g(x))=g(f(x))=x$

Step-by-step explanation:

1)

In this first method, we want to find the inverse function of $f(x)$ .

The original function is:

$f(x) = 3x-4$

We rewrite it as

$y=3x-4$

We swap the name of the variables:

$x=3y-4$

Adding +4 on both sides:

$x+4=3y-4+4\\x+4=3y$

And dividing by 3 on both sides:

$y=\frac{x+4}{3}$

which is identical to $g(x)$ :

$g(x)=\frac{x+4}{3}$

2)

In this second method, we want to use the output of one function as input to the other function, and show that the output value is equal to the imput value.

We start using the function

$f(x)=3x-4$

We choose $x=1$ . We find:

$f(1)=3(1)-4=3-4=-1$

Now we use this output value as input in the function

$g(x)=\frac{x+4}{3}$

Substituting $x=-1$ ,

$g(-1)=\frac{-1+4}{3}=\frac{3}{3}=1$

So, the final output value (1) is equal to the input value (1).

3)

Here we want to verify that the two are inverse functions by showing that

$f(g(x))=x$

We have

$f(x)=3x-4\\g(x)=\frac{x+4}{3}$

Substituting g(x) into f(x),

$f(g(x))=3g(x)-4 = 3(\frac{x+4}{3})-4=(x+4)-4=x$

Viceversa, we want to show that

$g(f(x))=x$

Substituting g(x) into f(x), we get

$g(f(x))=\frac{f(x)+4}{3}=\frac{(3x-4)+4}{3}=\frac{3x-4+4}{3}=\frac{3x}{3}=x$

So, the two functions are one the inverse of the other.

Learn more about inverse functions:

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